Monetary policy operations and the Financial System. Tutorial

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2 Monetary policy operations and the Financial System Tutorial Ulrich Bindseil January 2016 This tutorial complements the book Monetary policy operations and the financial system for the use in classrooms, or for anyone willing to try out classroom exercises on monetary policy implementation topics. In the field of monetary policy operations, there are many very simple models (the financial account system, how to control short term interest rates within a monetary policy implementation framework; funding market access of banks and multiple equilibria; mechanics through which a financial crisis destabilizes markets, etc.) which capture elements of reality, and which are suitable for classroom calculus. The tutorial follows the structure of the book with its 17 chapters and contains essentially three types of questions: (1) Questions which require a text answer that can be precisely found in the book; (2) exercises requiring simple calculus or the use excel; (3) text quotes, examples of non-conventional measures (mostly taken from the euro area), or data which readers are invited to analyze or interpret. The solutions in part II of the tutorial provide, for the first type of questions, only a reference to the relevant parts or page numbers of the book. For the other two types, at least a sketch of the solution is provided. Literature to which a reference is made can be found in the book s literature list (or otherwise a full reference is made here in the tutorial). Normally, it is sufficient to have read the book up to the relevant chapter to be able to answer the questions. In rare cases one needs to have read beyond - which is then indicated in the question. Obviously: trying to answer the questions before looking at the solutions is the best way to learn. I wish to thank the many students that went through previous versions of this tutorial. They were essential in reducing the number of errors, and in identifying which exercises are useful. The Excel spreadsheets with solutions (relevant for around 10% of the exercises) can be downloaded at my lecture website at the Technical University of Berlin. It is not strictly necessary to use these excel spreadsheets, as the relevant formulas and simulations are simple and can be programmed in any other spreadsheet program, programming language or math tool like e.g. Matlab. 2

3 Table of content Questions Page Solutions 1 Basic terminology and relationship to monetary macroeconomics Monetary policy in a closed system of financial accounts Short-term interest rate as the operational target of monetary policy Three basic techniques of controlling short term interest rates Several liquidity shocks, averaging, and the martingale property Standing facilities and the interest rate corridor Open market operations Reserve requirements Collateral Optimal frameworks in normal times The nature of a liquidity crisis Collateral availability and monetary policy Open market operations and standing facilities in a financial crisis The lender of last resort (LOLR) role of the central bank LOLR and central bank risk taking LOLR, moral hazard and liquidity regulation The international lender of last resort

4 Q1: Basic terminology and relationship to monetary macroeconomics Q1.1 Define the main types and sub-types of monetary policy instruments. Q1.2 To what extent is there a continuum of central bank market operations between the extreme, ideal-type standing facility and open market operation? Q1.3 Draw a matrix with the two dimensions {outright operations, credit operations} and {open market operations, standing facilities} and fill the four fields of the matrix with examples. Q1.4 What is the relationship between the operational target of monetary policy, its ultimate target, the transmission mechanism, and the monetary policy instruments? Q1.5 What does monetary policy implementation consist in? What is, in contrast, monetary macroeconomics, and what is the borderline between the two? How has the dichotomy between the two fields of central banking been blurred in theory, and how in practice? Q1.6 Poole (1970, Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model, Quarterly Journal of Economics, 84, ) defined an instrument to be a policy variable which can be controlled without error and considered three possible approaches to its specification (p. 199): First, there are those who argue that monetary policy should set the money stock while letting the interest rate fluctuate as it will. The second major position in the debate is held by those who favour money market conditions as the monetary policy instrument. The more precise proponents of this general position would argue that the authorities should push interest rates up in times of boom and down in times of recession, while the money supply is allowed to fluctuate as it will. The third major position is taken by the fence sitters who argue that the monetary authorities should use both the money stock and the interest rate as instruments...the idea seems to be to maintain some sort of relationship between the two instruments. How would you assess this from the point of view of the terminology proposed in chapter 1, and on substance? 4

5 Q2: Representing monetary policy implementation in a closed system of financial accounts Q2.1 Consider the following system of financial accounts. A. What monetary policy implementation technique does the central bank seem to apply (full answer requires having read chapters 2-4 of the book)? B. How are the following events reflected in this system of financial accounts? You may want to distinguish immediate effects and possible subsequent effects reflecting the reactions of economic actors (in particular of the central bank) to the initial event. a. The central bank buys new headquarters for 1 b. Due to progress in electronic payment technologies, banknote demand shrinks by 80% c. Because of a financial panic, the households substitute all bank deposits with banknotes. d. The CB decides to substitute all its securities holdings with reverse open market operations (as it decided to change its monetary policy implementation technique) e. The real assets of the corporate sector lose 50% of their value due to an earthquake Households Real assets 60 Equity 100 Banknotes 10 Deposits banks 10 Bank equity 10 Corporate equity 2 Corporate bond 1 Government bond 7 Total assets 100 Total liabilities 100 Government Real assets 20 Debt 20 Total assets 20 Total liabilities 20 Corporations Real assets 20 Equity 2 Debt 18 Total assets 20 Total liabilities 20 Banks Corporate bonds 7 Deposits of HH 10 Government bonds 8 Equity 10 Deposits with CB 5 Central bank credit 0 CB Deposit facility 0 Total assets 20 Total liabilities 20 Central bank Corporate bonds 10 Banknotes 10 Government bonds 5 Deposits of banks (RR=0) 5 Central bank credit 0 CB Deposit facility 0 Total assets 15 Total liabilities 15 5

6 Q2.2 Consider the following system of financial accounts. Household Real assets E-D -B Equity E Banknotes B Deposits D Corporate & Government sector Real assets B+D Bonds issued B+D Banks Bonds D+B-P Deposit D Excess reserves max(0, P-B) Central bank credit max(0, B-P) Credit to banks Bonds Central bank max(0, B-P) Banknotes P Excess reserves B max(0, P-B) (a) How does the length of the balance sheets of the four entities depend on B, D, P? (b) What are in reality the approximate proportions between B, D, P and the lengths of the various balance sheets of the sectors of the economy? What has in particular been simplified away in the balance sheets above? (c) How would the financial accounts change if the household sector also contains households who are indebted? Q2.3 Starting from the same financial accounts as in Q2.2, assume now that the banking system consists in a continuum of banks in the unit interval, and that household deposits are distributed linearly but not uniformly across banks in this unit space. The linear deposit distribution curve D(x) with x in [0,1] being defined as D(x) = D + (0.5-x)s The parameter s in [0,2D] is the slope factor (note that if s=2d, then the bank x=1 has no deposits at all; the bank x=0 is always the most deposit rich bank and would in this case have deposits of 2D). In Q2.2 s had obviously been set to 0. The larger s, the more uneven is the distribution of deposits with the banking system. We assume that initially, s=0, but then something happens (e.g. a liquidity crisis breaks out, and households start to re-allocate their deposits with banks) and s takes a positive value. Therefore, we assume that the banks assets are still uniform across banks at B+D, and central bank credit has to fill the funding gaps resulting from the assumed unexpected change of s away from zero and its impact on deposits (but not on the total assets per bank). (a) Draw the curve D i (x) for the four combinations of parameter values of {D,s,B,P} indicated in the table below. Comment on the four curves. Scenario 1 Scenario 2 Scenario 3 Scenario 4 Total Deposits D Inequality parameter s Banknotes B Portfolio P (b) Define as R i (x) the amount of central bank credit taken by bank x. Assume absence of interbank markets. Provide the formula for this function and draw it for the same four combinations of parameter values. Comment on the four curves. Draw the balance sheet of bank x. 6

7 (c) Assume now that there is an interbank market. Define as M i (x) the amount on interbank credit provided by bank x in scenario i (M i (x) can be positive or negative, in the latter case it means that bank x is a debtor on the interbank market). What are the conditions for an active interbank market? (d) How does in general the interbank market volume depend on D, s, B, P (assuming that interbank market transaction costs are always below the spread between central bank credit provision interest rates and the remuneration rate of excess reserves)? Provide intuition to your answers. (e) Assuming a perfectly efficient interbank market, what are, for the four parameter combinations shown in the table above, the (i) interbank market volumes; (ii) total recourse to central bank credit; (iii) Total excess reserves of the banking system; (iv) total length of the central bank balance sheet? (f) If money markets break down, how do these results change? (g) Starting from the first parameter combination, i.e. {D,s,B,P}={1,1,1,1}, illustrate that the interbank volume first increases and then decreases with the size of the central bank securities holdings. How does the recourse to central bank credit (R) and excess reserves (XSR) evolve as a function of the central bank s outright portfolio P? Differentiate the cases of efficient and broken interbank markets. (h) The model predicts that more cross-bank deposit inequality (s) often increases interbank market volumes. Why is this conclusion questionable in case higher deposit inequality is driven by negative views of households on some banks? Q2.4 Consider the following balance sheet of the Reichsbank of 1900 and 1922, Deutsche Bundesbank as of December 1998, and of the Bank of Latvia as of December 2001 Reichsbank, average weekly financial statements in 1900, in billion RM Gold and silver 817 Banknotes 1139 Banknotes of other issuing banks 14 Other liabilities (net) 150 Government bills 23 Discounted trade bills 800 Lombard lending 80 Current accounts of banks 513 Residual 68 Total assets 1802 Total liabilities 1802 Net foreign assets incl. gold 1 Government bills 1184 Discounted trade bills 660 Lombard lending 1 Reichsbank, end 1922, in billion RM Banknotes 1280 Other liabilities (net) 36 Current accounts of banks 530 Total assets 1846 Total liabilities 1846 Bundesbank, end 1998, in billion DM Net foreign assets incl. gold 112 Banknotes 260 Other liabilities (net) 33 Credit operations with domestic banks 235 CB bills issued 5 Current accounts of banks 49 Total assets 347 Total liabilities 347 Bank of Latvia, Dec 2001, in million Lats Net foreign assets incl. gold 563 Banknotes 484 Other liabilities (net) 55 Credit operations with domestic banks 39 Current accounts of banks 63 Total assets 602 Total liabilities 602 (a) For each of these central bank balance sheets, please provide: 7

8 (i) The level of total autonomous factors; (ii) the total liquidity provision through monetary policy operations; (iii) the original liquidity deficit of the banking system; (iv) the liquidity deficit post outright monetary policy operations; (v) the leanness of the balance sheet? (b) What do you find striking with regard to each the four balance sheet structures? Q2.5 What did James Tobin mean by the term fountain pen money? Q2.6 What are the various possible limits to the creation of fountain pen money? Q2.7 Why should a granular banking system make fountain pen money creation by individual banks more difficult? Q2.8 Consider the following system of financial accounts, in which both banks are creating fountain pain money in parallel: Real Assets E-D-B-F Deposits Bank 1 D/2 + C/2 Deposits Bank 2 D/2 + C/2 Bank Equity F Banknotes B Households / Investors Household Equity E Credit from bank 1 C/2 Credit from bank 2 C/2 Corporate / Government Real assets D+B+F Credits from banks D+B+F Lending to corporates D/2 + B/2 +F/2 Lending to households C/2 Lending to corporates D/2 + B/2 +F/2 Lending to households C/2 Bank 1 Household deposits / debt D/2 + C/2 Credit from central bank B/2 Equity F/2 Bank 1 Household deposits / debt D/2+C/2 Credit from central bank B/2 Equity F/2 Central Bank Credit operations B Banknotes B Assume the following four possible constraints for the creation of fountain pen money: (a) Capital adequacy requirements: assume that banks must not have less than 8% capital, and that capital charged on all bank assets are 100% (b) Reserve requirements on household deposits are 5% (c) Collateral: lending to corporates is central bank eligible collateral, whereby a haircut of 20% is applied. (d) Both reserve requirements apply as in (a) and collateral rules as in (c). For each of these constraints on their own, what is the maximum amount of central bank money creation? Which is the binding constraint? 8

9 Q2.9 The following system of financial account reflects the German 2013 financial and wealth accounts, in % of Germany s 2013 GDP (DeStatis, Deutsche Bundesbank, 2014, Sektorale und Gesamtwirtschftliche Vermögensbilanzen, , Statistisches Bundesbamt, Wiesbaden), with selective amendments made to ensure full internal consistency from the perspective of this exercise. Real assets are all assets that are non-financial, i.e. including intellectual rights etc. The sum of equity held as assets is only 190, while total equity as liability item is 528. The difference of 338 is the liability equity of Households (296) and the Government (42) sector, which is owned by nobody else than the sector itself (while all liability-equity of the NFC and financial corporate sectors is owned by other sectors of the economy). To simplify, net positions against the Rest of the World (RoW) are shown as real assets. The Bundesbank is shown separately below, but is also part of the financial corporate sector. The Bundesbank will not be relevant as separate entity in the rest of the exercise. Non-financial corporates Real goods 98 Debt 56 Fixed financial claims 39 Equity 121 Equity holdings 39 Total State Real goods 75 Debt 61 Fixed financial claims 17 Equity 42 Equity holdings 11 Total Financial corporates (banks, insurance, etc.) Real goods 5 Debt (including deposits) 241 Fixed financial claims 192 Equity 70 Equity holdings 114 Total Households Real goods 159 Debt (including deposits) 43 Fixed financial claims 154 Equity 296 Equity holdings 26 Total Sums from the four sectors Real goods 338 Debt 402 Fixed financial claims 402 Equity 528 Equity holdings 190 Total Deutsche Bundesbank (included in financial corporates) Real goods 0 Banknotes 6 Claims towards banks 2 deposits of banks 8 Securities 2 Equity 4 Claims to Rest of the world 13 Other claims 1 Total (a) What do you find most striking in these actual financial accounts? What do you think about the financial stability of the various sectors? (b) The accounts are not detailed enough to identify precisely which sector has which claims against (or shares of) a specific other sector. Assume general proportionality of financial claims and liabilities cross sector, and derive on that basis the precise inter-sector positions. 9

10 (c) Assume now that as a consequence of a negative external shock, all real assets decline by a percentage x, and that this percentage is sufficiently small that equity in the economy can take the loss and no sector on aggregate loses its solvency (and we assume that the sectors are constituted by homogeneous entities). How do the financial accounts look like after this shock? Make sure that not only first round effects are considered, but the eventual effects reflecting all interdependences (i.e. including subsequent effects transmitted via equity holdings). (d) What is the critical value of a percentage real asset value decline x* in which a first sector becomes on aggregate insolvent? (e) What happens beyond the point of insolvency of one sector (no need for an exact solution)? 10

11 Q3: The short term interest rate as the operational target of monetary policy Q3.1 What are desirable properties of an operational target of monetary policy? Q.3.2 Verify that short term interbank interest rates are a suitable operational target of monetary policy. Why is the overnight interest rate preferable to say the three months interest rate? Q3.3 Derive the non-accelerating nominal interest rate from an arbitrage relationship between the four goods money today and wheat today, money tomorrow and wheat tomorrow. What are important simplifying assumptions of this arbitrage logic, that require to be refined when applying it in central bank practice? Q3.4 Why is the monetary policy decision making body of the FED called the Federal Open Market Committee, although it decided (at least until 2009) on short term interest rates, such that it could better have been named Federal Short Term Interest Rate Committee? Q3.5 Friedman (1960: 50 1) argues that open market operations alone are a sufficient tool for monetary policy implementation, and that standing facilities (such as the US discount facility) and reserve requirements could thus be abolished: The elimination of discounting and of variable reserve requirements would leave open market operations as the instrument of monetary policy proper. This is by all odds the most efficient instrument and has few of the defects of the others... The amount of purchases and sales can be at the option of the Federal Reserve System and hence the amount of high-powered money to be created thereby determined precisely. Of course, the ultimate effect of the purchases or sales on the final stock of money involves several additional links... But the difficulty of predicting these links would be much less... The suggested reforms would therefore render the connection between Federal Reserve action and the changes in the money supply more direct and more predictable and eliminate extraneous influences on reserve policy. Friedman (1982) argues largely along the same lines and seems to suggest an open market operations volume target (1982: 117): Set a target path for several years ahead for a single aggregate for example M2 or the base.... Estimate the change over an extended period, say three or six months, in the Fed s holdings of securities that would be necessary to approximate the target path over that period. Divide that estimate by 13 or 26. Let the Fed purchase precisely that amount every week in addition to the amount needed to replace maturing securities. Eliminate all repurchase agreements and similar short-term transactions. Why have these policy advices never been set into practice? Q.3.6 What were the main reserve position doctrine concepts applied by the Federal Reserve across time? What could have been the specific problems with each of those? 11

12 Q4: Three basic techniques of controlling short term interest rates Q4.1 What is the basic idea behind the fundamental equation of controlling the overnight interest rate in a corridor system? What explicit or implicit assumptions does this equation depend on? Q4.2 What are the respective advantages and disadvantages of the three alternative approaches to interest rate control presented in chapter 4? Q4.3 Consider the balance sheets in exercise Q2.4 what approaches to monetary policy implementation did these central banks apply? Q4.4 Assume the bank and the central bank balance sheets shown below. Moreover, assume that deposits of banks with the central bank are not remunerated, and the central bank lending facility is charged at a rate of 1%. The central bank chooses the amount of open market operations OMO in the morning, then the interbank market takes place with the overnight rate i being established, and finally μ materializes, which is an N(0,1) distributed random variable. a) What level of OMO has the central bank to choose if it wants i to be (i) at 0.5; (ii) at 0.25; (iii) at 0.10? b) Now assume that μ is decomposed into μ = μ 1 + μ 2 and that μ 1 materializes before, and μ 2 after the interbank session. Also assume that the two are independently and identically N(0,1) distributed. What level of OMO does the central bank need to choose (early in the day) if the central bank wants the expected value of i to be (1) at 0.5; (2) at 0.25; (3) at Use excel to find an approximate answer. What is the volatility of the overnight rate in each of these cases? c) How do these findings depend on the absolute and relative volatility of the two autonomous factor shocks? Bank Government bonds 100-OMO Deposits of HH Loans to corporates 50 Deposits with CB Max(OMO-50- μ,0) CB Borrowing facility Central bank Government bonds OMO Banknotes CB borrowing facility Max(-(OMO-50- μ),0)) Deposits of banks μ Max(-(OMO-50- μ),0)) 50 + μ Max(OMO-50- μ,0) Q4.5 A corridor system with two facilities that are both liquidity providing or absorbing. The classical approach of the Reichsbank up to at least 1914 consisted to steer short term interbank rates in a corridor set by two liquidity providing standing facilities: a discount facility (in which banks could submit trade bills satisfying certain criteria) and a Lombard facility, priced at 100 basis points above the discount facility, which provided collateralised lending against a very broad collateral set. In 2015, the Fed announced a system after lifting off from the zero lower bound which Potter (Money Markets and Monetary Policy Normalization, April 15, 2015, speech by Simon Potter, Executive Vice President, FRBNY, Remarks at the Money Marketeers of New York University, New York City) describes as follows: Specifically, the Federal Reserve intends to target a range for the federal funds rate that is 25 basis points wide, and to set the IOER [Interest on excess reserves] rate and the offering rate associated with an ON RRP [overnight reverse repo] facility equal to the top and bottom of the target range, respectively. It intends to allow aggregate capacity of the ON RRP facility to be temporarily elevated to support policy implementation. It can also adjust the IOER rate and parameters of the ON RRP facility, and to use other tools such as term operations, as necessary for appropriate monetary control.the Federal Reserve intends to use adjustments to the IOER rate a rate it directly administers as the main tool for moving the fed funds rate and other short-term interest rates into 12

13 its target range. The IOER rate is essentially the rate of return earned by a bank on a riskless overnight deposit held at the Fed, thus representing the opportunity cost to a bank of using its funds in an alternative manner, such as making a loan or purchasing a security. In principle, no bank would want to deploy its funds in a way that earned less than what can be earned from its balances maintained at the Fed. Even though banks are the only institutions eligible to earn IOER, arbitrage should lift market rates up to the level of the IOER rate. In practice, however, with the large levels of excess reserves in the system, certain institutional aspects of money markets including bank-only access to IOER, credit limits imposed by cash lenders and other impediments to market competition, and the costs of balance sheet expansion associated with arbitrage activity appear to create frictions that have made IOER act more like a magnet that pulls up short-term interest rates than a firm floor beneath them. The FOMC will supplement the magnetic pull of changes in the IOER rate with an ON RRP facility to help control the federal funds rate. Under the facility, the Desk will offer general collateral reverse repurchase agreements at a specified offering rate to a broad set of counterparties including several types of nonbank financial institutions that are significant lenders in U.S. money markets. (a) How do such techniques generally insure that the interbank rates are kept with a corridor of same-sided standing facilities? (b) Do you believe that this technique allows for a very precise control of overnight rates? 13

14 Q5: Several liquidity shocks, averaging, and the martingale property of overnight rates Q5.1 What is the meaning of the martingale property of overnight interest rates intraday, and in a reserve averaging system? Q5.2 What are possible impediments to the martingale properties in the first and in the second case, respectively? Q5.3 Assume a central bank with banknotes outstanding of EUR 10 billion and a Lombard facility at 1% and a deposit facility at 0%. Consider the following daily sequence of events: OMO operation takes place (overnight maturity) A first autonomous factor shock materialises, which is N(0,1/q billion) distributed A morning trading session with half weight of total daily trading volume takes place A second autonomous factor shock materialises, which is N(0,1 billion) distributed An afternoon trading session with half weight of total daily trading volume takes place A third autonomous factor shock materialises, which is N(0,q billion) distributed (the three shocks are independently distributed; a, 1 are the variance) Build an excel tool which allows you to answer approximately the following questions: a) In a symmetric corridor system, what is the volatility of the morning, the afternoon, and the overall overnight rate for values of q of 0.5, 1, 2? b) Assume that the central bank targets an overnight rate of What OMO amount does it need to choose to achieve it for values of q 0f 0.25, 0.5, 1, 2, 4, 8? What is the volatility of the overnight rate in each of these cases? In how can one derive from that an important advantage of a symmetric corridor system? 14

15 Q6: Standing facilities and the interest rate corridor Q6.1 Explain the difference between a discount- and a Lombard facility. How did the two typically coexist in pre WW1 central banking? Q6.2 Why is the Fed been using the term discount facility for its Lombard credit facility? Q6.3 Why did monetarist strongly dislike standing facilities? Q6.4 Why was the discount window stigmatised for so long in the US? Q6.5 What are relevant considerations when choosing the optimal width of the interest rate corridor set by standing facilities in a symmetric corridor system? Q6.6 Explain the idea of a TARALAC standing facility. In which sense is it more effective and simple in stabilising overnight rates around the desired level? Q6.7 What is the main difference between the US Fed discount window ( primary credit ) and the Eurosystem marginal lending facility? Q6.8 On 22 December 1998, i.e. 10 days before the introduction of the euro, the ECB announced the interest rates applied to its standing facilities, including a transitory measure: With respect to the interest rates on the ESCB's standing facilities, which are designed to form a corridor for movements in short-term money market rates, the Governing Council decided that the interest rate for the marginal lending facility will be set at a level of 4.5% and the interest rate for the deposit facility at a level of 2%.. However, as a transitory measure, between 4 January 1999 and 21 January 1999, the interest rate for the marginal lending facility will be set at a level of 3.25% and the interest rate for the deposit facility at a level of 2.75%. This measure aims at smoothing the adaptation of market participants to the integrated euro money market during the initial days of Monetary Union. The Governing Council intends to terminate this transitory measure following its meeting on 21 January What would have happened in your view without this transitory measure? 15

16 Q7: Open market operations Q7.1 Why were both the US Fed and monetarist so enthusiastic about open market operations for many decades? Q7.2 What is the role of open market operations in the pre-2007 consensus? Q7.3 How would you assess the relative merits of credit- and outright- open market operations? How could they be combined efficiently? In which sense could the optimal combination between the two depend on the circumstances? Q7.4 How would you assess the relative merits of fixed and variable rate tenders? Q7.5 Why should tender procedures avoid discretionary elements in the allotment decision? Q7.6 Between 1999 and 2008, the ECB conducted all its credit operations with a maturity of more than a month as pure variable rate tenders with pre-announced amounts. In contrast, during the same period, the ECB applied various different procedures in its weekly main refinancing operations (fixed rate tender, variable rate tender with minimum bid rate, fixed rate tender with full allotment). Why this difference between the shortest and the longer maturities? 16

17 Q8: Reserve requirements Q8.1 Why is the fulfilment of reserve requirements not measured more frequently than once a day, e.g. once a minute? Why is it not measured less frequently, e.g. once a year? Q8.2 What are key parameters to specify a reserve requirement system? Q8.3 What objectives have been attributed to reserve requirements in the past and present? What does the choice of objective implies for the choice of specification? Q8.4 How convincing do you find the various possible objectives of reserve requirements? Please explain. Q8.5 What views did monetarist have on reserve requirements? And Keynes in his Treaties on Money (1930)? What is left today of these views? Q8.6 Consider the ECB announcement of its reserve requirement system made on 8 July 1998: The Governing Council sees three main functions which a minimum reserve system could usefully perform in Stage Three. First, it may contribute to the stabilisation of money market interest rates. Second, such a system will contribute to enlarging the demand for central bank money and thus creating or enlarging a structural liquidity shortage in the market; this is considered helpful in order to improve the ability of the ESCB to operate efficiently as a supplier of liquidity and, in the longer term, to react to new payment technologies such as the development of electronic money. Third, the ESCB's minimum reserve system may also contribute to controlling the expansion of monetary aggregates by increasing the interest rate elasticity of money demand. How would you assess these three objectives with hindsight? Q8.7 On 8 December 2011, the ECB announced the decision To reduce the reserve ratio, which is currently 2%, to 1% as of the reserve maintenance period starting on 18 January As a consequence of the full allotment policy applied in the ECB s main refinancing operations and the way banks are using this option, the system of reserve requirements is not needed to the same extent as under normal circumstances to steer money market conditions. While the press release provides an argument why the higher levels are no longer needed, it does not explain the benefits of lowering reserve requirements. How would you complete the reasoning? 17

18 Q9: Collateral Q9.1 Why should a central bank refrain from providing uncollateralized credit? Q9.2 What are desirable properties of central bank collateral (and why)? What are the differences to the desirable properties of collateral for interbank repo operations? Q9.3 Under what circumstances can losses arise even in collateralised lending? What risk control measures can be designed to address this? Against what can these protect, and against what can they not? Q9.4 Why would assets with lower credit quality tend to deserve higher haircuts, even after adjusting valuation? Why would assets with longer duration deserve higher haircuts? Q9.5 Consider two eligible assets of the same duration (say 2 years), asset 1 being a AAA rated sovereign bond and asset 2 being a BBB rated corporate bond. Asset 1 is credit risk free and liquid and can be liquidated without market impact in 3 business days. Asset 2 is less liquid and therefore it is realistic that liquidation without market impact takes 10 business days. Assume that the common (risk free yield curve) related market risk factor is normally distributed, and that the related one day price change is N(0,1%). Asset 2 is in addition subject to the following risk factors: the uncertainty on the true asset value at the moment of valuation is N(0,4%), the daily uncertainty stemming from spread and credit migration risks is N(0,2%). Assume that the daily price innovations are uncorrelated across time. Assume that the risk tolerance of the central bank has been defined as preventing with 95% probability that the asset value at liquidation falls short of the last valuation post haircut. What are the appropriate haircuts on the two assets? Q9.6 Assume an economy in which households would only hold banknotes and no bank deposits, such that the entire banks balance sheet would be financed with equity and central bank credit. Assume that the shadow cost of equity is captured in a 6% spread over risk free rates and that the central bank provides its credit at 4%. Also assume that banks have two type of assets, held in equal quantities: liquid and non-liquid assets. The central bank imposes on liquid assets a haircut of 10% and on illiquid assets a haircut of 30%. What amount of equity will the bank need? What will be its average funding costs? How will banks (assuming that they have no operating costs and are subject to full competition) price the loans to liquid and illiquid projects (assets)? What is the average funding cost of the real economy? In which sense is haircut policy in such a setting equal to monetary policy? Provide two alternative ways (via the central bank credit interest rate and via collateral haircuts) to tighten effective monetary conditions by one percentage point. In which sense can it influence the industry allocation of credit? Q9.7 Section (c) of the Eurosystem s General Documentation specifies that: The Eurosystem limits the use of unsecured debt instruments issued by a credit institution or by any other entity with which the credit institution has close links as described in section Such assets may only be used as collateral by a counterparty to the extent that the value assigned to that collateral by the Eurosystem after the application of haircuts does not exceed 5% of the total value of the collateral submitted by that counterparty after the haircuts. Show in a financial accounts system that indeed banks can create in this way fountain pen collateral. What risks would this create for the central bank? 18

19 Q10: Optimal frameworks for monetary policy implementation in normal times Q10.1 What are desirable properties of monetary policy implementation frameworks? Q10.2 If you compare the operational framework of the Reserve Bank of Australia (narrow corridor, no reserve requirements, daily open market operations) with the one of the Eurosystem in normal times (wider corridor, one month reserve requirement period, weekly open market operation) which approach seems preferable in your view an on what could the choice depend? Q10.3 How would you describe the pre-2007 consensus on monetary policy implementation technique? What issues seemed to remain unclear? Q10.4 The book covers mainly the case of industrialised countries central banks, and chapter 10 issues relating to their optimal operational framework. What would you believe are additional key issues of optimality for emerging market central banks? Q10.5 C. Ho (2008, Implementing monetary policy in the 2000s: operating procedures in Asia and beyond, BIS Working Paper No. 253) concludes (p. 26) that Another perhaps even more striking finding of this paper is that even within just the last couple of years, there have been many changes and new developments in virtually all aspects of monetary policy implementation from the redefinition of policy rates and operating targets, to the adoption of new instruments, to a complete overhaul of the reserve requirement framework. It is therefore also clear that no operating framework can be the right one for all times. Central banks everywhere in industrial and emerging economies alike have continued to refine their frameworks and procedures and to innovate where necessary, responding to changing needs in changing times. How do you assess this conclusion, and in particular that no operating framework can be the right one for all times? 19

20 Q11: The nature of a liquidity crisis Q11.1 Assume the following balance sheet of an indebted company. (You can use excel to approximate some of the answers). Company x Assets 100-e Senior debt 80 max(0,e-20) Equity 20-min(e,20) (a) What is the probability of default for senior debt, assuming that e is normally distributed and has an expected value of -5% and a standard deviation of (i) 5%, (ii) 15%, (iii) 25%? Assume that default occurs when equity is negative. (b) Assuming that investors are risk neutral and that the required remuneration rate for risk free assets (established by the central bank) is 4%, what is the remuneration rate of debt for the three alternative values of the standard deviation of e which compensates for the expected losses? (c) Assume now that there is a one off realised shock of e=-10. In the next period, asset value uncertainty is again an identically independently distributed e being N(-5, σ 2 ). What is now the remuneration rate of debt that compensates for expected losses, again depending on the standard deviation of asset value shocks? (d) In how far does the profitability of the corporate depend on asset price volatility (even with risk neutral investors)? Q11.2 Consider the following table indicating total Government financing needs and total eventual related increases of the debt/gdp ratio in the respective euro area country relating to the sovereign debt crisis. (data from: H. Maurer and P. Grussenmeyer, 2015, Financial assistance measures in the euro area from 2008 to 2013: statistical framework and fiscal impact, ECB Statistics Paper Series, No. 7). (a) How would you interpret the data? (b) What is the relationship between these measures of Government support and the role of central bank credit? Country Financial needs in % GDP (from table 2 in MG, 2015; ) Cumulated deficit effect due to Government interventions (from Table 4 in MG, 2015), in % of GDP DE IE GR ES FR IT Q11.3 Assume the lemons market model of section 11.2 and that before the outbreak of a financial crisis, the following parameter values apply: δ =0.4, p=0.9, and V G =1.2. (a) Will an active credit market prevail under such circumstances? (b) On the basis of the three parameters, explain why a financial crisis can lead to a break-down of credit markets. Provide illustrations from the current financial crisis. (c) Starting from the values above and varying each parameter individually: what are the critical values of each of the parameters? 20

21 Q11.4 Why would you expect haircuts to increase in a financial crisis? What is the effect on leverage? When could some collateral type become ineligible in interbank repos? Q11.5 Why do bid ask spreads posted by market makers typically increase in a financial crisis? Q11.6 Assume the following bank balance sheet. Assets Liabilities Assets D+1 Short term funding from Investor 1 D/2 Short term funding from Investor 2 D/2 Equity 1 Assume that a share Lambda, Λ (0<Λ<1) of assets is fully liquid (i.e. it can be sold without any fire sale losses). Assume also that the other assets, i.e. a share (1-Λ) of assets, are totally illiquid, i.e. if one would try to fire sell them, one would not generate a cent of liquidity, but only generate losses. Assume also that the central bank applies a homogeneous haircut h on all assets, and that all assets are eligible as central bank collateral. (a) Derive a sufficient condition for a unique no-run equilibrium. (b) Is funding stability ensured if Λ=0.4, h = 0.8, and D=2? (c) What is the maximum sustainable amount of short term funding? (d) Assume now that in a liquidity crisis Λ =0. What would the central bank need to do to maintain a unique no-run equilibrium (starting from the parameter values of b))? Q11.7 Consider the following case of a bank threatened by a bank run Assets Liabilities Liquid assets Λ(2+E) Depositor 1 1 Semi- liquid assets Π(2+E) Depositor 2 1 Non-liquid assets (1-Π-Λ)(2+E) Equity E Moreover, assume the following haircut and fire sales discounts, with f < h 2 : Central bank haircut Fire sale discount Liquid assets h 1 0 Semi-liquid assets h 2 f Non-liquid assets h 3 1 (a) What is the condition for a single no-run equilibrium? (b) Assume now that Λ=0.25, Π = 0.25, f = 10% and h 1 = 0%; h 2 = 20% and h 3 = 50%. What value of E will the bank choose? (c) What if f=25%? (d) What if Λ=0, f= 50% h 3 = 80%? Q11.8 Why is there a risk that a liquidity crisis pushes the economy into a deflationary trap? Explain this on the basis of an extended Wicksellian arbitrage equation. Q11.9 What measures can central banks take to address the risks of the economy falling into a deflationary trap in a financial crisis? (a) ex ante (b) ex post Q11.10 In particular German economists have warned repeatedly that the crisis response of the ECB would be inflationary. Examples (I wish to thank Adalbert Winkler for collecting these quotes): J. Starbatty, 22 April 2010: I think that the inflation rate will increase strongly: to above 5%. All evidence shows that countries that have high debt levels tend to inflation ; H-O Henkel, 25 Mai 2010: An increase of inflation is in front of the door ; S. Homburg, 18 December 2011, answering to a journalist s question Is a higher inflation rate unavoidable in the future? S. Homburg: Yes. So far, 21

22 the ECB has purchases sovereign bonds while at the same time absorbing the money supply elsewhere. But when Italy gets stressed, then the ECB will no longer be able to sterilize the bond purchases which would then be necessary. And if she is no longer able to do so, then unavoidably the monetary base, the quantity of money, and eventually prices will increase. Currently the inflation rate is 2.8%, so clearly above the target level of 2%. In principle the ECB would have to tighten its interest rate policy already now. J. Stark, 23 March 2012: History has shown that any particularly strong increase of central bank balance sheets has lead in the medium term to inflation J. Starbatty, 10 September 2012: In the long term there is only one reason for inflation: financing of fiscal deficits by central banks. Current recessionary tendencies may still hide that. But that this creates inflation is as certain as the Amen in the church. MJM Neumann, 6 November 2012: expects a creeping inflation rate of up to 6%. R. Vaubel, 11 October 2012: I expect that we will get in coming years inflation rates of up to 5% and more. This is because the monetary base has been increased since 2010 by more than 50%. I do not believe that the ECB will be able to turn this back in time. At least so far these economists were wrong, as inflation rates in the euro area trended down and both headline and core inflation reached new lows in early 2015 (core at 0.6%, headline negative). (a) What may explain that the inflation fears of these economists have not (yet) materialized? (b) How would you rank their different arguments in terms of merits? (c) Could they still be right in the long term with their inflation worries? Q The following chart shows NFC overall cost of funding (see the book, page 174), the 5Y OIS rate, and the average monthly EONIA rate during the crisis years. What does the evolution of the three time series tell us? What does the evolution of their relative level tell us? Q11.13 Before 2013, the ECB never lowered the rate of its deposit facility to below 0.25%, despite the fact that it started with non-conventional monetary policy measures in 2007 and continued to launch various such measures throughout all the crisis years. Only in 2013, the ECB set the deposit facility rate to 0%, and in 2014 even to -0.10% (in June) and -0.20% (in September). How would you interpret that various non-conventional monetary policy measures were taken by the ECB before it strictly reached the ZLB? 22

23 Q12: Collateral availability and monetary policy Q12.1 For what reasons does central bank collateral become scarcer in a financial crisis? Q12.2 How can increased collateral scarcity affect monetary policy transmission in a financial crisis? Q12.3 What can the central bank do to reduce collateral scarcity in a financial crisis and thereby contribute to restore the intended stance of monetary policy at a given interest rate level? Q12.4 Assume the following representative bank balance sheet. In normal (crisis) times, fire sale discounts of credit claims is 100% (100%) and of corporate bonds 25% (50%). Central bank haircuts are set in normal times to be 100% on credit claims (i.e. credit claims are not eligible central bank collateral) and 50% on corporate bonds. (a) What is the maximum sustainable level of d in normal times (assuming that the banks are myopic and do not anticipate crisis times)? (b) Assume that banks indeed chose to maximise their funding through short term deposits. How would the central bank need to adjust its collateral framework in crisis times to preserve a stable funding structure of banks and to prevent bank runs? Credit claims Corporate bonds Assets (d+2)/2 (d+2)/2 Liabilities Short term funding from Investor 1 d/2 Short term funding from Investor 2 d/2 Long term debt 1 Equity 1 Q12.5 In a press release on 4 September 2008, the ECB announced to increase haircuts applied to ABS when used by banks as collateral in Eurosystem credit operations. ABS will be subject to a haircut of 12% regardless of their residual maturity and coupon structure. This corresponds to the level of haircuts that was previously assigned to assets in this liquidity category with a fixed coupon and a residual maturity of over ten years. Furthermore, assets in this liquidity category that are given a theoretical value will be subject to an additional valuation haircut. This haircut will be applied directly to the theoretical value of the asset in the form of a valuation markdown of 5%, which corresponds to an additional haircut of 4.4%. How would you assess these measures, taking into account their timing? Was this decision compatible with the inertia principle of Bagehot? Q12.6 on 15 October 2008, the ECB announced that it would lower the credit threshold for marketable and non-marketable assets from A- to BBB-, with the exception of asset-backed securities (ABS), and impose a haircut add-on of 5% on all assets rated BBB-. How would you explain these decisions? 23

24 Q13: Open market operations and standing facilities in a financial crisis Q13.1 Besides improving collateral availability, how can central banks adjust their credit operations in financial crises to make them more convenient? Q13.2 What purposes can outright purchase programmes pursue in a financial crisis? Q13.3 What are suitable operational targets for outright purchase programmes? Can you give examples of outright purchase programmes with well-defined and not so well-defined operational targets? Q13.4 How would you measure the success of outright purchase programmes? Distinguish between operational, intermediate, and ultimate targets. What are the main difficulties? Q13.5 Should the success of outright purchase programme depend on whether the securities purchased come from the holdings of banks or from of the holdings of households? What if banks are subject to leveraging constraints? Draw the financial accounts of the economy and show what difference it makes where the securities come from. Q13.6 On 15 October 2008, the ECB announced that the Eurosystem will also enhance its provision of longer-term refinancing as follows: All longer-term refinancing operations will, until March 2009, be carried out through a fixed rate tender procedure with full allotment. How would you explain this decision? Q13.7 On 8 December 2011, the ECB announced to conduct two credit operations with duration of 36 months, specified as fixed rate full allotment operation. These were the longest monetary policy credit operation ever done by a central bank, and the keen interest of banks to participate also made them the largest ever (each had a volume of close to half a trillion). What speaks normally against such operations, and what spoke in their favour in the euro area of December 2011? Q13.8 Various LSAPs aimed at overcoming low inflation in the context of the ZLB (e.g. the Government bond purchase programmes of the FED, BOE, BoJ and ECB). What effects on yields do you expect from such programmes? Distinguish between a stock, a flow, and a fair value effect, and elaborate also on the time path of interest rates that you expect to materialise. Q13.9 Outright purchase programmes of a credit easing type aim also at compressing spreads of securities towards risk free Government bonds. To what extent can such spread compression be distortive and thereby undermine the efficient allocation of resources? Q13.10 On 10 May 2010, the ECB announced its Securities Market Programme. Accordingly, the Governing Council of the European Central Bank (ECB) decided to conduct interventions in the euro area public and private debt securities markets (Securities Markets Programme) to ensure depth and liquidity in those market segments which are dysfunctional. The objective of this programme is to address the malfunctioning of securities markets and restore an appropriate monetary policy transmission mechanism.. In making this decision we have taken note of the statement of the euro area governments that they will take all measures needed to meet [their] fiscal targets this year and the years ahead in line with excessive deficit procedures In order to sterilise the impact of the above interventions, specific operations will be conducted to re-absorb the liquidity injected through the Securities Markets Programme. This will ensure that the monetary policy stance will not be affected. (a) How should one understand in this announcement the term stance of monetary policy? (b) How would you assess the announcement of sterilisation in this context? (c) How do you assess the reference to a statement by Governments? (d) What would you expect to be the operational, intermediate, and ultimate target of the SMP? 24

25 Q14: The lender of last resort (LOLR) role of the central bank Q14.1 What are the fundamental reasons for central banks to act as lender of last resort? Q14.2 Explain why the LOLR role is also to some extent effective under central bank inertia, i.e. without the central bank taking active LOLR measures. What determines the limits of this built-in LOLR? Q14.3 What are key active LOLR measures? Q14.4 What are the distinct features of ELA, compared with normal central bank credit operations? What are generally accepted central bank principles applied to ELA? Q14.5 How would you assess the merits of constructive ambiguity regarding the provision of ELA? Q14.6 Consider the following heterogeneous banking system (with exogenous modelling of funding liquidity risk). Bank 1 Government bonds 80 Deposits of HH η + μ Corporate bonds 20 Borrowing from CB η - μ Loans to corporates 100 Equity 30 Deposits with CB 0 Total assets 200 Total liabilities 200 Bank 2 Government bonds 20 Deposits of HH η - μ Corporate bonds 80 Borrowing from CB η + μ Loans to corporates 100 Equity 30 Deposits with CB 0 Total assets 200 Total liabilities 200 Central bank Government bonds 50 Banknotes 200 +η Corporate bonds 50 Deposits of banks 0 Lending to banks 140 +η Equity 40 Total assets 240 +η Total liabilities 240 +η Assume moreover that 10 and 5 and that the haircut vector of the central bank is {0%, 20%, 100%}. a) What is the distance to illiquidity (DTI) and the Probability of Liquidity (PL) or Probability of illiquidity (PI = 1- PL) of the two banks? How does the system of accounts and the DTI and PL change under the following (independent) scenarios: Finally: b) Corporate bonds loose 30% of their value; c) The central bank purchases 50 more of corporate bonds (proportionally to bank holdings); d) The central bank starts accepting loans to corporates as collateral, applying a haircut of 50%; e) The central bank lowers corporate bond haircuts to zero; f) Under what circumstances is the central bank involved in absolute intermediation of the banking system? How likely is that? 25

26 Q14.7 On 16 September 2008, the Fed provided a credit to AIG, the biggest American Insurer: The Federal Reserve Board on Tuesday, with the full support of the Treasury Department, authorized the Federal Reserve Bank of New York to lend up to $85 billion to the American International Group (AIG) under section 13(3) of the Federal Reserve Act. The secured loan has terms and conditions designed to protect the interests of the U.S. government and taxpayers. The Board determined that, in current circumstances, a disorderly failure of AIG could add to already significant levels of financial market fragility and lead to substantially higher borrowing costs, reduced household wealth, and materially weaker economic performance. The purpose of this liquidity facility is to assist AIG in meeting its obligations as they come due. This loan will facilitate a process under which AIG will sell certain of its businesses in an orderly manner, with the least possible disruption to the overall economy. What was particular in this operation? Why the reference to section 13.3 of the Federal Reserve Act? Q14.8 On 14 September 2007, Northern Rock requested liquidity support facility from the Bank of England. According to the Financial Times of that day: It will lift the uncertainty that has been hanging over Northern Rock s future for much of the past month because it could not access the wholesale funding upon which it is heavily dependent. It will also allow Northern Rock to reassure thousands of customers that their deposits are secure. However, actually these announcements triggered a bank run with people queuing in front of branches to withdraw cash, i.e. the announcement to provide ELA contributed to worsen a panic, instead of stabilising the situation. How can this be explained? Q14.9 Consider the balance sheet charts on pages of the book. Which phases of the balance sheet lengthening of CBs do you associate with the LOLR, and which ones do you explain differently? Q14.10 Assume the following financial system Assume the following financial accounts. Household Real assets E-4 Equity E Banknotes 2+ η Deposits 2- η Corporate sector Real assets 4 Corporate bonds issued 2 Loans from banks 2 Bank 1 Corporate bonds 1 P/2 Depositors 1+μ-η/2 Loans to corporates 1 Central bank credit 1- μ + η /2 P/2 Bank 2 Corporate bonds 1 P/2 Depositors 1- μ - η /2 Loans to corporates 1 Central bank credit 1+ μ + η /2 P/2 Central bank Credit to banks 3-P+ η Banknotes 2 + η Corporate bond holdings P Central bank credit 1 Assume that the initial desire of the central bank to hold an outright portfolio is zero (P=0) and that also the households financial asset allocation shocks μ, η stand initially at zero. Assume moreover that the central bank applies a haircut h when accepting corporate bonds as collateral. This haircut is initially 20%. The haircut the central bank applies to credit claims is 40%. (a) How does relative and absolute central bank intermediation depend on μ, η? (b) How does distance to illiquidity change with P? How do changes in the haircut influence distance to illiquidity? 26

27 Q14.11 Assume the following financial accounts. Household Real assets E-D-B Equity E Deposits D Banknotes B Bank equity F Corporate/Government Real assets D+B Bonds issued D+B Bank 1 Bonds D/2 + B/2 + F/2 P/2 Depositor 1 D/4 Depositor 2 D/4 Central bank credit (B-P)/2 Equity F/2 Bank 2 Bonds D/2 + B/2 + F/2 P/2 Depositor 1 D/4 Depositor 2 D/4 Central bank credit (B-P)/2 Equity F/2 Credit to banks Bonds B-P P Central bank Banknotes B Assume moreover that fire sale costs of bonds are 60% and central bank collateral haircuts on them are 75%. How does the leveraging ability of the central bank depend on D, B, P? 27

28 Q15: LOLR and central bank risk taking Q15.1 Would you expect the central bank risk budget to increase or to decrease in a financial crisis? Q.15.2 Would you expect the central bank risk budget to increase or to decrease due to the adjustment measures taken by the central bank in a financial crisis? Q15.3 Bagehot claimed in 1873 that only the brave plan [of the Bank of England] is the safe plan. Why would this be the case, and under what circumstances? Q15.4 Consider the following example. Government bonds 10 Corporate bonds 10 Loans to corporates 70 Deposits with CB 0 Bank Deposits of HH1 40 Deposits of HH2 40 Borrowing from CB 10 Equity 10 Assume moreover that the haircut vector of the central bank is {0%, 20%, 50%} and that the fire sale discounts in normal times are {0%, 10%, 40%}. These fire sale discounts are also the basis for calculating the cost of default C (which we assume to imply immediate liquidation of all assets), and therefore C=29 in normal times. a) Is the funding structure of the bank stable? b) What is the probability of central bank losses? In what sense is this probability a function of haircuts (vary the haircuts proportionally)? c) What changes if the fire sales loss vector is {0, 30%, 50%} in terms of how central bank losses depend on haircuts? Q15.5 Assume the following bank balance sheet. Bank Assets D+d Deposits of HH1 d/2 Deposits of HH2 d/2 Long term credit D Also assume a central bank collateral haircut of h and fire sale losses of f per asset unit sold, with f < h. Under what circumstances is the risk talking of the central bank as a function of h upward sloping? Q15.6 On 5 Mach 2009, the ECB issued a press release on its end 2008 Annual accounts and a note on Monetary Policy Operations in 2008, in, which also explained the following. In autumn 2008, five counterparties defaulted on refinancing operations undertaken by the Eurosystem, namely Lehman Brothers Bankhaus AG, three subsidiaries of Icelandic banks, and Indover NL. The total nominal value of the Eurosystem s claims on these credit institutions amounted to some 10.3 billion at end The monetary policy operations in question were executed on behalf of the Eurosystem by three NCBs, namely the Deutsche Bundesbank, the Banque centrale du Luxembourg and de Nederlandsche Bank. The Governing Council has confirmed that the monetary policy operations in question were carried out by these NCBs in full compliance with the Eurosystem s rules and procedures, and that these NCBs had taken all the necessary precautions, in full consultation with the ECB and the other NCBs, to maximise the recovery of funds from the collateral held. The counterparties in question submitted eligible collateral in compliance with the Eurosystem s rules and procedures. This collateral, which mainly consisted of asset-backed securities (ABSs), is of limited liquidity under the present exceptional market conditions and some of the ABSs need to be restructured in order to allow for efficient recovery. Under current market conditions, it is difficult to assess when the eventual resolution will be achieved by the Eurosystem. The Governing Council decided that any shortfall, if it were to materialise, should eventually be shared in full by the Eurosystem NCBs in accordance with Article 32.4 of the Statute of the ESCB, in proportion to the prevailing ECB capital 28

29 key shares of these NCBs in The Governing Council also decided, as a matter of prudence, that the NCBs should establish their respective shares of an appropriate total provision in their annual accounts for 2008 as a buffer against risks arising from the monetary policy operations which were conducted with the counterparties mentioned above. The size of the total provision will amount to 5.7 billion, and it is already accounted for in the net result figures stated above. The level of the provision will be reviewed annually pending the eventual disposal of the collateral and in line with the prospect of recovery. On 20 February 2013, the Bundesbank issued a press release on the same subject: Since autumn 2008 the Bundesbank has gradually resolved the pledged securities, in some cases having to restructure them. In 2012, Diversity and Excalibur, the two largest positions in the LBB collateral portfolio, were sold, amongst other assets. The process of winding down the pledged securities is now complete. The situation after more than four years of resolving collateral is as follows. With proceeds from sales as well as interest and redemption payments totalling 7.4 billion, a considerable percentage of the original claims against LBB have been covered. After subtracting these 7.4 billion from the original claim of 8.5 billion, a difference of 1.1 billion is left over. After accounting for interest claims and costs totalling 0.8 billion, a residual claim of 1.9 billion is left over and will go into the German LBB bankruptcy proceedings. In addition, the Bundesbank is a creditor in the US LBHI bankruptcy proceedings; it has a nominal guaranteed claim of $3.5 billion against LBHI. Payments are expected from both bankruptcy proceedings. For this reason, the Eurosystem s provisions for counterparties in default, calculated according to the principle of prudence, and of which LBB is the largest position, were able to be reduced from 5.6 billion at end to 0.3 billion at end What are the ley lessons from this episode for central bank collateral frameworks? 29

30 Q16: LOLR, moral hazard and liquidity regulation Q16.1 In a report in 2009, the UK Financial Services Authority (p. 68) acknowledged that: [T]here is a trade-off to be struck. Increased maturity transformation delivers benefits to the nonbank sectors of the economy and produces term structures of interest rates more favourable to long-term investment. But the greater the aggregate degree of maturity transformation, the more the systemic risks and the greater the extent to which risks can only be offset by the potential for central bank liquidity assistance. What are the actual costs of potential central bank reliance which really justify the perception of a trade-off? Q16.2 How would you define Moral hazard? What is the distinction from legitimate optimisation behaviour? In which sense can substantial liquidity and maturity transformation of banks be considered moral hazard? Q16.3 What are key challenges in liquidity regulation? Q16.4 Sunday July 13, 1931 was a decisive day in German economic and financial history: it was the day in which Germany failed to find a solution for its banking crisis. After that, banks never reopened normally, gold convertibility of the Mark ended, and Germany defaulted on its foreign debt. Only around 20 years later, and the unprecedented human and political disaster of the Third Reich, normalisation occurred. Hans E. Priester (1932, Das Geheimnis des 13 Juli, Verlag von Georg Stilke, Berlin) describes a part of the decisive meeting in the Reichsbank as follows (own translation, p ): After a short welcome by Chancelor Brüning, state secretary Trendelenburg summarized the situation. There would be two ways to save Danat bank: a merger or supportive solidarity by all other banks. Otherwise, only a closure of Danat bank would remain. A discussion followed. The banks unanimously rejected the idea of solidarity as the situation of Danat bank was completely non-transparent. Eventually, the banks were ready to help Danat bank with 250 million Reichsmark, but only if the funding would come from the Reichsbank and in any case the Reichsbank would have to give up its restrictive policies. The President of the Reichsbank Dr. Luther completely rejected this proposal, and announced to the contrary that the restrictive policies would be sharpened even further in the future. Neither himself nor Brüning mentioned that the political negotiations with France [regarding inter-central bank loans] played an important role to explain his position. Harsh words were exchanged, including by Dr. Luther. He refused to tolerate that all of the burden was dumped on the Reichsbank, who would not be the drudge the banks seemed to perceive in it. She would not be ready to let itself be misused, as the first condition for maintaining the German economy would be that the central bank would remain faultless. If he would provide further discount loans, he would not be able to maintain the 40% gold cover ratio. The banks should think about the signal an under-fulfilment of the gold cover ratio would imply. Unrest would be created, which could easily be the starting point of a domestic bank run. Also for political reasons, the Reichsbank would not be in a position to engage in such support measures before the central bank meeting in Basel next Monday. Luther had spoken himself into a state of strong excitement. He stood there wildly gesticulating, in his hand his bible, the Reichsbank law. The representatives of the banks and the ministries were perplex, as they did not know enough about the political issues who had brought Luther towards such conclusions. Geheimrat Bücher of the AEG asked Luther ironically, what would be the benefit of a faultless Reichsbank, if the rest of the economy had broken down. He added that one should not only insist on legal articles, as unusual times also require unusual measures. The Reichsbank would be the institution that was responsible for the functioning of the German credit system. She would had the duty to do whatever was possible, to avoid the collapse of the German credit building. But Dr. Luther constantly insisted that the Reichsbank would not contribute funding in any sense to the rescue of Danat bank. 30

31 (a) What analogies and differences between the failed rescue of Lehman in September 2008, and the discussions on Danat Bank in July 1931 do you see? (b) How would you generally assess the merits of collective private solutions brokered by the central bank to solve liquidity problems of single institutions (similarly to the case of the LTCM rescue brokered by the Fed NY in [1998], or the liquidity support that German banks gave temporarily to Hypo Real Estate in 2007, brokered by the Deutsche Bundesbank)? (c) How important would you believe is it that the central bank sticks to the rules in LOLR operations, as a matter of principle (as argued by the President of the Reichsbank, Hans Luther)? (d) In which sense would Reichsank LOLR to Danat Bank has been a misuse of the Reichsbank, as argued by Luther? (e) What difference did the Gold standard make, and in which sense was the Gold standard the eventual main problem to an unconstrained LOLR by the Reichsbank (this question can best be answered after reading also chapter 17 of the book)? Q16.5 M. Carlson, B. Duygan-Bump, and W. Nelson ( Why do we need both liquidity regulation and a Lender of Last resort? A perspective from Federal Reserve Lending during the Financial Crisis, BIS Working Paper No. 493) conclude that while central banks can to some extent control the potential moral hazard associated with lending by pricing credit risk correctly or, more practically, by driving credit risk to zero by taking on lots of collateral, this approach may actually hinder their ability to address liquidity troubles at times. Consequently, it will also be important to establish sufficiently low-cost resolution regimes to reduce the cost of allowing an institution to fail, and that institutions be allowed to fail rather than lent to by a LOLR when their illiquidity is the consequence of solvency rather than liquidity concerns. What is the precise link between credit risk taking of the central bank when doing LOLR and bank solvency? 31

32 Q17: The international lender of last resort Q 17.1 Consider the case of a monetary area such as the euro area, with a system of national central banks (NCBs) and the ECB. The following accounts represent this case, whereby only two NCBs are distinguished (A and B) a) Comment on these initial financial accounts. How could one explain the main asymmetries between the two countries? b) Assume now that doubts arise on the solvency of the banking system of one country (or people realise that the deposit insurance in one country is less good than in other countries etc.). Represent the following five shocks in the system of financial accounts: i. households shift deposits of 5 from A to B banks ii. household shifts deposits from B to A banks amounting to 32 iii. decline on interbank lending to A banks to zero iv. households withdraw banknotes from A banks for 6 v. NCB A injects reserves into the A banks by purchases of corporate claims of 4 c) How would you represent a current account transaction in this system of financial accounts (hint: you need to split the household account into an A country and a B country household)? Assume a surplus of country B of 10. Euro area households Deposits with A banks 10 Equity 100 Deposits with B bans 40 Banknotes 10 Real assets 40 A country banking system Loans 20 HH Deposits 10 Deposits with NCB A (RR) 5 Eurosystem refinancing 5 Net interbank liability 10 B country banking system Loans 40 Net interbank claims 10 Deposits with NCB B (RR) 10 HH Deposits 40 Eurosystem refinancing 20 NCB A Eurosystem credit 5 Banknotes 3 Deposits of banks 5 Net intra Eurosystem claims 3 NCB B Eurosystem credit 20 Banknotes 7 Current accounts of banks 10 Net intra Eurosystem liabilities 3 32

33 Q Consider the case of a monetary area such as the euro area, with a system of two national central banks (but no ECB). The accounts below represent this case, with two stylised countries Greece and Germany which are initially identical. Assume that this represents the situation at end of Greek households Deposits with Greek banks 10 Equity 50 Deposits with German banks 10 Banknotes 5 Real assets 25 German households Deposits with Greek banks 10 Equity 50 Deposits with German banks 10 Banknotes 5 Real assets 25 Euro area corporate sector Real assets 50 Real assets 50 Greek banking system Loans 25 HH Deposits 20 Deposits with NCB A (RR=5) 5 Eurosystem refinancing 10 German banking system Loans 25 HH Deposits 20 Deposits with NCB B (RR=5) 5 Eurosystem refinancing 10 Bank of Greece Eurosystem credit 10 Banknotes 5 Deposits of banks 5 Intra Eurosystem claims 0 Intra Eurosystem liabilities 0 Deutsche Bundesbank Eurosystem credit 10 Banknotes 5 Deposits of banks 5 Intra Eurosystem claims 0 Intra Eurosystem liabilities 0 Eurosystem Eurosystem credit 20 Banknotes 10 Deposits of banks 10 (a) Assume now that Greece has in 2010 a current account deficit of 2 and a capital account deficit of 4. The current account deficit results from real asset transactions between households (whereby the Greek household uses his account with the Greek bank to pay for the net import of real assets), while the capital account deficit results from deposit transfers of which one half is done by the Greek, and one half by the German households (i.e. each household transfers 2 deposit units from one bank account to the other). How do the accounts look like at the end of 2010? (b) Assume that the central bank accepts Loans of banks to corporates as collateral but imposes a haircut of h. What is the critical level of the haircut h at which the flows above become constrained by the collateral scarcity of the Greek banking system? (c) Assume that after 2010, the same capital and current account flows continue. When will the consolidated Eurosystem balance sheet start to lengthen (i.e. when will the Eurosystem start to do absolute central bank intermediation, instead of only relative one)? Q17.3 Some observers have criticised that the TARGET2 system (which is the cross border payment system in the euro area) and the associated creation of Intra-Eurosystem claims and liabilities is problematic as it undermines hard budget constraints. The conclusion is drawn by these observers that the intra-eurosystem claims should be capped (i.e. a maximum limit should be imposed). How do you assess this proposal? 33

34 Q17.4 Consider the following example of a stylised state balance sheet. State A Assets 1 Short term foreign currency loans investor 1 d/2 Short term foreign currency loans investor 2 d/2 Equity 1-d Assume that the Government can generate liquidity in the short term, but at some increasing costs. Assume that the cost of liquidity function f(x) is a mapping from the state s assets ordered according to liquidity in [0,1] into marginal liquidation costs within [0,1], whereby f(0) = 0 and df(x)/dx 0. Also define F(x) the integral of f(x). The maximum amount of short term liquidity that the Government may generate is therefore 1-F(1). (a) Under what conditions does this state have stable access to international capital markets? (b) What are assets and equity in the case of a sovereign? (c) What are possible analogies to asset value shocks and a deterioration of asset liquidity for banks? (d) Assume now that f(x) = x^α. What is the highest possible level of short term funding as a function of α? (e) Assume now that d=0, 0.25, 0.5, 0.75, 1 and α=0.1, 0.5, 1, 5. In which cases does the Government has a stable funding basis? Q17.5 According to a Bloomberg News Article of 24 May 2011, European Union demands may require Greece to sell 15 billion euros of assets by the end of 2012, a year ahead of schedule, in order to win a new three-year loan package, a person familiar with the talks said today. EU Economic and Monetary Affairs Commissioner Olli Rehn said creating a vehicle to manage Greece s privatization program was being considered. The possibility to create a trust fund or a privatization agency is one option we re exploring among several, Rehn told reporters in Vienna today. The government said it would sell its stake in Hellenic Postbank SA and the country s ports in the first phase of the asset-sale program. The state s direct 34 percent stake in Postbank has a market value of about 275 million euros. The government also said it would create a sovereign-wealth fund composed of state assets to accelerate the sale process. The government plans to complete the stake of Hellenic Postbank by the end of the year, and to sell 75 percent stakes in Piraeus Port Authority and Thessaloniki Port Authority SA. It also intends to extend the concession for Athens International Airport this year. What are the strength and weaknesses of state asset sales in a Government funding / Balance of Payments crisis? Q17.6 In June 2015, Greek authorities introduced administrative measures in Greece to protect the funding of Greek banks. Show in a financial accounts system that both balance pf payment deficits and banknote withdrawals create funding gaps with banks that can only be closed with central bank credit. What key challenges would you expect for a capital controls framework to operate in a monetary union like the euro area? 34

35 Solutions S1: Basic terminology and relationship to monetary macroeconomics S1.1 See page 9-10 of the book. S1.2 The purest open market operation, and the most remote to a standing facility, is a bilateral outright purchase or sale of a security (or commodity, like gold) in the financial market using standard practices also applied between banks. A pure standing facility in today s sense is a credit operation with well-defined access criteria and procedures, accessible to eligible counterparties at any moment during the day, and overnight maturity and full allotment at the pre-announced interest rate. The following steps can each be seen as moving from the pure open market operation to the pure standing facility, and the continuum results from the fact that the steps can be gradual on some of the dimension. Instead of a bilateral trade in the open financial market using standard interbank practice, conduct an auction procedure with pre-defined access conditions and (idiosyncratic) procedures; Instead of outright purchases of securities, do credit operations; Shorten the maturity of credit operation to overnight; Conduct the credit operation as fixed rate tender (instead of as variable rate tender); more generally, be oriented towards interest rates, instead of towards quantities; Conduct the operation with full allotment; Conduct the operation late in the day (as intra-day credit anyway tends to be interest rate free, an end of day overnight operation tends to be economically equivalent to offering access at any moment during the day). One could say that an open market operation in the form of a fixed rate full allotment with overnight maturity and conducted at day end is practically equivalent to a liquidity-providing standing facility for overnight credit. S1.3 The matrix is as follows. Open market operation Standing facility Outright operations Purchase in the standard market (or through an auction) of a certain fixed quantity of a security (Example: ECB s Public Sector Purchase Programme, PSPP, 2015) Discount window in pre-1914 central banking (selling commercial bills to the central bank with the price being determined by the discount rate fixed by the central bank) Credit operations Auction central bank three months credit once a months in a variable rate tender with pre-announced volume (Example: ECB s LTRO, as conducted between 1999 and 2008) Modern liquidity providing standing facilities, e.g. marginal lending facility of the ECB 35

36 S1.4 See page of the book. S1.5 See pages of the book S1.6 From the point of view of the terminology as proposed in chapter 1 of the book, Poole mixes an instrument (a term the book uses for e.g. standing facilities and open market operations) with the concept of an operational target, which is a variable that the policy decision making body of the central bank sets, and which is then targeted on a day-by-day basis through central bank market operations. On substance, the following critical remarks are permitted: First, the money stock is neither an instrument nor an operational target but if anything an intermediate target or an information variable. It cannot at all be steered on a day-to-day basis. Second, the fence sitters is what this paper of Poole aims at contributing to: a model which justifies such an intermediary approach, depending on what shocks hit the economy. However, from today s perspective, we would say that this idea of fence-sitting and of the associated model of Poole was more an academic exercise, and that it cannot be applied to practical central banking. In reality, short term interest rates are a meaningful operational target, and the money stock is not. The only relevant question is what information content is attributed to the money stock in the macroeconomic model of the central bank. The macroeconomic model is a key input to the decisions on the setting of short term interest rates as operational target. 36

37 S2: Representing monetary policy implementation in a closed system of financial accounts S2.1 (A) The implementation technique seems to be based on a symmetric corridor approach (as recourse to both facilities seems to be zero). Liquidity is steered through outright purchases and sales in a way to achieve neutral liquidity before recourse to central bank facilities. (B) Transactions are reflected as follows (a) Real assets of corporates and corporate debt decline by one; Corporate bonds held by central bank decline by one; A new real asset item is added to the central bank balance sheet with a value of 1. (Of course the central bank does not pay the corporate directly with a corporate bond. Instead, the central bank will initially credit the central bank deposit account of the bank of which the corporate is a client. But the corporate will then in a second step want to reduce its excess cash, and redeem with it some of its bond, as this allows to reduce the related interest rate cost). (b) Household: banknotes down by 8 to 2, deposits of households with banks up by 8; CB balance sheet shortens by 8 as banknotes go down by 8; to shorten also its asset side, we assume that the central bank sells corporate bonds of 8. Banks take these corporate bond from the central bank, and pay for them with the cash they got from the inflow of deposits of 8. This is how accounts look like afterwards (we do not show the corporate and government sectors, as they are unaffected). Households Real assets 60 Equity 100 Banknotes 10-8 Deposits banks Bank equity 10 Corporate equity 2 Corporate bond 1 Government bond 7 Banks Corporate bonds 7 +8 Deposits of HH Government bonds 8 Equity 10 Deposits with CB 5 Central bank credit 0 CB Deposit facility 0 Central bank Corporate bonds 10-8 Government bonds 5 Central bank credit 0 Banknotes 10-8 Deposits of banks (RR=0) 5 CB Deposit facility 0 (c) Banknotes held by household increase to 20, deposits go down to zero. Banks take recourse to central bank credit for 10 to substitute for the deposit outflows. The CB balance sheet lengthens by 10, as banknotes and CB credit both increase by that amount. (d) The central bank sells all Corporate and Government bonds (15 in total) to the banks, the banks have to refinance those with additional central bank credit. The central bank undertakes an asset switch, while banks see their balance sheet lengthen by 15. (e) Corporations see their asset value being reduced from 20 to 10, and see their equity being wiped out and also the value of debt has to decline from 18 to 10 (write-offs applied to the holders of these securities). For banks that means that corporate bonds decline from 7 to 7*10/18 = 3.89, i.e. by Their equity declines 37

38 accordingly from 10 to The central banks corporate bonds decline from 10 to 10*10/18 = 5.56 and CB equity becomes negative (having been zero before), namely an asset side equity of Finally, also the household suffers a shrinkage of corporate bod values by a factor 10/18 (i.e. by to 0.555) on its corporate bonds and experiences the same drop of its equity. Moreover, the households has large losses on corporate and bank equity (as he is the only holder of this equity). In fact the only loss that does not end up directly with the household is the central bank loss. This will however end later on with it, in the form of higher taxes to compensate for the absence of seignorage for some years. The financial accounts look as follows after applying these changes. Households Real assets 60 Equity Banknotes 10 Deposits banks 10 Bank equity Corporate equity 2-2 Corporate bond Government bond 7 Corporations Real assets Equity 2-2 Debt 18-8 Total assets 20 Total liabilities 20 Banks Corporate bonds Deposits of HH 10 Government bonds 8 Equity Deposits with CB 5 Central bank credit 0 CB Deposit facility 0 Total assets 20 Total liabilities 20 Central bank Corporate bonds Government bonds 5 Central bank credit 0 Equity gap 4.44 Banknotes 10 Deposits of banks (RR=0) 5 CB Deposit facility 0 Total assets 15 Total liabilities 15 38

39 S2.2 (a) Impact on length of BS (in the table R = Real assets held by household) Factor: Length of balance sheet of: B (HH choice) D (HH choice) P (CB choice) Household No impact as asset switch with D or R No impact as asset switch with B or R No effect Corporate sector Depends on the HH s substitute asset: If HH:B +D : Neutral. If HH:B +R : Increases (as corporate takes over real assets from HH). Depends on the HH s substitute asset: If HH:D +B : Neutral. If HH:D +R : Increases (as corporate takes over real assets from HH). No effect Banks If HH:B +D : Neutral. If HH:D +B : Neutral. Shortens bank BS If HH:B +R : Increases If HH:D +R : Increases CB Balance sheet always lengthens If HH:D +B : shortens If HH:D +R : neutral Asset side switch, balance sheet length unchanged (b) Take the example of the euro area (see table 2.2 on page 35 of the book this data refers to June 2011) the length of the Eurosystem central bank balance sheet was around EUR 1.9 billion with banknotes of EUR 0.8 billion. Deposits are around EUR 21 trillion; The length of the household balance sheet is around 19 trillion; banks balance sheet have a length of around EUR 30 trillion (note that monetary financial institutions include the central bank). Important simplifications in the stylised financial accounts: Households are also leveraged, i.e. take credit from banks; some sectors are missing: Government; non-bank financials; Rest of the world. (c) As follows (the debt of the household is called L ). If the households uses the credit to buy real assets (e.g. real estate), then this goes at the expense of the length of the balance sheet of the corporate sector: Household Real assets E+L-D B Equity E Banknotes B Loans from banks L Deposits D Corporate sector Real assets B+D-L Bonds issued B+D-L Banks Bonds D+B-P-L Deposit D Loans to households L Central bank credit B-P 39

40 If the HH uses the bank credit to hold more deposits, then instead: Household Real assets E -D -B Equity E Banknotes B Loans from banks L Deposits D+L Corporate sector Real assets B+D Bonds issued B+D Banks Bonds D+B-P Deposit D+L Loans to households L Central bank credit B-P In none of these cases, the central bank balance sheet is affected (therefore it is not shown). S2.3 (a) The charts can be drawn easily in Excel see the excel file Q2 3. These are the deposit curves across individual banks for the four proposed combinations of the four parameters. Notes: D 1 (x) and D 2 (x) are identical. Under both D 3 (x) and D 4 (x), the banks with the weakest deposit base have no deposits at all. D 3 (x) can be interpreted as the result of a reallocation of household financial assets out of bank deposits into banknotes. D 4 (x) can be interpreted as a re-allocation of household financial assets from deposits of weak banks to deposit of strong banks (a run on individual banks, presumably by those households having accounts with weak banks opening accounts with strong banks and transferring their deposits). (b) Define R i (x) now as the recourse of bank x to central bank credit under scenario i. The formula for R i (x) is: R i (x) = B-P-(D i (x)-d) = B-P-(0.5-x)s. In the same excel file the recourse to the central bank curves are drawn, for the same four scenarios also examined under (a). 40

41 Notes: In the initial case R 1 the position of banks vis-à-vis the central bank (before money markets) is symmetric, i.e. some banks are short, others are long. Therefore, there are opportunities for interbank trading, and eventual recourse to the central bank after a perfectly efficient interbank market would have cleared is zero (as B-P=0). The same applies for R 4. Because of the higher value of s, there is even more scope for interbank trading. In the cases R 2 and R 3, in contrast, all banks are on the same side relative to the central bank even before interbank markets, and therefore there is no reason to expect the existence of an interbank market. The bank x s balance sheet looks as follows: Bonds Excess reserves D+B-P max(0, -(B-P-(0.5-x)s)) Deposit Central bank credit D+(0.5-x)s max(0, B-P-(0.5-x)s) (c) An interbank market takes place if some banks are in a surplus to the central bank and some in a deficit (before interbank trading). This is the case if R(0) < 0 and R(1) >0, i.e. B-P-0.5s < 0 and B P + 0.5s > 0. This means that -0.5s < B-P < 0.5s. The size of the interbank market for a given s is maximised if the liquidity neutral bank x* is right in the middle, i.e. x* = 0.5 => B-P = 0 B=P, which means that we are in the symmetric corridor case. Another necessary condition for an interbank market to take place is that interbank market transaction costs, including those relating to credit risk concerns, are not too high, and in any case do not exceed the spread between the rate at which the central bank provides credit to banks and the remuneration rate offered by the central bank for excess reserves. (d) One can show that if a liquidity neutral x* exists in [0,1], then x* = 0.5-(B-P)/s (if 0.5-(B- P)/s>1, then all banks have excess liquidity, and if 0.5-(B-P)/s<0, then all banks need to take recourse to central bank credit; in both cases there is no bank with a neutral liquidity position towards the central bank and M=0). If x* = 0.5, then the interbank volume (under efficient markets) will be M=s(0.5^3)=0.125s. If x* deviates from 0.5, then market volumes shrinks with the square of the proportional deviation of x* from 0.5, because, graphically spoken, both sides of the triangle, the surface of which represents the market volume, shrink proportionally. Therefore the shrinkage factor is ((0.5 - abs(x*-0.5))/0.5)^2. Therefore, the interbank market volume formula is: M = s(0.5^3)((0.5 abs((b-p)/s))/0.5)^2 = 0.5s(0.5 abs((b-p)/s))^2. 41

42 (e) The results are shown in the following table. For (i) apply formula derived in (d); If interbank markets function perfectly, then all aggregate balance sheet figures will correspond to the ones that hold in the aggregate model. Therefore: (ii) max(b-p, 0); (iii) max(p-b, 0); (iv) B + max(p-b, 0). (f) The results are shown in the following table. If money markets break down, then both the recourse to central bank borrowing and the excess reserves held by banks with the central bank increase by what was under functioning markets the interbank volume. Therefore, if the interbank volume under functioning markets was M for some parameter constellation, then (ii) max(b-p,0) + M; (iii) max(p-b, 0) + M; (iv) B + max(p-b,0)+m. Table resulting from the formulas above: Input parameters Total Deposits D = 1 1 0,5 1 inequality parameter s Banknotes B 1 1 1,5 1 Portfolio P Functioning MM Interbank volume 0,125 0* 0 0,25 Recourse to CB credit 0 0 0,5 0 XS Reserves Length of CB balance sheet 1 2 1,5 1 Broken MM Recourse CB credit 0, ,5 0,25 XS Reserves 0, ,25 Length of CB balance sheet 1, ,5 1,25 *In this case x* is outside [0,1] and therefore the formula for x* does not apply, but x*=0 (g) We vary P from 0 to 2 in steps of 0.5 to obtain the following central bank recourse (before MM) curves (functions of x cross banks). This provides some intuition on how the triangles evolve. 42

43 The following two charts show the evolution, as a function of P, of the MM volume, total excess reserves and total recourse to the central bank for efficiently functioning and broken money markets, respectively. M, R, XSR as a function of P, for functioning MM: M, R, XSR as a function of P, for broken MM: Evolution of BS length as a function of P, for functioning and broken money markets, respectively: 43

44 The following table shows data for five different values of P Total Deposits D = inequality paramete Banknotes B Portfolio P 0,5 0,75 1 1,25 1,5 Functionning MM: Interbank volume 0 0, ,125 0, Recourse to CB credit 0,5 0, XS Reserves ,25 0,5 Length of cb balance sheet ,25 1,5 Broken MM Recourse CB credit 0,5 0, ,125 0, XS Reserves 0 0, ,125 0, ,5 Length of CB balance sheet 1 1, ,125 1, ,5 (h) If s increases because of households suspicion that some banks are weak, then probably also strong banks are worried about their weaker competitors and will not lend to them in the interbank market. Therefore, a significant increase in s will likely be correlated with a switch from efficient to broken markets, and therefore also the simulations assuming broken markets are more relevant. S2.4 (a) The definitions of the various central bank balance sheet concepts can be found in Chapter 2 of the book. In short: (i) (ii) (iii) (iv) (v) The level of total autonomous factors = total net sum of all balance sheet items that are not under the control of the monetary policy function, i.e. all items except monetary policy items and sight deposits of domestic banks with the central bank; netted typically on the liability side of the balance sheet; the total liquidity provision through monetary policy operations = the (net asset) sum of monetary policy operations, i.e. both outright and reverse; the original liquidity deficit of the banking system = autonomous factors + reserve requirements = liquidity that needs to be provided through MPI including outright operations; In historical central bank balance sheets, one should also account for a large demand for working balances by banks, which one may regard as a component of the liquidity deficit that needs to be satisfied by liquidity provision through monetary policy operations. the liquidity deficit post outright monetary policy operations = liquidity needs that need to be covered by central bank credit operations, i.e. after outright monetary policy operations = AF + RR outright MPOs; the leanness of the balance sheet = total length of BS / banknotes Be aware that assigning certain balance sheet items to either autonomous factors or monetary policy is not necessarily trivial. For example, government bonds can reflect (i) an investment portfolio; (ii) a facility granted to the Government; (iii) a monetary policy portfolio. In the first two 44

45 cases it would be classified as autonomous factor, in the last case obviously as monetary policy item. A classification can normally be achieved by reading in e.g. the annual report of the central bank its further explanations. Below we solved these ambiguous cases in one way or the other, as it can be seen in the calculus provided within the matrix. Another issue is that in principle one would need to know reserve requirements (which itself is not a balance sheet item) to calculate the liquidity deficit. Again ideally one can find out the level of reserve requirements from publications of central banks. The following table provides the results for the five central banks and the five measures: Measure Central bank Total autonomous factors Total liquidity provision through MPOs Original deficit liquidity Liquidity deficit post outright operations Leanness balance sheet of Reichsbank = 367 Reichsbank = 131** = = 889* /1139 = = = /1280 = 1.44 Bundesbank = = = 230*** /260 = 1.33 Latvia, = = /484 = 1.24 * We interpret current accounts in the case of the Reichsbank as inevitable demand for reserve balances and therefore as a component of the liquidity deficit. ** We interpret the large outright holdings of T-bill as result of a funding facility offered to the Government by the Reichsbank this implies the classification as autonomous factor *** In these cases we interpret current account as being equal to reserve requirements (b) Striking features of balance sheets Reichsbank 1900: large size of voluntary reserves, suggesting a not so efficient payment system and/or a high number of small depositors with the central bank. Large precious metal reserves relative to the monetary base, and reliance on discounting as monetary policy tool. Reichsbank 1922: depleted precious metal reserves, instead lots of Government bills of a presumably not so healthy sovereign, implying that in reality the Reichsbank may have had negative capital. Still reliance on discounting of trade bills as tool to provide liquidity. Bundesbank 1998: Lean balance sheet, reliance on central bank credit operations for MPI. Bank of Latvia, 2001: More foreign reserves than banknotes, compatible with currency board framework. Very small liquidity deficit. S2.5 With fountain pain money, James Tobin meant the fact that in principle bank directors can, by signing loan contracts and at the same time crediting the account of the client for the amount lent, create money (in the sense of sight deposits with banks) by a mere signature. S2.6 Limits to the creation of fountain pen money: (i) household preferences and the fact that fountain pen money is not cost free to create (banks require higher interest rate on loans than they pay on deposits, such as to be able to cover their operating costs and to be compensated for risk taking. (ii) capital adequacy (risk-weighted assets or leverage ratio); (iii) reserve requirements and collateral constraints, jointly, limit also the simultaneous creation of fountain pen money by banks; (iv) in case of a diverging speed of fountain pen money creation by say two banks, the one creating it faster will need to increase its refinancing with the central bank and will eventually run into collateral issues even without reserve requirements. 45

46 S2.7 Assume a banking system composed of two banks only. Two banks may co-ordinate and create fountain pen money more or less in parallel, and this effectively will soften some of the constraints. For a granular banking system, the outflow of large parts of created fountain pen money is unavoidable, and co-ordination is more difficult. Therefore, for example, collateral haircuts alone are sufficient to limit money expansion. S2.8 (a) Capital adequacy requirements. 8% capital, 100% risk weighting of all assets. Therefore: (D/2 + B/2 + F/2 + C/2)*0.08 F/2 => C F/ D-B (b) Reserve requirements on household deposits are 5%. Therefore, a bank s balance sheet now looks as follows, whereby we assume that the bank refinances the additional liquidity needs with the central bank. In so far, provided central bank liquidity provision is elastic, there does not seem to be a direct limit following from reserve requirements. Lending to corporates D/2 + B/2 +F/2 Lending to households C/2 Required reserves 0.05*(D/2 +C/2) Bank i Household deposits / debt D/2+C/2 Credit from central bank B/ *(D/2+C/2) Equity F/2 If the central bank refuses to provide additional central bank credit, then a constraint kicks in directly (and a necessary condition for fountain pen money creation is that banknotes decline, which may be achieved with very high interest rates). (c) Collateral: lending to corporates is central bank eligible collateral, whereby a haircut of 20% is applied. This is not relevant in the case that credit creation by the two banks moves in parallel, as central bank funding does not increase as a consequence of parallel credit creation. This is different in the case only one bank would try to expand. (d) Both reserve requirements apply as in (a) and collateral rules as in (c). Available collateral is: 0.8*(D/2 + B/2 +F/2). This must be larger or equal the central bank funding: B/ *(D/2+C/2). So we have to solve the following inequality for the amount C: 0.8*(D/2 + B/2 +F/2) B/ *(D/2+C/2) => C 20*(0.8*(D + B +F)-B) D/2 C 15.5D +16F 4B S2.9 (a) The very different equity ratios are striking. Households are by far the least leveraged, followed by NFCs. Most leveraged are financial corporates. Another striking difference is the relevance of real assets versus financial assets, with the highest share of real assets held by the state, followed by households and NFCs with both having broadly one half of their balance sheet in the form of real assets. Finally, financial corporates have obviously the by far lowest share of real assets. What the composition of assets in terms of real vs. financial, for a given level of equity, means for financial stability, is not a priori clear. Both financial and real assets can lose value, and which ones are more risky will depend on circumstances and the financial interdependencies. This will be illustrated further in (c). The following table shows the shares of real assets and the share of equity in total balance sheet length of the four sectors. NFC State FCs HHs Share of real goods 56% 73% 2% 47% Share of equity 68% 41% 22% 87% (b) Exact inter-sector financial linkages are easily calculated in excel under the assumption of proportionality. The following table that can be found with underlying formulas in the excel spreadsheet. Each row of the table provides one sector (and the total) from the asset 46

47 perspective, while each column shows the column sector s respective liability to the row-sector. The left part of the table covers equity, while the right hand part of the table covers debt. Assets' perspective Liabilities' perspective Equity: Debt: All sectors NFC State FCs HH All sectors NFC State FCs HH All sectors NFCs State FCs HH Let us call the matrix of exposures to equity E, with E(i,j) being the claim on equity of sector i on sector j, in the order of the table above. Call D(i,j) be the corresponding matrix of fixed financial claims and debt. The full effects of declines of real asset values can be calculated using matrix algebra, or by substitution. We follow the latter, simpler but less elegant approach below. Note that R, FFC, EA, D, EL stand for different balance sheet positions, namely for real assets, fixed financial claims, equity as asset item (i.e. holdings of stocks and shares), debt and equity as liability item, respectively. The indices stand for the relevant sectors. We know that: EL HH = R HH + FFC HH + EA HH D HH, with EA HH = 17/121 EL NFC + 10/70 EL FC EL NFC = R NFC + FFC NFC + EA NFC D NFC, with EA NFC = 25/121 EL NFC + 14/70 EL FC EL S = R S + FFC S + EA S D S, with EA S = 7/121 EL NFC + 4/70 EL FC EL FC = R FC + FFC FC + EA FC D FC, with EA FC = 72/121 EL NFC + 42/70 EL FC We assume now that x is below a certain threshold, such that Debt and Fixed financial claims are not negatively affected yet by the negative real asset shock. We substitute the net (FFC- D) figures from the financial accounts, and put the initial real assets R, but with a multiplier (1-x)R to obtain: EL HH = (1-x) /121 EL NFC + 10/70 EL FC EL NFC = (1-x) /121 EL NFC + 14/70 E LFC EL S = (1-x) /121 EL NFC + 4/70 E LFC EL FC = (1-x) /121 EL NFC + 42/70 EL FC This is a system of four linear equations with four unknowns. Because of the ultimate nature of liability side equity of the state and of households, the easiest solution is to solve first the two equations - two unknown systems of the NFCs and FCs: EL NFC = (1-x) /121EL NFC +14/70EL FC and EL FC = (1-x) /121 EL NFC +42/70 EL FC EL NFC = (121/96)(1-x)98 (121/96)17 +(14*121)/(70*96)EL FC and EL FC = (70/28)(1-x)5 (70/28)49 + (72*70)/(121*28)EL NFC EL NFC =123.5(1-x) EL FC and EL FC = 12.5(1-x) EL NFC EL NFC = x EL FC and EL FC = x EL NFC EL NFC = x EL NFC EL NFC = x Moreover: EL FC = * ( *202) x EL FC = x Now we can also complete the equity of the two ultimate sectors, HH and S: EL HH = (1-x) /121 EL NFC + 10/70 EL FC EL HH = x EL S = (1-x) /121 EL NFC + 4/70 EL FC EL S = x 47

48 Finally, we can now also express the Equity positions on the asset side of the four entities as EA HH = 17/121 EL NFC + 10/70 EL FC EA HH = 26-73x EA NFC = 25/121 EL NFC + 14/70 EL FC EA NFC = x EAS = 7/121 EL NFC + 4/70 EL FC EA S = 11-30x EA FC = 72/121 EL NFC + 42/70 EL FC EA FC = x We can write now all the financial accounts such as to be prepared to reflect an x% decline in all asset values. For example the accounts of NFCs will look as follows: Non-financial corporates Real goods 98(1-x) Debt 56 Fixed financial claims 39 Equity x Equity holdings x Total x x We can present the entire financial account in a more compact way as follows. There is a need to be careful in interpreting effects of real asset value declines on totals in the last row. Remember that all the results were calculated on the basis of the assumption that no sector was insolvent. Once real asset value declines go beyond a certain threshold where this is no longer the case, the table no longer applies as such. The threshold of x (beyond which this table no longer applies) will be provided in the next part of this exercise. Assets Liabilities Totals Real Fixed Equity Debt Equity BS total BS total assets x-term claims assets x-term x-term asset x-term liability x-term HH State NFC FC Total (c) Financial corporates (FCs) are most vulnerable to real asset value declines in the sense that they end up first in insolvent territory. Indeed, as can be read in the table above from the two columns on equity liability, a real asset value decline by more than 22% would make the aggregate FC sector insolvent. This may surprise in view of the fact that the FC sector has the by far lowest direct exposure to real assets. However, secondary effects via equity exposure matter (even in the present example where we did not consider the case of losses on fixed financial claims), and the low equity ratio of the Financial corporates is eventually decisive. (d) Once the equity of one sector is exhausted, then the secondary effects of the real asset value declines transmitted from this sector to the other sectors changes, with no longer the debt exposure shares of the other sectors being the transmittance coefficients, but the equity shares. Solving for the properties of the system from the point of insolvency of the first sector to the point of insolvency of the second, is in principle identical to (b) for the case that all sectors are still solvent (actually, one can reset the exercise to restart from the new real asset values after the 22% decline, and the new equity of the insolvent sector is now its debt (as if the insolvent sector is a sector that is financed only by equity). The table below shows these initial accounts (in compact representation). The debt liabilities of Financial corporates have been reclassified as equity, and the corresponding switch has been done on the asset side of all sectors (applying the shares in the Financial corporate debt according to the table in sub-exercise (a)). The variable x is still defined as a percentage decline in real asset values taking into account the very initial level of real assets. 48

49 Assets Liabilities Real Fixed Equity Debt Equity assets x-term claims assets x-term x-term HH State NFC FC Total Note that we have not assumed any additional damage from the insolvency of the financial sector (while in reality there would be such extra damage, which we could calculate using empirical estimates from the literature, and input into the table above). Once one has established how the system reacts to further real asset value declines (using the same technique as in sub-exercise (b)), one can complete the x-term columns above for equity, and one can calculate when the second sector gets insolvent. Then again the system changes properties as also the second sector transmits further real asset declines via the debt shares of the other sectors, etc. 49

50 S3: The short term interest rate as operational target of monetary policy S3.1 See page 10 of the book (four properties listed note that on page 36 of the book, only three properties are listed, which is an inconsistency). S3.2 Short term, say overnight interest rates, (i) can be controlled by the central bank, since the central bank can control both the supply of and the demand for reserves (not perfectly, but almost); (ii) it is economically relevant as through the expectations hypothesis short and long term interest rates are linked, and long term interest rates determine funding costs of the economy (and the rate of returns on savings) and thereby, essentially via the Wicksellian arbitrage logic, impact on inflation; (iii) it is a clearly defined variable (either in the form of an overnight interbank interest rate target, or in the form of a central bank policy rate that will determine market rates) that can be decided and communicated by decision making bodies; (iv) it gives clear guidance to market operations experts in the central bank on what they need to do. S3.3 The Wicksellian arbitrage logic is derived on pages of the book. At least four sets of simplifying assumptions are inherent in the simple Wicksell arbitrage diagram. First, the system will most of the time be outside steady state equilibrium. Adjustment dynamics are non-trivial and will invoke more challenging modelling. Prices and real rates of return on capital are hit constantly by exogenous shocks. This implies that one needs to differentiate between the expected (ex ante) and the actual (ex post) real rate of return on capital, E(r t ) and r t (e.g. the actual rate of return on wheat is affected by weather conditions). Moreover, when non-anticipated price pressures (relative to expected prices) occur, adjustment of prices is typically sticky. Amongst other things, this implies that the real rate of return on capital needs to be distinct from the real rate of return on money investments in particular ex post. Indeed, the fact that ex ante i t =E(r t )+E(π t ) does not imply that ex post i t = r t + π t. The real rate of return on money investments is equal to (ex post) i t π t. The real rate of return on capital is (ex post) r t. There is a third concept that needs to be distinguished, which is the ex-ante real rate of return on money investments which is i t E(π t ). In an ex ante arbitrage steady state equilibrium, this should be equal to E(r t ). However, in reality, this is not the case as ex ante adjustments to reach an arbitrage equilibrium are imperfect and slow. The following table summarises the four concepts of real rates that need to be distinguished, as they will, for the reasons mentioned above, not be identical in reality. (It may be noted that we have assumed that the nominal interest rate on money is identical ex post and ex ante. This holds as long as debtors do not default.) Four concepts of the real rate of interest Ex ante Ex post capital good investment E(r t ) r t money investment i t -E(π t ) i t - π t The general idea of the dynamics triggered by a perceived arbitrage opportunity is as follows: If i t > E(r t ) + E(π t ) => it is profitable to sell real goods and hold more money investments => demand for goods today => disinflationary pressures => actual inflation will fall below expected inflation: π t < E(π t ) If i t < E(r t ) + E(π t ) => buy more real goods for real investment projects, hold less money investments (or be short in money, i.e. borrow money), => demand for goods today => inflationary pressures => actual inflation will turn out to be above expected inflation: π t > E(π t ) 50

51 While this intuition is clear, it is not obvious to fully specify this dynamic process in a discrete two point in time arbitrage diagram. Modern macroeconomic monetary theory aims at capturing such dynamics. Second, in reality there is not only one good ( wheat ) which is at the same time a consumption and an investment good, but there is a wide range of goods with very different properties. Investment goods are supposed to determine the real rate of return on capital, while consumer goods determine inflation. Consumer and investment good prices are eventually linked, but in reality such links will be imperfect and exhibit time lags. Third, nominal funding costs of the real economy are not identical to the short term nominal interest rate that the central bank sets. Nominal funding costs of the real economy can be estimated by producing a weighted average of funding rates, the weights reflecting the share of that type of funding in the total funding of the real economy. The weighted average nominal lending rate of the economy can be thought to reflect three main factors: (i) The short term interbank interest rate which is normally controlled precisely by the central bank; (ii) The slope of the risk free benchmark yield curve; (iii) The various instrument specific liquidity and credit risk premia. The challenge for the central bank is then no longer limited to the estimation of the real rate of return on capital goods (such as to be able to shift the nominal short term interest rate across time in parallel to it), but in addition to estimate and take into account the varying spread between the weighted average funding costs of the real economy and the risk free interest rate. Fourth, it has to be kept in mind that the actual availability of credit to the real economy cannot necessarily be measured by contemplating interest rates alone (e.g. Stiglitz and Weiss, 1981; in the book the adverse selection model in section 11.2, pages ). Indeed, funding markets for some indebted companies can break down completely due to an increase of uncertainty and information asymmetries. These four complications are the reason for why the theory of optimal short term central bank interest rate setting is complex, diverse and inconclusive, and also why central banks have large economics departments and cannot follow simplistic mechanic formulas in interest rate setting. S3.4 For the reasons provided on pages in the book, the Fed seemed to have gotten convinced after the first world war, at least officially, that monetary policy implementation is about controlling the amount of (excess) reserves of banks with the central bank (or the monetary base) through liquidity providing and absorbing open market operations (ideally outright purchases or sales of treasury securities). Therefore, the monetary policy decision making would consist in deciding essentially about quantities of open market operations, and hence the policy committee was called Federal Open Market Operations. S3.5 Because these views are based on a number of misunderstandings and would lead to extreme volatility of interest rates and strong erratic monetary policy impulses. Reserve position doctrine, including in the variant of M. Friedman, is wrong in particular for the following reasons. First, the monetary base cannot reasonably be controlled in the short run. An operational target variable should be a variable that can be controlled in the very short run by the central bank and for which a concrete figure is set by the decision-making committee for the inter-meeting period to (a) tell the central bank s implementation experts what to do, and (b) indicate the stance of monetary policy to the public. However, this obviously does not make sense for the monetary base. Its normally biggest component, banknotes in circulation, is in the short term purely demand-driven, with innovations to demand rarely linked to macroeconomic developments. Its second component, current account holdings, is mainly determined by reserve requirements. Under a lagged reserverequirement system, required reserves are given. 51

52 The monetary base also should not be controlled in the short run. First, the monetary base is a heterogeneous aggregate since it is composed of banknotes and reserves (which are themselves subdivided into required and excess reserves). Why should changes in these three completely different components be equivalent in terms of requiring the sum of the three to be controlled? Moreover, the predictability and stability of the money multiplier is very doubtful, especially in the event that one wishes to base policy actions on it. In particular, the multiplier is unlikely to remain stable when interest rates move towards zero, since banks then no longer really care about holding excess reserves. To that extent, when monetary growth is deemed insufficient and excess reserves are injected to make the banks expand credit, the result will be first that, in an efficient market, short-term inter-bank interest rates drop to zero (if there is no deposit facility). The fact that interest rates have dropped to zero is, of course, relevant and, if judged to be permanent for a longer period of time, medium- and longer-term rates also will drop and economic decisions will be affected. However, once inter-bank rates have fallen to zero and the central bank continues to increase excess reserves through open market operations at zero interest rates, not much more should happen: that is, the money multiplier should fall with every further reserves injection. It is to that extent difficult to really construct a case where an injection of reserves by the central bank through open market operations sets in motion monetary expansion independently from the interest rate channel. Third, any attempt to control in the short run the monetary base leads to extreme volatility of interest rates since the market will, due to stochastic and seasonal fluctuations in the demand for base money, permanently either be short or long of reserves, as already observed by Bagehot (1873). One of the core ideas of central banking is to provide an elastic currency, that is, one in which the important transitory fluctuations in base money demand no longer need to disturb economic conditions via interest rate effects. What matters for the key economic decisions, namely, to save or consume, to borrow or invest, are mainly medium and long term interest rates. With extreme volatility of short-term rates, the volatility of medium and longer-term rates will also increase. Such volatility will create significant noise in economic decisions, and hence lead the economy away from equilibrium. S3.6 The main reserve position doctrine concepts applied by the Federal Reserve across time are explained in the book on pages

53 S4: Three basic techniques of controlling short term interest rates S4.1 The fundamental equation states that the overnight interbank market rate should consist in a weighted average of the standing facility rates, i.e. the deposit facility rate and the borrowing facility rate, the weights being the probabilities perceived by market participants of having at the end of the maintenance period an excess or tightness or reserves relative to minimum reserves, respectively: i = P( short )*i b + P( long )*i D Short means the event that reserves are short of required reserves, and long means the event that reserves are in excess of required reserves. For example, in the symmetric corridor approach, the central bank keeps the two probabilities equal (at 0.5) via open market operations, so that the interbank interest rate should remain in the middle of the interest rate corridor. Important simplifying assumptions are: No additional costs or access restrictions to either facility. Typically, borrowing from the central bank requires providing collateral, which may be scarce and not cost free. Therefore the true costs of being short are likely to be somewhat higher than i b. Interbank rates have in addition a credit risk premium, which will bias the interbank rate to slightly above the mid point of the corridor. Money market participants do not necessarily have access to the standing facilities. Therefore, unless the banks that have access to the facilities are perfect cost-free intermediaries, market rates may be subject to an additional bias (a material phenomenon affecting the Fed funds rate in the US since 2012). In case of an averaging period for the fulfilment of reserve requirements, an asymmetry is introduced because reserve over-fulfilment is unlimited (a bank can in theory fulfil on the first day of the reserve maintenance period the entire reserve requirements for the maintenance period) while banks must never end the day with negative reserve balances (i.e. under-fulfilment of reserve requirements cannot exceed the size of reserve requirements). This can create a systematic upwards trend of interest rates (Perez-Quiros and Mendizabal 2006). S4.2 Symmetric corridor approaches generally maximise interbank market activity, in particular relative to one sided approaches (see also Q2.3). Symmetric corridor approaches with discretionary allotment have the advantage relative to discretionary allotment asymmetric approaches (e.g. targeting an interest rate of 1.25% in a corridor from 1.00% to 2.00%) that they require only to forecast the expected value of autonomous factors, and not higher order moments. An advantage of approaches with discretionary allotments relative to the full allotment approach is the central bank can ensure that its ability to predict the sum of aggregate autonomous factors as they will be relevant for the banking system on aggregate can be used to determine allotment volumes in open market operations and therefore liquidity conditions. The symmetric corridor approach based on fixed rate full allotment has the advantage that it is more automatic and does not require any forecasting of autonomous factor and decision making on the allotment amount of open market operations on the side of the central bank. However, the banking system will not be able to forecast and aggregate autonomous factors in the same way as the central bank can. This can create additional volatility of overnight interest rates. One sided, standing facility based approaches have the advantage that they allow for a close control of the operational target, the short term interest rate, without precise autonomous factor forecasts 53

54 of the central bank and without the need for the banks to bid in a way that is consistent with aggregate autonomous factors ex ante. The disadvantage is that interbank market volumes will be lower than in the symmetric corridor approach (which however does not imply in itself a lengthening of the central bank balance sheet see Q2.3). The extent to which interbank market activity suffers depends on the size of the average recourse to the one standing facility. There is a trade-off: the larger the average recourse (and hence the smaller the role of interbank markets), the more certain is the control of the interest rate. There should be an inner optimum to this trade-off. S4.3 Reichsbank 1900: one sided standing facility based system (systematic recourse to discount window). Reichsbank 1922: In principle the Reichsbank still implemented monetary policy through offering recourse to the discount facility. However, liquidity conditions and interest rates were also determined by the quasi- full funding facility offered to the Reich. Bundesbank 1998: There is no mentioning of standing facilities in this balance sheet. This can reflect that recourse was negligible, or that they did not exist. One can find out that the Bundesbank offered a liquidity providing facility (called Lombard facility ), but no deposit facility. Essentially the Bundesbank controlled interest rates in an asymmetric corridor in which it controlled liquidity through open market operations with allotment volumes set by the central bank. Bank of Latvia, 2001: Again, it is not clear why standing facilities are not shown in this simplified balance sheet. In any case, one can conclude without having more information that the Bank of Latvia did not pursue a one-sided standing facility based system. (Note that the monetary policy strategy of the Bank was to maintain a currency board with the euro). S4.4 (a) With i D =0 and i B =1%, to achieve i=i* one needs to achieve: P( short )=P(OMO-50-μ < 0) = Φ(- (OMO-50- μ)/1) = i* => OMO = - Φ -1 (i*) As Φ -1 (0.5) = 0; Φ -1 (0.25) = ; Φ -1 (0.1) = , this implies that OMO will need to be 50, , 51.28, respectively. (b) Solution: See excel spreadsheet. In the spreadsheet, 500 random draws (see rows 5 to 505) of μ 1, are simulated, using the excel randomizer (x=rand()) and transforming the obtained draws of a uniformly distributed random variable in [0,1] via the inverse of the cumulative normal distribution (Norm.Inv(x, expected value, variance)) into a standard normal distributed random variable). Result: i*= 0.5 requires OMO* = 50; Implied stdev(i) = 0.28 i*= 0.25 requires OMO* = 51; Implied stdev(i) = 0.22 i* = 0.10 requires OMO* = 51.8; Implied stdev(i) = 0.14 The interest rate volatility is 28, 22, 14 basis points, respectively, i.e. the closer the rate is steered towards one standing facility, the lower the volatility. (c) One can easily verify that when the two autonomous factor shock volatilities develop proportionally, the properties of overnight rates do not change. When the end day autonomous factor shock volatility grows in relative terms, then for the OMO* evolves as follows: μ 1 / μ 2 = 0.5 => OMO* = 50.8; stdev(i) = 0.32 μ 1 / μ 2 = 1 => OMO* = 51.0; stdev(i) = 0.22 μ 1 / μ 2 = 2 => OMO* = 51.5; stdev(i) = 0.14 μ 1 / μ 2 = 4 => OMO* = 52.7; stdev(i) =

55 In sum, if the autonomous factor volatility early in the day is relatively high, then the central bank needs to increase the expected level of excess liquidity to achieve the desired expected level of the overnight rate, and volatility of the overnight rate is relatively low. S4.5 (a) These techniques rely on the idea that the less attractively priced of the two facilities is accessible without binding limits in terms of counterparties and collateral (the latter relevant only for liquidity providing operations), while the more attractively priced of the two facility must suffer from some access limitations (only a limited set of counterparties, in the case of liquidity providing operations also scarce collateral). Interbank rates will fluctuate between the two, and the position within the corridor will depend on: - How strong are effectively the access constraints to the more attractively priced facility (how limited is the number of counterparties, how constrained are they in arbitraging, in case of a providing facility how scarce are eligible assets). - How big is the liquidity deficit or surplus that needs to be covered by the two facilities (the lower the necessary recourse, the closer the interbank rate will be to the constrained, more attractively priced facility). In the case of the Reichsbank, mainly availability of discountable trade bills for the discount window was a constraint that often pushed the interbank overnight rate to levels above the discount facility rate. In the case of the Fed s planned post-lift off, as Potter writes, bank only access to IOER, credit limits imposed by cash lenders, and other impediments to market competition, and the costs of balance sheet expansion associated with arbitrage activity all may let the fed funds rate deviate fall below the IOER rate. (b) Probably, control of the overnight rate will not be extremely precise, since access limitations will vary in their effectiveness over time, and are not so well predictable as e.g. the factors affecting interest rates in the classical symmetric corridor system. 55

56 S5: Several liquidity shocks, averaging, and the martingale property of overnight rates S5.1 See page 66 of the book. The general definition of a martingale is a stochastic process for which the conditional expected future values are equal to the latest available observation. S5.2 An important impediment that only holds for reserve maintenance periods (i.e. not intra-day) is the one identified by Peres-Quiros and Rodriguez (2006). It results from the asymmetry of the corridor in the sense that unlimited over-fulfilment on any single day is possible but under-fulfilment cannot exceed the level of required reserves because of the no-end of day overdraft constraint. Moreover, banks may arbitrage only imperfectly because of cost, procedural or regulatory reasons. S5.3 The following chart reflects the sequence of events. Three subsequent independent autonomous factor shocks Morning trading Afternoon trading End-day recourse to standing facilities OMO The simulation tool used, which follows a similar logic as the one in Q4.4, is in the Excel workbook. (a) The following table summarises the answer. Volatility of interest rate in Q: Morning afternoon Day Unsurprisingly, volatility of interest rates is higher when the autonomous factor volatility is frontloaded during the day. (b) The following table summarises the answer OMO to Volatility of interest rate in q achieve interest rate of 0.25 morning afternoon day

57 Volatility of interest rates again increases (decreases) with the frontloading (backloading) of autonomous factor volatility. More remarkably, the OMO volume to achieve i=0.25 first decreases and then increases again when q increases from 0.25 to 8. This provides an additional illustration of the complexity of an asymmetric corridor model. The following table provides plots of the morning and afternoon interest rates for three values of q. In the strongly frontloaded autonomous factor volatility case, interest rates are mostly absorbed by one of the corridor rates, and the OMO volume needs to determine the probability weights of being absorbed by one or the other. In the strongly backloaded autonomous factor volatility case, interest rates are in both sessions centred around their target value. Note that the average interest rate is equal to 0.25 in all cases of q both in the morning and in the afternoon session (and not only on average over the two sessions) although the target only referred to the overall daily average rate. This must be the case because of the martingale property of interest rates. Interest rate morning Interest rate afternoon q=0.25 OMO= 13 q=1 OMO= 11.3 q=8 OMO= 16 57