MFE8812 Bond Portfolio Management

Transcription

1 MFE8812 Bond Portfolio Management William C. H. Leon Nanyang Business School January 16, / 126 William C. H. Leon MFE8812 Bond Portfolio Management 1 Overview Some Facts 2 Overview General Characteristics of Bond Non-Standard by Issuers Central Bank Some Money-Market Instruments 3 Overview Key Interest Rate Related Risk Other Risk 2 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

2 Overview Some Facts The capital market is composed of the debt market, in which debt securities are issued and traded, and the stock market, in which shares of ownership in companies are issued and traded. In the United States as well as worldwide, the debt market is much larger than its stock market counterpart. 3 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Some Facts Global Market Capitalization of Debt & Stock 4 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

3 Some Facts Reasons for Differences in Market Capitalization Debts still accounted for 75 percent of corporate financing even though stocks may be a cheaper source of capital for corporations as they do not require fixed interest payments and the stock market was enjoying record highs in the two decades before the 2008 global financial crisis. The debt market is larger than the stock market for various reasons: 1 Both governments and corporations issue debt securities, whereas only corporations issue stocks. The U.S. Treasury is the largest issuer of debt securities worldwide. Because U.S. Treasury securities are backed by the full faith and credit of the government, investors perceive them as risk-free and highly liquid. 2 Most investors are older and risk-averse, and they may prefer the regular income of debt securities. 5 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Some Facts 6 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

4 Global Financial Stock Some Facts The worlds stock of equity and debt rose by $11 trillion in 2010, reaching a total of $212 trillion. This surpassed the previous peak of $202 trillion in Nearly half of this growth came from an $6 trillion increase in the market capitalization of global stock. The total value of all debt reached $158 trillion, an increase of $5.5 trillion from the previous year. Government debt grew by 12 percent and accounted for nearly 80 percent of net new borrowing, or $4.4 trillion. This reflected large budget deficits in many mature economies, amplified by a slow economic recovery. Bond issues by non-financial businesses remained high in 2010 at $1.3 trillion thats more than 50 percent above the level prior to the 2008 crisis. This reflected very low interest rates and possibly tighter access to bank credit. Corporate bond issuance was widespread across regions. Bank lending grew in 2010 as well, with the global stock of loans held on the balance sheets of financial institutions rising by $2.6 trillion. 7 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Some Facts 8 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

5 Growth in Global Debt Some Facts Global debt outstanding has more than doubled over the past ten years, increasing from $78 trillion in 2000 to $158 trillion in Debt grew faster than GDP over this period, with the ratio of global debt to world GDP increasing from 218 percent in 2000 to 266 percent in Most of this growth ($48 trillion) has been in the debt of governments and financial institutions. Although government debt has been the fastest-growing category, it is notable that bonds issued by financial institutions to fund their balance sheets have actually been a larger class of debt over the past ten years. issued by financial institutions around the world has increased by $23 trillion over the past decade. In 2010, this shrank by $1.4 trillion as banks moved to more stable funding sources. Non-securitized lending is still the largest component of all debt and continued to grow in / 126 William C. H. Leon MFE8812 Bond Portfolio Management Some Facts 10 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

6 Growth of Total Public Debt Some Facts Government debt has increased significantly. There was some growth between 2000 and 2008, but the amount of government debt has jumped in 2009 and Public debt outstanding stood at $41.1 trillion at the end of 2010, an increase of nearly $25 trillion since This was the equivalent of 69 percent of global GDP, 23 percentage points higher than in In just two years (2009 and 2010), public debt has grown by $9.4 trillion or 13 percentage points of GDP. In 2010, 80 percent of the growth in total debt outstanding came from government debt. While stimulus packages and lost revenue due to anemic growth have widened budget deficits since the crisis, rising global public debt also reflects long-term trends in many advanced economies. Pension and health care costs are increasing as populations age, and unfunded pension and health care liabilities are not reflected in current government debt figures. Without fiscal consolidation, government debt will continue to increase in the years to come. 11 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Some Facts 12 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

7 Some Facts Growth of Public Debt Among Countries Public debt in many developed economies have steadily increased over time. In the 1970s, 1980s, and 1990s, there were numerous sovereign debt crises in emerging markets that proved very costly in terms of lost output, lower incomes, and years of slower economic growth. But today it is developed country governments that must act to bring their growing public debt back under control. In most emerging markets, public debt has grown roughly at the same pace as GDP since 2000 and the ratio of government debt to national GDP remains rather small. In contrast, Japan, the United States, and many Western European governments have seen their debt rise significantly. Japans government debt began rising after its financial crisis in 1990 and has now reached 220 percent of GDP. In both the United States and Western Europe in 2010, the ratio of public debt grew by 9 percentage points to stand at more than 70 percent of GDP by the end of the year. 13 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Some Facts 14 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

8 Some Facts Non-Financial Corporate Bond Issuance Issuance of corporate bonds by non-financial issuers nearly doubled in 2009 compared with 2008 as bank lending standards tightened and interest rates stayed at historic lows. Historic high issuance totaled $1.5 trillion in 2009, with $548 billion in Western Europe. Corporate bond issuance remained high in 2010 at $1.3 trillion, more than 50 percent above 2008 levels. Given the pressures on the banking system, those corporations that could access the capital markets directly did so in order to secure long-term financing. Although the majority of growth occurred in developed countries, corporate bond issuance has also grown rapidly in recent years in emerging economies. In total, emerging markets accounted for 23 percent of global corporate issuance in 2010, up from just 15 percent three years earlier. 15 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Some Facts Non-Financial Corporate Bond Issuance There is still significant room for further growth in corporate bond markets in virtually all countries outside the United States. The United States is the only country where corporations rely on debt capital markets to provide a sizable share of their external financing. account for 53 percent of corporate debt financing in the United States compared with 24 percent in Western Europe and only 16 percent in emerging economies. Given the higher cost of bank financing, especially in light of new capital requirements, there may be more rapid expansion of debt capital markets in Europe and in emerging markets. 16 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

9 Some Facts 17 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Some Facts Growth of On-Balance-Sheet Loans Loans held by banks, credit agencies, and other financial institutions account for the largest share of global debt outstanding (at 31 percent). On-balance-sheet loans grew from $31 trillion in 2000 to $49 trillion in 2010, an increase of 4.8 percent per annum. However, this global total hides key differences between regions. Since 2007, outstanding loan volumes in both Western Europe and the United States have been broadly flat with a decline in 2009 followed by a modest increase in In Japan, the stock of loans outstanding has been declining since 2000, reflecting de-leveraging by the corporate sector. Lending in emerging markets has grown at 16 percent annually since 2000, and by 17.5 percent a year in China. In 2010, loan balances increased worldwide by $2.6 trillion. Emerging markets accounted for three-quarters of this growth. Chinas net lending grew by $1.2 trillion, partly reflecting government stimulus efforts, while lending in other emerging markets rose by $800 billion. 18 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

10 Some Facts 19 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Issuance of Securitized Assets Some Facts Securitized lending was the fastest-growing segment of global debt from 2000 to 2008 with outstanding volumes increasing from $6 trillion to $16 trillion (average growth of 13 percent per year). Roughly 80 percent of securitization issuance over this period occurred in the United States. The issuance of mortgage-backed securities by government-sponsored enterprises more than doubled between 2000 and 2007 and hit a peak in 2002 that was nearly four times as large as in The creation of asset-backed securities by US banks and other non-government issuers tripled over this period, as did securitization in the rest of the world albeit from much lower levels. Since 2008, securitization by the US private sector and in other parts of the world has fallen dramatically. Only US government-supported mortgage issuers have sustained activity in the market over the past few years and new issuance in 2009 surged and roughly matched the peak level of / 126 William C. H. Leon MFE8812 Bond Portfolio Management

11 Issuance of Securitized Assets Some Facts Future prospects in the securitization market are unclear. Regulators are seeking to curtail the shadow banking system. Financial institutions argue that securitization facilitates lending to those in need of credit. 21 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Overview Fixed-income markets are populated with a vast range of instruments. We will discuss some of these instruments, namely, bonds and money-market instruments, and describe their general characteristics. A bond is a financial claim by which the issuer, or the borrower, is committed to paying back to the bondholder, or the lender, the cash amount borrowed (called the principal), plus periodic interests calculated on this amount during a given period of time. A money-market instrument is a short-term debt instrument with a maturity typically less than or equal to 1 year. 22 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

12 Definition of a Bond A bond is a financial claim by which the issuer (or the borrower) is committed to paying back to the bondholder (or the lender) the cash amount borrowed, called principal, plus periodic interests, called coupon, calculated on this amount during a given period of time. A bond can have either a standard or a non-standard structure. A standard bond is a fixed-coupon bond without any embedded option, delivering its coupons on periodic dates and principal on the maturity date. The purpose of a bond issuer is to finance its budget or investment projects at an interest rate that is expected to be lower than the return rate of investment (at least in the private sector). Through the issuance of bonds, it has a direct access to the market, and so it avoids borrowing from investment banks at higher interest rates. A bondholder has the status of a creditor, unlike the equity holder who has the status of an owner of the issuing corporation. This is generally why a bond is less risky than an equity. 23 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Example of a Bond 24 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

13 Terminology & Convention: Forms of Bond Bearer form. This means the bond is traded without any record of ownership, so physical possession of the bond is the sole evidence of ownership. Registered form. This means the bond issuer keeps records of bond owners and mails out payments to those bond owners. Most bonds issued today are in registered form. Book-entry form. This means the bond ownership is recorded electronically. Book-entry bonds eliminate the need to issue paper certificates of ownership. When such bonds are traded, accounting entries are changed in the books of the institutions where traders maintain accounts. 25 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Terminology & Convention: Bond Issuers The issuers name. For example, Bundesrepublik Deutschland for a Treasury bond issued in Germany. The issuers type. This is mainly the sector the issuer belongs to: for example, the oil sector, if Total S.A., a French multinational integrated oil and gas company, is the bond issuer. The issuers domicile. 26 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

14 Terminology & Convention: Bond Issues The bonds currency denomination. An example is the U.S. Dollar (USD) for a US Treasury bond. The market in which the bond is issued. It can be the domestic market of any country; the eurodollar market, which corresponds to bonds denominated in USD and issued in any other country than the US. The announcement date. This is the date on which the bond is announced and offered to the public. The total issued amount. The maturity date. This is the date on which the principal amount is due. The minimum amount and minimum increment that can be purchased. The minimum increment is the smallest additional amount of a bond that can be bought above the minimum amount. 27 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Terminology & Convention: Bond Issues The interest accrual date. This is the date when interest begins to accrue. The first coupon date. This is the date of the first interest payment. The settlement date. This is the date on which payment is due in exchange for the bond. It is generally equal to the trade date plus a number of working days. The type of guarantee. This is the type of underlying guarantee for the bondholder. The guarantee type can be a mortgage, an automobile loan, a government guarantee, etc. The seniority of claim. This refers to the order of repayment in the event of a sale or bankruptcy of the issuer. The rating. The task of rating agencies consists in assessing the default probability of corporations through what is known as rating. A rating is a ranking of a bonds quality, based on criteria such as the issuers reputation, management, balance sheet, and its record in paying interest and principal. 28 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

15 29 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Terminology & Convention: Bond Issues The issuance price. This is the percentage price paid at issuance. The spread at issuance. This is the spread in basis points to the benchmark Treasury bond. The outstanding amount. This is the amount of the issue still outstanding. The identifying code. The most popular ones are the ISIN (International Securities Identification Number) and the CUSIP (Committee on Uniform Securities Identification Procedures) numbers. 30 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

16 Terminology & Convention: Bond Coupons The coupon type. It can be fixed, floating, a multi-coupon (a mix of fixed and floating or different fixed). For example, a step-up coupon bond is a kind of multi-coupon bond with a coupon rate that increases at predetermined intervals. The coupon frequency. The coupon frequency for Treasury bonds is semiannual in the United States, the United Kingdom and Japan, and annual in the Euro zone, except for Italy where it is semiannual. The coupon rate. It is expressed in percentage of the principal amount. The nominal amount (or par amount or principal amount). This is the face value of the bond. Note that this amount is used to calculate the coupon bond. For example, consider a bond with a fixed 5% coupon rate and a $1,000 nominal amount. The coupon is 5% $1, 000 = $ / 126 William C. H. Leon MFE8812 Bond Portfolio Management Terminology & Convention: Bond Coupons The day-count type. The most common types are Actual/Actual, Actual/365, Actual/360 and 30/360. Actual/Actual (respectively Actual/365, Actual/360) means that the accrued interest between two given dates is calculated using the exact number of calendar days between the two dates divided by the exact number of calendar days of the ongoing year (respectively 365, 360). 30/360 means that the number of calendar days between the two dates is computed assuming that each month counts as 30 days. 32 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

17 Terminology & Convention: Bond Redemptions The redemption value. This is expressed in percentage of the nominal amount, it is the price at which the bond is redeemed on the maturity date. In most cases, the redemption value is equal to 100% of the bond nominal amount. The redemption feature. Non-standard bonds may have callable, puttable and convertible features. Call feature grants issuer the right to retire a bond, fully or partially, before maturity. Put feature grants bondholder the right to sell a bond back to the issuer at some fixed value on designated dates. Convertible feature usually grants bondholder the right to convert a bond into a predetermined amount of the issuer s equity at designated dates. 33 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Example: A US Treasury Bond Consider the US Treasury bond, with coupon rate 3.5% and maturity date 11/15/2006 (Month/Day/Year), that bears a semiannual coupon with an Actual/Actual day-count basis. The issued amount is equal to $18.8 billion; so is the outstanding amount. The minimum amount that can be purchased is equal to $1,000. The T-bond was issued on 11/15/01 on the US market, and interests began to accrue from this date on. The price at issuance was The first coupon date is 05/15/02, that is, 6 months after the interest accrual date (semiannual coupon). This bond has a AAA rating. 34 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

18 35 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Market Quotes: Bond Quoted Price are usually quoted in price, yield or spread over an underlying benchmark bond. Bond price is always expressed in percentage of the bond nominal amount. The quoted or market price of a bond is usually its clean price, i.e., its invoice price minus the accrued interest. When an investor purchases a bond, he is entitled to receive all the future cash flows of this bond, until he no longer owns it. If he buys the bond between two coupon payment dates, he logically must pay for it at a price reflecting the fraction of the next coupon that the seller of the bond is entitled to receive for having held it until the sale. 36 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

19 Market Quotes: Bond Quoted Price The price an investor has to pay when he purchases a bond is called the dirty price (or full price or gross price or invoice price). Dirty price is computed as the sum of the clean price and the portion of the coupon that is due to the seller of the bond. This portion is called the accrued interest. Note that the accrued interest is computed from the last coupon payment date to the settlement date. 37 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Clean Price, Dirty Price & Accrued Interest Quoted price of bond is a clean price. Settlement price of a bond is dirty price. Clean price of a bond is equal to the dirty price on each coupon payment date. Dirty Price }{{} PV (CFs) = Clean Price }{{} Market Quote Accrued Interest Period (n) Coupon Period (N) + Accrued Interest }{{} n N Coupon Last Coupon Date Settlement Date Next Coupon Date 38 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

20 Example On 10 Dec 2xx1, an investor buys the 5-year US Treasury bond with coupon 3.5% and maturity 15 Nov 2xx6. The current clean price is Hence the market value of $1 million face value of this bond is equal to % $1, 000, 000 = $961, There are 26 calendar days between the last coupon payment date (15 Nov 2xx1) and the settlement date (11 Dec 2xx1), and there are 181 calendar days between the last coupon payment date (15 Nov 2xx1) and the next coupon payment date (15 May 2xx2). Hence, because the coupon frequency is semiannual, the accrued interest is 3.5% 2 To buy this bond, the investor will pay = %. ( % %) $1, 000, 000 = $964, / 126 William C. H. Leon MFE8812 Bond Portfolio Management Exercise Consider a bond that pays coupon on the first of January and July every year. Suppose you sold the bond and settled the transaction on 3 Mar 2xx6. Suppose there are 181 days between 1 Jan 2xx6 and 1 Jul 2xx6, and 61 days between 1 Jan 2xx6 and 3 Mar 2xx6. What are the accrued interest you are entitled to based on the 1 actual/actual day-count basis, and 2 30/360 day-count basis? 40 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

21 Answer 41 / 126 William C. H. Leon MFE8812 Bond Portfolio Management EXCEL Functions Last Coupon Date Settlement Date Next Coupon Date COUPDAYBS COUPDAYSNC COUPDAYS COUPDAYS(Settlement, Maturity, Frequency, Basis). Returns the number of days in the coupon period that contains the settlement date. COUPDAYBS(Settlement, Maturity, Frequency, Basis). Returns the number of days from the beginning of the coupon period to the settlement date. COUPDAYSNC(Settlement, Maturity, Frequency, Basis). Returns the number of days from the settlement date to the next coupon date. 42 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

22 EXCEL Functions Options. Frequency. Basis. 1 = Annual coupon payments. 2 = Semiannual coupon payments. 0 or omitted = US (NASD) 30/360. 1=Actual/actual. 2 = Actual/ = Actual/ = European 30/ / 126 William C. H. Leon MFE8812 Bond Portfolio Management US (NASD) 30/360 Day-Count Basis The US (NASD) 30/360 day-count basis assumes that each month has 30 days and the total number of days in the year is 360. There are adjustments for Februaryandmonthswith31days. 1 Given Date 1 = D 1 /M 1 /Y 1 and Date 2 = D 2 /M 2 /Y 2 (in the form of Day/Month/Year) where Date 2 is later than Date 1. 2 If D 1 = 31, change D 1 to If D 2 =31and D 1 =30, change D 2 to The number of days between Date 1 and Date 2 is (Y 2 Y 1 ) (M 2 M 1 ) 30 + (D 2 D 1 ). 44 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

23 30/360 Day-Count Basis The 30/360 day-count basis is different outside the United States, where the calculation in step 3 was further simplified. 1 Given Date 1 = D 1 /M 1 /Y 1 and Date 2 = D 2 /M 2 /Y 2 (in the form of Day/Month/Year) where Date 2 is later than Date 1. 2 If D 1 = 31, change D 1 to If D 2 = 31, change D 2 to The number of days between Date 1 and Date 2 is (Y 2 Y 1 ) (M 2 M 1 ) 30 + (D 2 D 1 ). 45 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Exercise Suppose you sold a corporate bond with a nominal value of $1,000. The bond matures on 29 Nov 2xx8 and it pays 8% coupon semi-annually on 29 May and 29 Nov during its lifetime. If the settlement date is on 31 January 2xx3, what is the interest accrued on the bond? 1 Assume the US 30/360 day-count basis. 2 Assume the 30/360 day-count basis. 46 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

24 Answer 47 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Market Quotes: Bond Quoted Yield The quoted yield of a bond is the discount yield that equalizes its dirty price times its nominal amount to the sum of its discounted cash flow. Consider the previous example where, on 10 Dec 2xx1, an investor buys the 5-year US Treasury bond with coupon 3.5% and maturity 15 Nov 2xx6; the bond has the clean price of and the dirty price of The cash flow schedule of the bond with $1 million face value is as follows: Date Cash Flow Date Cash Flow 15/05/x2 17,500 15/11/x4 17,500 15/11/x2 17,500 15/05/x5 17,500 15/05/x3 17,500 15/11/x5 17,500 15/11/x3 17,500 15/05/x6 17,500 15/05/x4 17,500 15/11/x6 1,017,500 The quoted yield of the bond is 4.375% (see next slide street convention). The equivalent 1-year compounded yield of the bond is 4.423%. 48 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

25 49 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Market Quotes: Bond Quoted Spread Corporate bonds are usually quoted in price and in spread over a given benchmark bond rather than in yield. So as to recover the corresponding yield, you simply have to add this spread to the yield of the underlying benchmark bond Consider the Ford Motor Credit bond with coupon 6.75% and maturity 15 Aug 2xx8 (see next slide). The bond has a spread of basis points (see Interpolated Spread (ISPRD) function) over the interpolated USD swap yield, a spread of 234 basis points over the interpolated US Treasury benchmark bond yield; a spread of 259 basis points (Spread (SPRD) function) over the US Treasury benchmark bond with the nearest maturity; and a spread of 191 and 144 basis points over the 10-year Treasury benchmark bond and the 30-year Treasury benchmark bond, respectively. Quoting spreads over treasury bonds is fairly common on bond markets. Note that using an interpolation on the treasury bond curve may lead to different results depending on the two bonds and the interpolation method. 50 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

26 51 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Bid vs. Ask Quoted Price & Yield Note that every traded bond has a bid as well as an ask quoted price. The bid price is the price at which an investor can sell a bond. The ask price is the price at which he can buy it. The ask price is of course higher than the bid price, which means that the ask yield is lower than the bid yield. The difference between two yields is known as the bid-ask spread. It is a kind of transaction cost. It is very small for liquid bonds such as US or Euro Treasury bonds. It is large for fairly illiquid bonds. The bonds mid price is simply the average of its bid and ask prices. The same holds for the mid yield. 52 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

27 53 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Non-Standard : Strips Strips are zero-coupon bonds mainly created by stripping government bonds of the G7 countries. In August 1982, Merrill Lynch and Salomon Brothers bought long-term Treasury bonds and created synthetic zero-coupon Treasury receipts collateralized by the payments on the underlying Treasury bonds. Merrill Lynch marketed its Treasury receipts as Treasury Income Growth Receipts and Salomon Brothers marketed its receipts as Certificates of Accrual on Treasury Securities. The U.S. Treasury announced its Separate Trading of Registered Interest and Principal (STRIPS) program to facilitate the stripping of designated Treasury securities in February Although the trademark synthetic zeros were a success, but because of the higher liquidity of strips, they were dominated by strips. 54 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

28 Non-Standard : Strips The investors who buy strips are usually long-term investors like pension funds and insurance companies. One of their aims is to secure a return over their long-term investment horizon. Consider an investor who is supposed to guarantee 6% per annum over 20 years on its liabilities. If he buys and holds a strip with a maturity equal to its investment horizon, that is 20 years, and a YTM of 6%, he perfectly meets his objective because he knows today the return per annum on that bond, which is 6%. In contrast, coupon-bearing bonds do not allow him to do so, because first they bear an interest reinvestment risk and second their duration hardly ever, if not never, reaches 20 years. 55 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Non-Standard : Strips There exist two types of strips coupon strips and principal strips. Coupon strips and principal strips are built by stripping the coupons and the principal of a coupon-bearing bond, respectively. The main candidates for stripping are government bonds (Treasury bonds and government agency bonds). Strips are not as liquid as coupon-bearing bonds; hence, their bid-ask spread is usually higher. 56 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

29 Non-Standard : Floating-Rate Notes Floating-Rate Notes (FRN) are bond securities that bear floating coupon rates. This generic denomination encompasses two categories of bonds: Floating-rate bonds. Thesearebondswhosecouponratesareindexedonashort-term reference with a maturity inferior to 1 year, like the 3-month Libor. The coupons of floating-rate bonds are reset more than once a year. Variable-rate bonds or adjustable-rate bonds. These are bonds whose coupon rates are indexed on a longer-term reference with a maturity superior to 1 year, like the 10-year Constant Maturity Treasury (CMT) bond yield. The coupons of variable-rate bonds may have a reset frequency exceeding 1 year. Usually, the reset frequency is equal to the coupon payment frequency. 57 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Non-Standard : Floating-Rate Notes FRNs differ from each other as regards the nature of the coupon rate indexation. Coupon rates can be determined in three ways: First, as the product of the last reference index value and a multiplicative margin. Second, as the sum of the last reference index value and an additive margin. Third, as a mix of the two previous methods. Note that when the sign of the multiplicative margin is negative, the bond is called an inverse floater. The coupon rate moves in the opposite direction to the reference index; thus, to prevent it from becoming negative, a floor is determined that is usually equal to zero. Such bonds have become fairly popular under a context of decreasing interest rates. 58 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

30 Example of Floating-Rate Bond Consider an investor who buys a floating-rate bond whose coupon rate is equal to 3-month Libor + 20bp. He is entitled to receive, every period determined in the contract (usually every 3 months), a coupon payment inversely proportional to its annual frequency and principal payment on the maturity date. The coupon rate will be reset every 3 months in order to reflect the new level of the 3-month Libor. 59 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Example of Inverse Floater Consider an investor who buys an inverse floater whose coupon rate is equal to max(0, 16% 2x), where x is the 2-year T-Bond yield. He is entitled to receive, every period determined in the contract (usually every year), a coupon payment inversely proportional to its annual frequency and principal payment on the maturity date. The coupon rate will be reset every 2 years in order to reflect the new level of the 2-year bond yield. 60 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

31 Example: French 10-Year CMT Bond Consider the French 10-Year CMT Bond with maturity date 25/10/2xx6 that bears a quarterly floating coupon that is indexed on TEC10 (see next slide). TEC10 is a French 10-year Constant Maturity Treasury reference. It is determined on a daily basis as the 10-year interpolated yield between two active Treasury bond yields with very close maturity dates. The bond coupon rate is equal to TEC10 100bp and entitles the bondholder to receive every quarter on January 25th, April 25th, July 25th and September 25th a coupon payment equal to (1 + TEC10 100bp) 1 4 1, and principal payment on 25/10/2xx6. Coupon rates are reset every quarter with an Actual/Actual day-count basis. For example, the coupon paid on April 25th is determined using the TEC10 index five working days before January 25th. 61 / 126 William C. H. Leon MFE8812 Bond Portfolio Management 62 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

32 Non-Standard : Floating-Rate Notes An investor who buys a FRN typically hedge against parallel shifts of the interest rate curve because the coupons of the bond reflect the new level of market interest rates on each reset date. FRNs usually outperform fixed-rate bonds with the same maturity when interest rates shift upwards and under-perform them when interest rates shift downwards. For inverse floaters, the issue is more complex because of the way they are structured. A decrease in interest rates will not necessarily result in the price appreciation of inverse floaters despite the increase in the coupon rate. Their performance depends actually on the evolution of the interest-rate curve shape. 63 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Non-Standard : Inflation-Indexed Inflation-indexed bonds deliver coupons and principal that are indexed on the future inflation rates. They are structured so as to protect and increase an investors purchasing power. They are mainly issued by governments to make it clear that they are willing to maintain a low inflation level. They are more developed in the United Kingdom, followed by the United States. An inflation-indexed bond can be used to hedge a portfolio, to diversify a portfolio or to optimize assetliability management. Investors can use inflation-indexed bond to hedge against a rise in the inflation rate. Inflation-indexed bond presents a weak correlation with other assets such as stocks, fixed-coupon bonds and cash, which makes it an efficient asset to diversify a portfolio. Insurance companies and pension funds that guarantee performances indexed on inflation to their clients can buy inflation-indexed bonds to reduce the mismatch between assets and liabilities. 64 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

33 Government & Municipal : The US Market Government securities. Government securities can be divided into two categories: Treasury securities and Federal Agency securities. Treasury securities. Treasury securities are issued by the US Department of the Treasury and backed by the full faith and credit of the US government. The Treasury market is the most active market in the world, thanks to the large volume of total debt and the large size of any single issue. The amount of outstanding marketable US Treasury securities is huge, with $18 trillion as of December 31, The Treasury market is the most liquid debt market, that is, the one where pricing and trading are most efficient. The bid ask spread is by far lower than in the rest of the bond market. 65 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Government & Municipal : The US Market Treasury securities (continue). On-the-run securities are recently issued Treasury securities, as opposed to off-the-run securities, which are old issued securities. Benchmark securities, which are recognized as market indicators. As they are over-liquid, they trade richer than all their direct neighbors. There typically exists one such security on each of the following curve points: 2 years, 5 years, 10 years and 30 years. 66 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

34 Example of Treasury Securities Consider the following bonds on 07/12/2001: The 5-year US Treasury benchmark bond had a coupon of 3.5%, a maturity date 15/11/2006 and an issuance date 15/11/2001. Its yield is 4.45%. The 5-year off-the-run US T-bond had a coupon of 7%, a maturity date 15/07/2006 and an issuance date 15/07/1996. Its yield is 4.48%. The difference of coupon level between the two bonds is becasue: The 5-year off-the-run T-bond was originally a 10-year T-bond. Its coupon reflected the level of 10-year yields at that time. The level of the US government yield curve on 15/07/1996 was at least 200 basis points over the level of the US government yield curve on 15/11/2001. Furthermore, the yield of the off-the-run bond was higher than that for the benchmark bond, which illustrates the relative richness of the latter. 67 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Government & Municipal : The US Market Federal agency securities. Agency securities are issued by different organizations, seven of which dominate the market in terms of outstanding debt: The Federal National Mortgage Association (Fannie Mae). The Federal Home Loan Bank System (FHLBS). The Federal Home Loan Mortgage Corporation (Freddie Mac). The Farm Credit System (FCS). The Student Loan Marketing Association (Sallie Mae). The Resolution Funding Corporation (REFCO). The Tennessee Valley Authority (TVA). 68 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

35 Government & Municipal : The US Market Federal agency securities (continue). Agencies have two common features: They were created to fulfill a public purpose. For example, Fannie Mae and Freddie Mac aim to provide liquidity for the residential mortgage market. The FCS aims at supporting agricultural and rural lending. REFCO aims to provide financing to resolve thrift crises. The debt of most agencies is not guaranteed by the US government. Whereas federally sponsored agency securities (Fannie Mae, FHLBS, Freddie Mac, FCS, Sallie Mae, REFCO) are generally not backed by the full faith and credit of the US government, and so contain a credit premium, federally related institution securities (GNMA: Government National Mortgage Association) are generally backed by the full faith and credit of the US government, but as they are relatively small issues, they contain a liquidity premium. 69 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Government & Municipal : The US Market Federal agency securities (continue). Agencies are differently organized. Fannie Mae, Freddie Mac and Sallie Mae are owned by private-sector shareholders. Farm Credit System and the Federal Home Loan Bank System are cooperatives owned by the members and borrowers. Tennessee Valley Authority is owned by the US government 70 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

36 Government & Municipal : The US Market Municipal securities. Municipal bonds are issued by state and local governments, such as counties, special districts, cities and towns, to raise funds in order to finance projects for the public good such as schools, highways, hospitals, bridges and airports. Municipal bonds are exempt from federal income taxes, which makes the municipal sector being referred to as the tax-exempt sector. There are two generic types of municipal bonds: general obligation bonds and revenue bonds. General obligation bonds have principal and interest secured by the full faith and credit of the issuer and are usually supported by either the issuers unlimited or limited taxing power. Revenue bonds have principal and interest secured by the revenues generated by the operating projects financed with the proceeds of the bond issue. Many of these bonds are issued by special authorities created for the purpose. 71 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Government & Municipal : Credit Risk Treasury securities are considered to have no credit risk. Federal agencies debt are high-quality debt. All rated agency senior debt issues are triple-a rated by Moodys and Standard & Poors. This rating often reflects not only healthy financial fundamentals and sound management, but also and above all, the agencies relationship to the US government. Municipal debt issues, when rated, carry ratings ranging from triple-a, for the best ones, to C or D, for the worst ones. 72 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

37 Government & Municipal : Other Characteristics Government and municipal securities can be distinguished by their cash flow type, their maturity level, their maturity type and their interest-rate type. Cash flow type. There are discount securities, and fixed and floating coupon securities. Maturity level. The 1-year maturity is the frontier separating money-market instruments (with maturity below it) from bond instruments (with maturity above it). Treasury securities with original maturity equal or below 1 year are called Treasury bills; they are discount securities. Treasury securities with original maturity between 2 years and 10 years are called Treasury notes, and Treasury securities with original maturity over 10 years are called Treasury bonds; both are coupon securities, and some of them are stripped. 73 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Government & Municipal : Other Characteristics Maturity type. A security with a single maturity is called a term security. A security that can be retired prior to maturity is called a callable security. Although the US government no longer issues callable bonds, there are still outstanding issues with this provision. Treasury bonds are bullet bonds, meaning that they have no amortization payments. Interest-rate type. Agency securities, municipal securities and most Treasury securities are nominal coupon-bearing securities. Only a few Treasury securities are inflation-linked, that is, they bear real coupons. They are called Treasury Inflation Protected Securities (TIPS). 74 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

38 Government & Municipal : Markets Treasury securities are traded on four markets: the primary market, the secondary market, the when-issued market and the repo market. The primary market. This is the market where newly issued securities are first sold through an auction which is conducted on a competitive bid basis. The auction process happens between the Treasury and dealers according to regular cycles for securities with specific maturities. Auction cycles are as follows: 2-year notes are auctioned every month and settle on the 15th. Five-year notes are auctioned quarterly (in Feb, May, Aug & Nov of each year), and settle at the end of the month. Ten-year notes are auctioned quarterly (in Feb, May, Aug & Nov of each year), and settle on the 15th of the month. Thirty-year bonds are auctioned semiannually (in Feb & Aug of each year), and settle on the 15th of the month. Auction is announced by the Treasury one week in advance, the issuance date being set one to five days after the auction. 75 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Government & Municipal : Markets The secondary market. This is the market where previously issued securities are bought and sold, a group of US government security dealers offering continuous bid and ask prices on specific outstanding Treasury securities. It is an over-the-counter market. The when-issued market. This is the market where Treasury securities are traded on a forward basis before they are issued by the Treasury. 76 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

39 Government & Municipal : Markets The repo market. This is the market where securities are used as collateral for loans. A distinction must be made between the general-collateral (GC) repo rate and the special repo rate. GC repo rate applies to the major part of Treasury securities. Special repo rates are specific repo rates. They typically concern on-the-run and cheapest-to-deliver securities, which are very expensive. Special repo rates are at a level below the GC repo rates. Indeed, as these special securities are very much in demand, the borrowers of these securities on the repo market receive a relatively lower repo rate compared to normal Treasury securities. 77 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Government & Municipal : Main Issuers The four major government bond (i.e., bond and note issued by the Treasury of each country) issuers in the world are Euroland, Japan, the United Kingdom and the United States. 78 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

40 Corporate : Main Characteristics Corporate bonds are issued by entities (firms, banks) belonging to the private sector. They represent what market participants call the credit market. They are far less liquid than government bonds: they bear higher bid ask spreads. Issuer of a corporate bond has the obligation to honor his commitments to the bondholder. A failure to pay back interests or principal according to the terms of the agreement constitutes what is known as default. There are two sources of default: The shareholders of a corporation can decide to break the debt contract. This comes from their limited liability status: they are liable of the corporations losses only up to their investment in it. They do not have to pay back their creditors when it affects their personal wealth. Creditors can prompt bankruptcy when specific debt protective clauses, known as covenants, are infringed. 79 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Corporate : Main Characteristics Corporate bonds are affected by default or credit risk. Their yields contain a default premium over Treasury bonds. In case of default, there are typically three eventualities: Default can lead to immediate bankruptcy. Depending on their debt securities seniority and face value, creditors are fully, partially or not paid back, thanks to the sale of the firms assets. The percentage of the interests and principal they receive, according to seniority, is called the recovery rate. Default can result in a reorganization of the firm within a formal legal framework that depends on the countrys legislation. e.g. under Chapter 11 of the American law, corporations that are in default are granted a deadline so as to overcome their financial difficulties. Default can lead to an informal negotiation between shareholders and creditors. This results in an exchange offer through which shareholders propose to creditors the exchange of their old debt securities for a package of cash and newly issued securities. 80 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

41 Corporate : The Corporate Bond Market Market size. In the context of a historically low level of interest rates, the corporate bond market is rapidly developing and growing. Within the four major bond markets in the world, the the US Dollar (USD) corporate market is the most mature, followed by the Sterling (GBP) market and the Euro (EUR) market, the growth of the latter being reinforced by the launching of the Euro. The Japanese Yen (JPY) market differentiates itself from the others, because of the credit crunch situation and economic difficulties it has been facing. The USD corporate bond market is much bigger and also more diversified than the others: it is, for instance, more than twice as big as the Euro market, and low investment-grade ratings are much more represented. 81 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Corporate : The Corporate Bond Market Sector breakdown. The corporate bond market can be divided into three main sectors: financial, industrial and utility. Apart from the USD market, the financial sector is over-represented. It is another proof of the maturity of the USD market, where the industrial sector massively uses the market channel in order to finance investment projects. 82 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

42 Definition of Money-Market Instruments Money-market instruments are short-term debt instruments with a maturity typically less than or equal to 1 year. Some of these instruments such as certificates of deposit may have a maturity exceeding 1 year. These instruments are very sensitive to the Central Bank monetary policy. There are basically three categories of issuers on this market: government (at both the federal and local levels), banks and corporations. 83 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Role of the Central Bank The central bank, through its privileged triple status of governments banker, banks banker and nations banker, steers the general level of interest rates. As the governments banker, it finances budget deficits. As the banks banker, it supervises and regulates the banking system. As the nations banker, it conducts the monetary policy of the nation. All these tasks are guided by two objectives: First, the stability of prices. Second, the support of a sustainable economic growth. In order to meet these targets, the Central Bank has the responsibility of setting the official interest rate of the nation, through its open market operations, i.e., the purchase and sale of government securities, which allows it to control money supply. This key interest rate is basically an interest rate at which banks can borrow. 84 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

43 Role of the Central Bank: Setting Interest Rate The Central Bank set the key interest rate at which banks can borrow at. It is either the overnight (means for one trading day) interest rate at which banks can borrow from the Central Bank (e.g. UK, Euro area) in exchange for eligible securities such as Treasury Bills. In this case, it is called a repo rate. Or, it is the overnight interest rate set in the Central Bank funds market, at which banks can borrow or lend Central Bank funds so as to meet their reserve requirements (e.g. US, Japan) with the Central Bank. It is called the Fed Funds rate in the United States and the unsecured overnight call rate in Japan. The two types of interest rates, which both exist in each of the above-mentioned countries, are very close to one another. The repo rate being lower owing to the fact that the corresponding loan is collateralized by a security. 85 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Role of the Central Bank: Setting Interest Rate This key interest rate then affects the whole spectrum of interest rates that commercial banks set for their customers (borrowers and savers), which in turn affects supply and demand in the economy, and finally the level of prices. The shorter the debt instrument, the greater its sensitivity to monetary policy action. Indeed, medium-term and long-term debt instruments are more sensitive to the market expectations of future monetary policy actions than to the current Central Bank action itself. 86 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

44 Treasury Bills Treasury Bills (T-Bills) are Treasury securities with a maturity below or equal to 1 year. They entail no default risk because they are backed by the full faith and creditworthiness of the government. They bear no interest rate and are quoted using the yield on a discount basis or on a money-market basis depending on the country considered. The liquidity of T-Bills may be biased by the so-called squeeze effect, which means that the supply for these instruments is much lower than the demand, because investors buy and hold them until maturity. This phenomenon is particularly observable in the Euro market. 87 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Treasury Bills Yield on a discount basis. The yield on a discount basis denoted by y d is computed as y d = F P F N n where F is the face value, P the price, N the year-basis (360 or 365) and n the number of calendar days remaining to maturity. It is the yield calculation used in the Euro zone, in the United States and in the United Kingdom. The year-basis is 360 in the United States, can be 360 or 365 in the Euro zone depending on the country considered, 365 in the United Kingdom. The yield on a discount basis can retrieve the T-bill price as ( P = F 1 y d n ). N 88 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

45 Treasury Bills Yield on a money-market basis. The yield on a money-market basis denoted by y m is computed as 1 y d n N = 1 1+y m n N y m = y d N N y d n. The yield on a money-market basis can retrieve the T-bill price as P = F 1+y m n N. It is the yield calculation used in Japan where the year-basis is / 126 William C. H. Leon MFE8812 Bond Portfolio Management Exercise 1 Compute on a discount basis the yield on a 90-day US T-bill with price $9,800, and face value $10, Compute the price of a US T-bill with maturity 28/03/2xx2 and a discount yield of 1.64% as of 17/12/2xx1. 3 Compute the yield on a money-market basis on a 62-day Japan T-bill with price 99 yens and face value 100 yens. 4 Compute the price of a French T-bill with maturity 07/03/2xx2 and a money-market yield of 3.172% as of 17/12/2xx1. 90 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

46 Answer 91 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Certificates of Deposit Certificates of deposit are debt instruments issued by banks in order to finance their lending activity. They entail the credit risk of the issuing bank. They bear an interest rate that can be fixed or floating, and that is paid either periodically or at maturity with principal. Their maturity typically ranges from a few weeks to three months, but it can reach several years. They trade on a money-market basis. The price is computed using the following equation P = F 1+c n c N 1+y m n m N where c the interest rate at issuance, n c is the number of days between issue date and maturity date, and n m is the number of days between settlement and maturity. 92 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

47 Bankers Acceptances Bankers acceptances are drafts that are drawn and accepted, and therefore guaranteed by banks. These bills of exchange mainly guarantee foreign trade transactions. They bear no interest rate. So, the market price of a bankers acceptance is calculated in the same manner as the price of a T-Bill. They trade on a discount basis in the United States and on a money-market basis in the Euro area. Its discount or money-market yield accounts for the credit risk that neither the importer nor the bank honor their commitment. 93 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Commercial Papers Commercial papers are unsecured short-term debt securities issued by corporations including industrial and financial companies. They entail the credit risk of the issuing entity. They are slightly riskier than bankers acceptances as the latter are guaranteed by the accepting bank beside the guarantee of the issuing company. Corporations typically use them either as a way of raising short-term funds or as interim loans to finance long-term projects while awaiting more attractive long-term capital market conditions, which is called bridge financing. Commercial papers are usually rolled over by the issuing corporation until reaching its lending horizon. They bear no interest rate. So, the market price of a commercial paper is calculated in the same manner as the price of a T-Bill. Their maturity ranges from 2 to 270 days. They trade on a discount basis in the United States and on a money-market basis in the Euro area. 94 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

48 Repo & Reverse Repo Market Instruments Repurchase (repo) and reverse repurchase (reverse repo) agreement transactions are commonly used by traders and portfolio managers to finance either long or short positions (usually in government securities). A repo is a means for an investor to lend bonds in exchange for a loan of money. More precisely, a repo agreement is a commitment by the seller of a security to buy it back from the buyer at a specified price and at a given future date. It can be viewed as a collateralized loan, the collateral here being the security. A reverse repo is a means for an investor to lend money in exchange for a loan of securities. A reverse repo agreement is a repo transaction viewed from the buyers perspective. The repo rate is computed on an Actual/360 day-count basis. When the maturity of the loan is 1 day, the repo is called an overnight repo. When the maturity exceeds 1 day, the repo is called a term repo. 95 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Example of a Repo Transaction Suppose an investor lends EUR 1 million of the 10-year Bund benchmark bond (i.e., the Bund 5% 04/07/2x11 with a quoted price of , on 29/10/2x01) over 1 month at a repo rate of 4%. There is 117 days accrued interest as of the starting date of the transaction. At the beginning of the transaction, the investor will receive an amount of cash equal to the gross price of the bond times the nominal of the loan, i.e., ( )% EUR 1, 000, 000 = EUR 1, 057, At the end of the transaction, in order to repurchase the securities he will pay the amount of cash borrowed plus the repo interest due over the period, i.e., EUR 1, 057, 350 (1 + 4% ) = EUR 1, 060, / 126 William C. H. Leon MFE8812 Bond Portfolio Management

49 Repo & Reverse Repo Market Instruments From an investment point of view, the repo market offers several opportunities: The opportunity of contracting less expensive loans than traditional bank loans (because repo loans are secured loans). The opportunity of investing in a very liquid short-term market. The opportunity of investing cash over tailor-made horizons, by rolling over either several overnight transactions or different repo transactions with various maturity horizons. This is particularly attractive for an investor who has a short-term undefined horizon. It allows him to avoid the price risk he would incur if he had chosen to invest in a money-market security. The opportunity for a buy-and-hold investor of putting idle money to work. Indeed, by lending the securities he owns in his portfolio, he receives some cash that he can invest in a money market instrument. His gain will be the difference between the money-market income and the repo cost. 97 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Repo & Reverse Repo Market Instruments The opportunity to take short positions that enable portfolio managers to construct alternative strategies by combining long and short positions. For a short-term investor with an unknown investment horizon, the strategy of buying a money-market security and the strategy of rolling over cash on the repo market do not entail the same interest-rate risk. The former bears the risk that the security may be sold before its maturity date (price risk) at an unknown price, while the latter bears the risk that the cash may be reinvested at an unknown repo rate (reinvestment risk). 98 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

50 Risks of Fixed-Income Securities Key Interest Rate Related Risk Other Risk The risks associated with investing in fixed-income securities include: Interest rate or market risk. Yield curve risk. Volatility risk. Reinvestment risk. Call risk. Prepayment risk. Credit risk. Default risk, downgrade risk and credit spread risk. Inflation or purchasing power risk. Currency or exchange rate risk. Liquidity or marketability risk. 99 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Risks of Fixed-Income Securities Key Interest Rate Related Risk Other Risk Event risk. Corporate takeovers, restructuring or regulatory changes. Country or sovereign risk. Risk risk. 100 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

51 Interest Rate or Market Risk Key Interest Rate Related Risk Other Risk The price of a fixed-income security will change in the opposite direction to the change in interest rates or yields. Consider a 20-year bond with 6% semi-annual coupon. If the yield investors require to buy this bond is 6%, the price of this bond would be $100. However, if the required yield increased to 6.5%, the price of this bond would decline to $ Thus, for a 50 basis point increase in yield, the bonds price declines by 5.55%. If, instead, the yield declines from 6% to 5.5%, the bonds price will rise by 6.02% to $ The risk that an investor faces is that the price of a bond held in a portfolio will decline if market interest rates rise. This risk is referred to as interest rate risk or market risk, and is the major risk faced by investors in the fixed-income market. 101 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Key Interest Rate Related Risk Other Risk Relationship between Interest Rates & Price The price of a bond changes in the opposite direction to the change in interest rates. So, for an instantaneous change in interest rates the following relationship holds: if interest rates increase, price of a bond decreases; if interest rates decrease, price of a bond increases. A bond will trade at a price equal to par when the coupon rate is equal to the yield required by market. A bond will trade at a price below par (sell at a discount) or above par (sell at a premium) if the coupon rate is different from the yield required by the market. 102 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

52 Key Interest Rate Related Risk Other Risk Bond Features that Affect Interest Rate Risk A bond s price sensitivity to changes in market interest rates depends on various features of the issue, such as maturity, coupon rate, and embedded options. The longer a bond s maturity, the greater the bond s price sensitivity to changes in interest rates. The lower the coupon rate, the greater the bond s price sensitivity to changes in interest rates. As interest rates decline, the price of a callable bond may not increase as much as an otherwise option-free bond. The higher a bond s yield, the lower the bond s price sensitivity to changes in interest rates. 103 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Measuring Interest Rate Risk Key Interest Rate Related Risk Other Risk What we are interested in is a first approximation of how a bond s price will change when interest rates change. We can look at the price change in terms of the percentage price change from the initial price or; the dollar price change from the initial price. The duration of a bond refers to the estimate of the percentage price change in the its price for a 100 basis points change in its yield. It is important to note that the computed duration of a bond is only as good as the valuation model used to get the prices when the yield is shocked up and down. If the valuation model is unreliable, then the duration is a poor measure of the bond s price sensitivity to changes in yield. 104 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

53 Yield Curve Risk Key Interest Rate Related Risk Other Risk There is a structure of interest rates and not just one interest rate or yield in the economy. One important structure is the relationship between yield and maturity. The graphical depiction of this relationship is called the yield curve. When interest rates change, they typically do not change by an equal number of basis points for all maturities. In other words, the changes in the yield curve may not be confined to parallel shifts. 105 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Parallel Shift in the Yield Curve Key Interest Rate Related Risk Other Risk 106 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

54 Key Interest Rate Related Risk Other Risk Non-Parallel Shift in the Yield Curve 107 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Yield Curve Risk Key Interest Rate Related Risk Other Risk Fixed-income securities have different exposures to how the yield curve shifts. This risk exposure is called yield curve risk. The implication is that any measure of interest rate risk that assumes that the interest rates changes by an equal number of basis points for all maturities (referred to as a parallel yield curve shift ) is only an approximation. The yield curve is a series of yields, one for each maturity. It is possible to determine the percentage change in the value of a portfolio if only one maturity s yield changes while the yield for all other maturities is unchanged. This is a form of duration called rate duration, where the word rate means the interest rate of a particular maturity. Consequently, there is not one rate duration but a rate duration for each maturity. 108 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

55 Yield Curve Risk Key Interest Rate Related Risk Other Risk In practice, a rate duration is not computed for all maturities. Instead, the rate duration is computed for several key maturities on the yield curve and this is referred to as key rate duration. Key rate duration is therefore simply the rate duration with respect to a change in a key maturity sector. Vendors of analytical systems report key rate durations for the maturities that in their view are the key maturity sectors. 109 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Volatility Risk Key Interest Rate Related Risk Other Risk Volatility risk is the risk of a change in the price of a bond as a result of changes in the interest rate volatility. For bonds with embedded options, changes in expected volatility have effects on the values of their options. For a callable bond, if expected yield volatility increases, the price of the embedded call option will increase. As a result, the price of a callable bond will decrease (because the former is subtracted from the price of the option-free bond). For a putable bond, if expected yield volatility decreases, the price of the embedded put option will decrease. Therefore, the price of a putable bond will decrease. 110 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

56 Reinvestment Risk Key Interest Rate Related Risk Other Risk Reinvestment risk is the risk that the proceeds received from the payment of interest and principal (i.e., scheduled payments and principal prepayments) that are available for reinvestment must be invested at a lower interest rate than the security that generated the proceeds. Reinvestment risk is present when an investor purchases a callable bond. When the issuer calls a bond, it is typically done to lower the issuers interest expense because interest rates have declined after the bond is issued. The investor faces the problem of having to reinvest the called bond proceeds received from the issuer in a lower interest rate environment. Reinvestment risk also occurs when an investor purchases a bond and relies on the yield of that bond as a measure of return. For the yield computed at the time of the bond purchase to be realized, the investor must be able to reinvest any coupon payments at the computed yield. 111 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Call Risk & Prepayment Risk Key Interest Rate Related Risk Other Risk For an investor in callable bond, there are at least three disadvantages to call provisions: The cash flows of a callable bond is not known with certainty because it is not known when the bond will be called. Because the issuer is likely to call the bonds when interest rates have declined below the bonds coupon rate, the investor is exposed to reinvestment risk. The price appreciation potential of the callable bond will be reduced relative to an otherwise comparable option-free bond. These disadvantages faced by the investor in a callable bond is said to expose the investor to call risk. The same disadvantages apply to mortgage-backed and asset-backed securities where the borrower can prepay principal prior to scheduled principal payment dates. This risk is referred to as prepayment risk. 112 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

57 Credit Risk Key Interest Rate Related Risk Other Risk An investor who lends funds by purchasing a bond issue is exposed to credit risk. There are three types of credit risk: 1 default risk, 2 credit spread risk, and 3 downgrade risk. 113 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Default risk Key Interest Rate Related Risk Other Risk Default risk is defined as the risk that the issuer will fail to satisfy the terms of the obligation with respect to the timely payment of interest and principal. The percentage of a population of bonds that is expected to default is called the default rate. If a default occurs, this does not mean the investor loses the entire amount invested. An investor can expect to recover a certain percentage of the investment. This is called the recovery rate. Given the default rate and the recovery rate, the estimated expected loss due to a default can be computed. 114 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

58 Credit Spread Risk Key Interest Rate Related Risk Other Risk The yield on a bond is made up of two components: (1) the yield on a similar default-free bond issue and (2) a premium above the yield on a default-free bond issue necessary to compensate for the risks associated with the bond. The risk premium is referred to as a yield spread. The part of the risk premium or yield spread attributable to default risk is called the credit spread. The price performance of a non-treasury bond issue and the return over some time period will depend on how the credit spread changes. If the credit spread increases, investors say that the spread has widened and the market price of the bond issue will decline (assuming U.S. Treasury rates have not changed). The risk that an issuer s debt obligation will decline due to an increase in the credit spread is called credit spread risk. 115 / 126 William C. H. Leon MFE8812 Bond Portfolio Management Downgrade Risk Key Interest Rate Related Risk Other Risk Investors may gauge the default risk of an issue by its credit ratings assigned to the issue by rating agencies. A credit rating is an indicator of the potential default risk associated with a particular bond issue or issuer. It represents in a simplistic way the credit rating agencys assessment of an issuers ability to meet the payment of principal and interest in accordance with the terms of the indenture. Once a credit rating is assigned to a debt obligation, a rating agency monitors the credit quality of the issuer and can reassign a different credit rating. An improvement in the credit quality of an issue or issuer is rewarded with a better credit rating, referred to as an upgrade. A deterioration in the credit rating of an issue or issuer is penalized by the assignment of an inferior credit rating, referred to as a downgrade. 116 / 126 William C. H. Leon MFE8812 Bond Portfolio Management

59 Downgrade Risk Key Interest Rate Related Risk Other Risk An unanticipated downgrading of an issue or issuer increases the credit spread and results in a decline in the price of the issue or the issuer s bonds. This risk is referred to as downgrade risk and is closely related to credit spread risk. A popular tool used by managers to gauge the prospects of an issue being downgraded or upgraded is a rating transition matrix. This is simply a table constructed by the rating agencies that shows the percentage of issues that were downgraded or upgraded in a given time period. 117 / 126 William C. H. Leon MFE8812 Bond Portfolio Management One-Year Rating Transition Matrix Key Interest Rate Related Risk Other Risk 118 / 126 William C. H. Leon MFE8812 Bond Portfolio Management