Πανεπιστήμιο Πειραιώς, Τμήμα Τραπεζικής και Χρηματοοικονομικής Διοικητικής Μεταπτυχιακό Πρόγραμμα «Χρηματοοικονομική Ανάλυση για Στελέχη» Capital Markets Section 3 Hedging Risks Related to Bonds Michail Anthropelos, Ph.D. anthropel@unipi.gr http://web.xrh.unipi.gr/faculty/anthropelos 1
Risk related to fixed-income securities (bonds) Although the bonds are less risky than other financial securities (such as stocks, derivatives), there are considerable sources of risk for the bondholders and the bond-issuers: 1) The interest rate risk (as we have seen the changes in the market interest rates changes the price of the bond and make the issuer s obligations more difficult to meet). 2) The bondholder faces the default risk of the bond-issuer (the issuer may default during the life of the bond and be unable to pay his obligations). 3) The reinvestment rate risk (as we have seen it is likely that the bondholder can not reinvest the bond coupons at the same rate). 4) Other risk such as call risk (in the case of callable bonds), liquidity risk (bondholder may not be able to sell his bond in the secondary market) and inflation risk. 2
Hedging interest rate risk Issuer case: How could a bond-issuer hedge the interest rate risk and make sure that she is able to meet her obligation? By matching the duration Example: Suppose that the firm CM has issued an 8 yrs zero-coupon bond with par value $10,000 and the ytm is 7%. This means that is obligated to pay 10,000 in eight years and the price of the bond (amount received by CM now) is 10,000/(1.035) 16 = $5,767 (MaD = 8yrs). Suppose also that there are only two other available bonds (of similar yield) for CM: the 4%/25yrs and the 7%/5yrs coupon bonds. CM can use the $5,767 and create a portfolio of the two available bonds in order to hedge the interest rate risk. How? If CM buys these bonds, an increase (decrease) in interest rate will cause bond prices to fall (rise) but reinvestment interest rate to increase (decrease); two offsetting influences. Idea: The right portfolio is the one that matches the duration of the obligation. 3
Hedging interest rate risk cont d MaD of 4%/25yrs = 13.66yrs MaD of 7%/5yrs = 4.3yrs (see slide at page 32, Section 2). The portfolio weights (w,1-w) are the ones that solve the following equation: 13.66w + 4.3(1-w) = 8 w = 39.5% Hedging portfolio: Put 0.395x5,767 = $2,280 in 4%/25yrs bound and the rest $3,487 in 7%/5yrs bond. Notes: Duration of the hedging portfolio = Duration of the obligation This hedging technique is called the target date immunization (εμβολιασμός). The immunization is achieved when (1) the duration of the assets bought is equal to the duration of the liabilities and (2) the initial present value of the assets bought equals (or at least as large) as the present value of the liabilities. Immunization is an almost perfect hedging of the interest rate risk. 4
Flaws of the immunization strategy 1) The duration of the bonds is not stable through time. This means that the hedging portfolio has to be rebalanced. Portfolio rebalancing may be costly, time-consuming and in some cases impossible (due to illiquidity). 2) Since this method is based on the concept of duration, it endows all of its flaws. 3) The main problems come as results of the flat yield curve assumption and the fact that only one single factor drives the entire yield curve. 4) It is really insufficient for large interest rate changes. 5) It does not work for floating-rate coupon bonds. 6) It needs an update research on other bonds of similar yield and default risk. 5
Interest rate swaps (IRS) The interest rate swaps can be to: 1. Transform a fixed-rate liability to a floating-rate liability and vise versa. 2. Transform a fixed-rate periodic income to a floating-rate one and vise versa. Example A: Consider a bondholder whose bond is a 7%/25yrs and has $10,000 par value. He believes that the interest rate is going to rise for at least in short term. If interest rate increases the bond price decreases. He may sell the bond (not always a good idea) but he can also use an IRS in order to replace the 7% fixed-rate to a floating-rate (or short-term rate). The life of the swap is usually less (sometimes much less) than the life of the bond. By entering a swap, the bondholder makes his bond income a floating-rate one and hence he hedges the risk of an interest rate increase. However, he does not hedge the risk of the bond price decrease. 6
Interest rate swaps (IRS) cont d Example B: Consider a firm that has issued a long term coupon bond of fixed coupon rate. If the market interest rate decreases it may have difficulties to meet its obligations. This risk can be hedged by entering a IRS and converting its liabilities into floating-rate ones, where the floating rate is connected with the interest rate at which the firm can lend. Notes: Swaps are usually made between a FI which enjoys a fee income for acting like a stock of floating and fixed rates and undertaking some of the credit risk. IRS is one of the mostly used short-term hedging techniques. IRS has low transaction costs compared to bond market. 7
Forward-rate agreements (FRAs) A forward-rate agreement (FRA) is a forward contract where the parties agree that a certain interest rate is applied to a certain principal during a specified future time period. It is like an interest rate swap covering a single period. In an FRA one part is going to borrow an amount L at some future time T 1 and is going to pay the part two back at some time T 2 (T 1 < T 2 ) with an interest rate r F specified now. A series of FRAs can lock in the reinvestment interest rates for a bondholder. Similarly, FRAs can be used from the bond-issuer in meeting her liabilities. It cost nothing to enter an FRA (its initial value is equal to zero). At the inauguration of an FRA the agreed interest rate should be equal to the so-call forward interest rate, which is induced naturally by the zero-coupon bond rates (spot rates). If the swap is exclusively referred to a bond coupon, the transaction is called asset swap. 8
The default risk One of the most important concept in the fixed income securities market is the default risk; a bondholder faces the risk that the issuer may not be able to meet (part of) his liabilities. In other words, the actual payments are uncertain; they depend to some extend on the creditability of the issuer. Bond default risk is measured by credit rating agencies known as Nationally Recognized Statistical Rating Organizations such as Moody s Investor Services, Standard & Poor s Corporation and Fitch Inc. Nationally Recognized Statistical Rating Organizations classify the bond issues into categories based on their creditability. This rating is based on the current information about the probability of default, the nature of the debt obligations and the protection afforded by the obligation in the event of bankruptcy. Bond issuers with low (of at least not very high) credit rate has to offer higher coupon rates (risk premium) in order to make the investors buy their bonds. 9
The default risk and ytm In the case where the concern about the default risk is intense, the investors should distinguish between the promised yield and the expected yield. The promised yield is the one that will be realized if the issuer manages to repay all of his debt. The promised yield for a 10-year bond issued by the government of Australia is around 3.59% (13/09/2014). Do investors expect to get such an annual return? This high yield is the so-called default premium (sometimes called spread). Yield spreads tend to be wider when economy is in recession. 10
Dealing with the default risk One way to deal (hedge) the default risk is to buy protection (insurance) against the bond-issuer default event. This protection can be bought with a Credit Default Swap (CDS). The credit default swap is a derivative contract in which the seller (protection seller), in return for a periodic fixed fee (or an onetime premium) agrees to pay the buyer (protection buyer) the losses that is going to suffer in case any of specified credit events occurs. A diagram of a typical CDS transaction is the following: 11
Credit default swaps Basic Structure: B has bought a bond from R, which pays periodic coupons to B. In order to reduce or eliminate the credit risk associated with R, B signs a CDS with S. According to the CDS, B pays periodic premium payments until maturity or until R defaults. If R defaults, S pays B a default payment (usually equal the loss that B suffers from R s default). 12
Terminology Reference asset is the asset on which the protection is bought (bond, baskets of bonds, bond indices, tranches, loans, asset backed securities). Credit events are those events whose realization means default (bankruptcy of the reference entity, restructuring of the debt under unfavorable terms for the lender, failure to meet schedule obligation requirements). Premium payments are the periodic (quarterly) payments paid by the protection buyer to the seller (usually annual percentage on the reference asset par value). Credit spread is the percentage on the notional value of the reference asset that equals the premium payment. Default payment is the payment that the protection seller pays to the buyer in case of default. 13
Credit default swaps Notes: The CDS enables the bondholder to hedge the credit risk without having to sell the bond itself (of course this comes with a cost). The bond issuer does not need to know about the swap transaction. It is an OTC transaction (there is no clearing house). More than 93% of the transactions are made under the terms of the ISDA (International Swaps Derivative Association) Master Agreement. According to ISDA the net notional amount that is protected by some CDS contract is $1.3tr. More than 50% is related to the reporting dealers (26% to other banks and FIs and 2-3% to hedge funds). Only 25% of the CDS activity is about a single-name reference entity. The rest are referred to indices. Even in relatively mature markets (like big corporate bonds), default payments are frequently disputed. 14
Credit default swaps Volume Source: www.swapsinfo.org 15
Why CDS became so popular? i. The CDS enables two parties to swap and diversify the credit risk associated with a reference security without transferring the security itself. ii. It enables the protection buyer to reduce or eliminate his credit exposure without having to sell the reference security. iii. It enables the speculation on the credit (mis)rating. Facts Because of their market size, pricing of the CDS s can reveal a great deal of market information about the expected credit risk and the estimated probability of default. Even in relatively mature markets (like corporate bonds), default payments are frequently disputed. The ISDA has provided help on the disputing operations. 16
The market of CDS The CDS activity has been growing rapidly in last decade because CDS help firm to manage their credit risk exposure. During the current financial crisis, CDS activity remains robust (perhaps the only tool that is used to hedge the credit risks). It has been argued that CDS strengthen the financial system (risk transferring, risk distribution, credit information about the credit conditions). There have been intense efforts on the improvement of the transparency in the CDS market. Since 2007, there have been 60 credit events (like Fannie Mae, Washington Mutual, Republic of Ecuador, Lehman Brothers, Japan Airlines and of course Hellenic Republic). 17
Pricing of CDS and arbitrage When we talk about the price of CDS, we really mean the premium payments. Consider the following bond example: Par value = $1,000 Price of the bond = $800 Maturity = 1 year Coupons = 0 Risk-free interest rate = 2%. How should we price the CDS insurance in that case? Suppose that premium is 8%. Then, one can make the following arbitrage: 18
Pricing of CDS and arbitrage cont d Now Borrow $880 with interest rate 2%. Use the $800 of those to buy the bond. Pay $80 in order to buy protection on this bond through a CDS. This leaves you with zero dollar. After a year a) In case there is no default: Get $1000 from the bond issuer and use $898 of those in order to pay back your loan. Total profit $1000-$898 = $102. b) In case there is a default: Get $1000 from the bond issuer and the seller of the CDS and use $898 of those in order to pay back your loan. Total profit $1000-$898 = $102. What should be the non-arbitrage price of the CDS? 19
Pricing of CDS and arbitrage cont d In this simplified example, the non-arbitrage price of the CDS is bounded below by: 1000 (1 2%)800 Premium 1000(1 2%) or more generally, Premium Par Value ( 1 r) Bond Price Par Value ( 1 r) If the price of the bond increases the premium decreases and vise versa. What about an upper bound? In order to have equality, we need to be able to (short) sell the bound (usually not a feasible thing especially for illiquid bonds). 20
Pricing of CDS and arbitrage cont d Assume now that the premium is 19%. Now Short sell the bond at $800. Sell the CDS at $190. Invest $990 at the risk-free rate 2%. This leaves you with zero dollar. After a year a) In case there is no default: Get $1009.8 from the investment and buy and return the bond at $1000 Total profit $1009,8 - $1000 = $9,8. b) In case there is a default: Get $1009.8 from the investment and buy back the bond and pay the CDS protection. Total profit $1009,8 - $1000 = $9,8. 21
Pricing of CDS and arbitrage cont d Hence, 1000 (1 2%)800 PremiumPayment (1 2%) From both inequalities: Premium Payment PV(Par Value) BondPrice which means that in our example CDS protection costs around $180. Generally, we have the following approximation rule: Credit default premium Bond spread short selling costs 22
Facts about CDS prices For the more general examples, the same arguments can also be applied, by taking into account the asset swap spread, that is, the additional to LIBOR interest rate paid by the seller of a swap rate. However, deviations of arbitrage prices do exist (short-selling constraints, transaction costs, inefficiency of the market, regulation concerns, concerns about the creditability of the protection seller). An alternative way of pricing CDS is to calculate the expected default losses. Then, the CDS spread will be the premium that make the following equality hold: Present Value of expected losses = Present Value of expected CDS payments After all, CDS prices are the outcome of the supply and demand equality. 23
Criticism on CDS It has been argued that the credit risk transferring through the CDS market destabilizes the capital markets, because parties do not have the same information and the same technology about the involved credit risk. The fact that there is no regulation agency creates reasonable concerns about the structural strength of this market, especially nowadays. It has also been cited that the existence of the CDS market reduces the incentives of the lenders to monitor the creditability of the bond issuers. This may create an overall reduce of credit quality. Large speculation with CDS may cause incorrect signals about the underlying bond markets. 24
Hedging bonds on news Ukraine failed to redeem a $500 million bond on Wednesday as it restructures $18 billion of debt to shore up an economy battered by a 17-month conflict in its easternmost regions. The ISDA ruling may allow investors who bought CDS contracts that expired Sept. 20 to be eligible for a payout if the matured bond isn t redeemed by the end of the grace period. From Bloomberg.com (ISDA ruling is necessary for the CDS payout). The cost to insure against a Japanese sovereign default was 36 basis points on 16/09, after sliding 31 basis points since the start of the year. For South Korea, it was 63 1/2 basis points, rising nine basis points so far in 2015. The gap between them widened to 38 basis points on Aug. 24 at the height of a Chinaled stock rout that had wiped out more than $8 trillion from global equities. From Bloomberg.com (Note that Japan is the most heavily indebted nation in the world). The cost of insuring Volkswagen AG s debt against default rose to the highest in more than three years (136.56 bps)after the carmaker admitted to cheating on U.S. emissions tests. From Bloomberg.com (A now days example showing the sensitivity of the CDS premium and the issuer s developments). 25
Bibliography Z. Bodie, A. Kane & A.J. Marcus: Investments, 3 th ed., chapters 13, 14 and 15. J.C. Hull: Options, futures and other derivatives, 7 th ed., chapters 4, 6 and 22. Rene M. Stulz: Risk Management & Derivatives, chapters 9 and 16. M. Anthropelos: A Short Introduction to CDS, available on-line. David Mengle: Credit Derivatives: An Overview. Federal Reserve Bank of Atlanta, Economic Review-4 th Quarter, 2007. 26