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Finance Finance means, literally, borrowing – The borrower thinks it is debt – The lender thinks it is investment – Stock has been standard for hundreds of years – Debt is the area of huge development » A fascinating story of how to borrow money and invest at the cutting edge of financial innovation – But can be very quantitative and full of jargons – Takes time and efforts to master Andrei Simonov - debt and money markets 1 Old stuff Idea of Lending – Villages: lending=insurance – Cities: implicit agreement becomes explicit, interest appear Interest: Idea of lending livestock (give 30 cattles, expect 40 next year) – Hammurabi explicitly limited the rate of interest to 20% on loans of silver, 33 1/3 % on loans of grain. Andrei Simonov - debt and money markets 2 Andrei Simonov - debt and money markets 3 Not the whole picture… Andrei Simonov - debt and money markets 4 Andrei Simonov - debt and money markets 5 Andrei Simonov - debt and money markets 6 Andrei Simonov - debt and money markets 7 Japan Started in 70-es from 10% of GDP, reach 160% now… Cost of carrying is not very high although, low interest rates. Andrei Simonov - debt and money markets 8 Andrei Simonov - debt and money markets 9 Andrei Simonov - debt and money markets 10 Andrei Simonov - debt and money markets 11 Andrei Simonov - debt and money markets 12 Andrei Simonov - debt and money markets 13 Andrei Simonov - debt and money markets 14 Why should you care? Andrei Simonov - debt and money markets 15 Rate of Return: Common Measures The term interest rate is sometimes referred to the price a borrower pays a lender for a loan. Unlike other prices, this price of credit is expressed as the ratio of the cost or fee for borrowing and the amount borrowed. – This price is typically expressed as an annual percentage of the loan (even if the loan is for less than one year). – Today, financial economists often refer to the yield to maturity on a bond as the interest rate. Yield to Maturity In Finance, the most widely acceptable rate of return measure for a bond is the yield to maturity, YTM. YTM is the rate that equates the price of the bond, P0B, to the PV of the bond’s CF; it is similar to the internal rate of return, IRR. In our illustrative example, if the price of the 10-year, 9% annual coupon bond were priced at $938.55, then its YTM would be 10%. P0B M C M t M ( 1 YTM ) ( 1 YTM ) t 1 10 $90 $1000 $938.55 YTM .10 t 10 (1 YTM ) t 1 (1 YTM ) Yield to Maturity The YTM is the effective rate of return. As a rate measure, it includes: – Return from coupons – Capital gains or losses – Reinvestment of coupons at the calculated YTM Bond Equivalent Yield The rate on bonds are often quoted as a simple annual rate (with no compounding). For bonds with semi-annual coupon payments, this rate can be found by solving for the YTM on a bond using 6-month CFs and then multiplying that rate by 2. This rate is also known as the bond-equivalent yield. C C M ... (1 r ) (1 r ) 2 (1 r ) n C C M ... Y Y Y (1 ) (1 ) 2 (1 ) n 2 2 2 M C An Y / 2 Y (1 ) n 2 where r is the half - year discount rate, Y is the annualized P semi - annual compoundin g discount rate, and n is the number of half - year periods. Bond Equivalent Yield Example: 10-year, 9% bond with semi-annual payments, and trading at 937.69 would have a YTM for a 6-month period of 5% and a bond-equivalent yield of 10%. Note: The effective rate is 10.25%. Bonds with different payment frequencies often have their rates expressed in terms of their bondequivalent yield so that their rates can be compared to each other on a common basis. Yield to Call Many bonds have a call feature that allows the issuer to buy back the bond at a specific price known as the call price, CP. Given a bond with a call option, the yield to call, YTC, is the rate obtained by assuming the bond is called on the first call date, CD. Like the YTM, the YTC is found by solving for the rate that equates the present value of the CFs to the market price. CD Ct CP P t (1 YTC ) M t 1 (1 YTC ) B 0 Yield to Worst Many investors calculate the YTC for each possible call date, as well as the YTM. They then select the lowest of the yields as their yield return measure. The lowest yield is sometimes referred to as the yield to worst. Bond Portfolio Yield The yield for a portfolio of bonds is found by solving the rate that will make the present value of the portfolio's cash flow equal to the market value of the portfolio. For example, a portfolio consisting of a two-year, 5% annual coupon bond priced at par (100) and a three-year, 10% annual coupon bond priced at 107.87 to yield 7% (YTM) would generate a three-year cash flow of $15, $115, and $110 and would have a portfolio market value of $207.87. The rate that equates this portfolio's cash flow to its portfolio value is 6.2%: $15 $115 $110 $207.87 1 (1 y) (1 y) 2 (1 y)3 y .062 Bond Portfolio Yield Note: The bond portfolio yield is not the weighted average of the YTM of the bonds comprising the portfolio. In this example, the weighted average (Rp) is 6.04%: R P w1 (YTM 1 ) w 2 (YTM 2 ) $100 $107.87 Rp (.05) (.07) .0604 $207.87 $207.87 Thus, the yield for a portfolio of bonds is not simply the average of the YTMs of the bonds making up the portfolio. Federal Marketable Debt: July 31, 12 Type Marketable Debt Bills Notes Bonds Inflation-Indexed (TIPS) Total Marketable Amount 2010($ billions) 1785 4978 816 577 ___ 8,156 Amount 2011($ billions) Amount 2012($ billions) 1,490 6,199 987 681 1,578 7,061 1,166 783 ------9,357 ------10,588 Source: Board of Governors of the Federal Reserve System, to http://www.treasurydirect.gov/govt/reports/pd/mspd/2012/opds072012.pdf Types of Treasury Securities – Market Series: » Treasury Bills » Treasury Bonds » Treasury Notes » Treasury-Inflation Index Bonds – Non-Market Series: Securities that cannot be traded. » Government Agency Series » Foreign Series » U.S. Savings Bonds Initial offering Initial offering: the auction process – Treasury securities are sold by a single-price auction technique. – Bidders can enter competitive or noncompetitive bid. – Competitive bid states amount and yield required. – Competitive bids accepted based on lowest yield (known as the stop yield) – All competitive bids offering to receive a yield equal to or lower than the stop yield are accepted and priced on the basis of the stop yield (the highest yield of all accepted offers). – Noncompetitive bids receive the stop yield Initial maturity from 13 weeks to 30 years Some securities: – Treasury bills : No more than 1 year, no coupon – Treasury notes; 1 – 10 years – Treasury bonds: > 10 years Andrei Simonov - debt and money markets 27 List of primary dealers as of Sept 2011 BNP Paribas Securities Corp. Barclays Capital Inc. Cantor Fitzgerald & Co. Federal Reserve Bank of New York: Citigroup Global Markets Inc. www.newyorkfed.org/markets/pridealers_listing.html Credit Suisse Securities (USA) LLC Daiwa Capital Markets America Inc. Deutsche Bank Securities Inc. Goldman, Sachs & Co. HSBC Securities (USA) Inc. Jefferies & Company, Inc. J.P. Morgan Securities LLC MF Global Inc. Merrill Lynch, Pierce, Fenner & Smith Incorporated Mizuho Securities USA Inc. Morgan Stanley & Co. LLC Nomura Securities International, Inc. RBC Capital Markets, LLC RBS Securities Inc. SG Americas Securities, LLC UBS Securities LLC. Andrei Simonov - debt and money markets 28 Auction example $10 billion issue of 10-year notes, $1 billion of non-competitive bids, $2 billion purchase from Federal Reserve, $7 billion left for competitive bids Offers: $0.5 billion @ 3.10% $0.6 billion @ 3.11% $1.4 billion @ 3.12% $2.6 billion @ 3.13% $3.2 billion at 3.14% Accepted yield is 3.14%, the rate necessary to sell the whole issue. 3.13% would have been sufficient for $5.1 billion of competitive bids. 3.14% is sufficient for $8.3 billion. All bidders offering to accept a rate lower than 3.14% are accepted. Only $1.9 billion of $3.2 billion bid at 3.14% is needed, so competitive bidders at this rate receive 1.9/3.2 = 59.375% of the amount bid for Noncompetitive bids, nonpublic purchases, and all accepted competitive bids will receive notes with a yield of 3.14%. The coupon rate is likely to be 3.125% (in units of 1/8 of 1%, and makes the price closest to, but no higher than par) What is the price of the bond? Andrei Simonov - debt and money markets 29 Salomon Squeeze Primary dealers routinely submitted huge bids – On June 27, 1990, Salomon submitted a bid that exceeded the total value of the issue. Two weeks later when Salomon submitted a massive bid of $30 billion for $10 billion in 30-year notes Rules prevents any participants from obtaining more than 35% Rules require dealer to obtain prior authorization from the clients when bidding Salomon’ Mozer admitted that on February 21, 1991, he submitted an unauthorized bid for 35% of the $9 billion 5-year note auction in the name of Warburg, a Salomon customer, in addition to a bid for 35% in Salomon's name. Salomon's two bids turned out to be at the stop-out yield and the Fed awarded $1.7 billion in notes each to Salomon and Warburg. And then he did it again on May 22nd getting $bln10.6 out of $bln12 of 2 year notes (together with Quantum and Tiger funds). What is so bad about it? One player has a control over the secondary market of T-notes, it also affects significantly REPO market. Andrei Simonov - debt and money markets 30 Price yield relationship Inverse relationship between yields and prices If YTM = coupon rate, price = par value - Bond sells at par If YTM > coupon rate, price < par value - Bond sells at a discount If YTM < coupon rate, price > par value – Bond sells at a premium Andrei Simonov - debt and money markets 31 Price yield relationship Assume the coupon rate is a constant 10 percent. maturity Yield : 12% Yield: 7.8% 20 $849.54 $1,221.00 15 $862.35 $1,192.54 10 $882.36 $1,155.75 9 $891.72 $1,140.39 7 $907.05 $1,116.97 5 $926.40 $1,089.67 3 $950.83 $1,057.85 2 $965.35 $1,040.82 1 $981.67 $1,020.78 0 1000.00 1000.00 Andrei Simonov - debt and money markets 32 Yield price relationship Even if the discount rate is a constant – Price of discount bonds will increase with time – Price of premium bonds will decrease with time – Par bonds will remain at par – All bond prices converge to the face value at maturity – Discount bonds have a built-in capital gain. – Premium bonds have a built-in capital loss. – Don’t be surprised to find that bond prices change everyday Andrei Simonov - debt and money markets 33 Price Path of Premium or Discount Bonds over Time Price Premium Bond Par Bond Par value Discount Bond 0 Time to Maturity 34 Bond Risk Investment risk is the uncertainty that the actual rate of return realized from an investment will differ from the expected rate. There are three types of risk associated with bonds and fixed income securities: 1. Default Risk 2. Call Risk 3. Market Risk Default Risk Premium Because there is a default risk on corporate, municipal, and other non-U.S. Treasury bonds, they trade with a default risk premium (also called a quality or credit spread). This premium is often measured as the spread between the rates on a non-Treasury security and a U.S. Treasury security that are the same in all respects except for their default risk. Another measure of default risk – CDS (Credit default spreads) Andrei Simonov - debt and money markets 37 In 2014 (Q1) https://www.capitaliq.com/media/179529-Sov_Report_Q1_2014.pdf Andrei Simonov - debt and money markets 38 Best… Andrei Simonov - debt and money markets 39 Call Risk Call Risk is the uncertainty that the realized return will deviate from the expected return because the issuer calls the bond, forcing the investor to reinvest in a market with lower rates. Note: When a bond is called the holder receives the call price (CP). Since the CP usually exceeds the principal, the return the investor receives over the call period is often greater than the initial YTM. The investor, though, usually has to reinvest in a market with lower rates that often causes his return for the investment period to be less than the initial YTM. WSJ, April 15, 2009 WASHINGTON -- In effort to save billions of dollars, the U.S. Treasury Department Wednesday announced "a bond call" of the 12.5% Treasury bonds of 2009-2014 originally issued Aug. 15, 1984, and due Aug. 15, 2014. According to Wednesday's announcement, securities not redeemed on Aug. 15, will stop earning interest. In general, when Treasury "calls" a bond, it stops paying interest on the date of the call -- before the maturity date. The Treasury said there are $4.4 billion of the 12.5% bonds issued in August 1984 outstanding -- $3.4 billion of which are held by private investors. The cusip number on the bonds is 912810DL9. "These bonds are being called to reduce the cost of debt financing," said Treasury. It noted that the 12.5% interest rate is significantly above the current cost of securing financing for the five years remaining to their maturity. Using current market projections, Treasury estimates gross savings from the call to be about $2 billion. Andrei Simonov - debt and money markets 41 US Treasury bonds calls since 2000 Andrei Simonov - debt and money markets 42 Call Risk Premium Call Risk Premium: Call RP YTM Callable YTM Non Callable RP greater in higher interest rate periods Valuation of Callable Bonds Theoretically, the price of a callable bond, PC, should be equal to the price of an identical, but noncallable bond, PNC, minus the value of the call feature or call premium, VC. P P C NC V C The value of the call feature can be estimated using the option pricing model developed by Black and Scholes. Market Risk Market Risk is the uncertainty that the realized return will deviate from the expected return because of interest rate changes. Recall, the return on a bond comes from: – Coupons – Interest earned from reinvesting coupons: interest on interest – Capital gains or losses A change in rates affects interest on interest and capital gains or losses. Can yields become negative? Andrei Simonov - debt and money markets 46 Market Risk A change in interest rates has two effects on a bond's return: price effect and interest-on-interest effect. Price Effect: Interest rate changes affect the price of a bond; this is referred to as price risk. If the investor's horizon date, HD, is different from the bond's maturity date, then the investor will be uncertain about the price he will receive from selling the bond (if HD < M), or the price he will have to pay for a new bond (if HD > M). Interest-on-Interest Effect: Interest rate changes affect the return the investor expects from reinvesting the coupon -- reinvestment risk. Thus, if an investor buys a coupon bond, he automatically is subject to market risk. Market Risk (INT on INT) (INT on INT) r PtB r PtB (INT on INT) r PtB Market Risk One obvious way an investor can eliminate market risk is to purchase a pure discount bond with a maturity that is equal to the investor's horizon date. If such a bond does not exist (or does, but does not yield an adequate rate), a bondholder will be subject (in most cases) to market risk. Reinvestment risk Suppose you are an investor that is willing to hold bonds for 5 years, and try to choose among the following bonds: bond coupon maturity YTM 1 5% 3 9.0% 2 6% 20 8.6% 3 11% 15 9.2% 4 8% 5 8.0% Which bond would you choose? – 3: highest YTM, have to sell the bond after 5 years – 1: have to reinvest the interest as well as the principal – 4: no reinvestment of principal, but have to reinvest interest YTM does not help much in choosing the bonds – If yield changes In order to calculate the “right” return, we have to project the future reinvestment rates and the selling price We assume that reinvestment opportunities will be available Andrei Simonov - debt and money markets 50 Total return In order to calculate the “right” return, we have to project the future reinvestment rates and the selling price Example: An investor with a 3-year investment horizon wants to buy a 20-year 8% coupon bond for $82.84, with YTM as 10%. He expects to be able to reinvest the coupon interests at 6%, and 3 years later he can sell the bond to offer a YTM of 7%. What is the total expected return of this investment? 4 F 6 0.03 25.874, Step 1: the future value of coupons 3 years later is Step 2: the price of the bond 3 years later is ((1 r ) n 1) 4 A340.035 100 109.851 (1.035)34 F nr r Step 3: The total return is Y 109.851 25.874 (1 ) 6 2 82.84 109.851 25.874 1/ 6 Y 2 1 17.16% 82.84 Andrei Simonov - debt and money markets 51 Treasury STRIPS STRIPS is an acronym for Separate Trading of Registered Interest and Principal of Securities Converts each coupon and principal payment into a separate zero-coupon security. Example: a 30-year bond can be broken down into 60 separate coupon receipts (1 for each semiannual coupon payment with the first maturing in 6 months and the last maturing in 30 years) and 1 principal receipt. Originated as products offered by investment banks (Merrill Lynch TIGERs and Salomon Brothers CATS). STRIPS are direct obligations of the U.S. Treasury and thus have no credit risk. All Treasury notes and bonds are eligible to be stripped. Stripped securities can be “reconstituted” Market for fixed-principal STRIPS is very active (liquid) Andrei Simonov - debt and money markets 52 Interest rate: the crystal ball of financial market Andrei Simonov - debt and money markets 53 Yield curve Yield curve – The plot of yield to maturity against time to maturity – The bench mark for the cost of credit for loans of various maturities – http://www.bloomberg.com/markets/rates/index.html The shape of yield curve – Normal yield curve – Inverted yield curve – Humped yield curve – Exhibit 5-3 The changes of the shape of yield curve – Parallel shifts (corresponding to the duration assumption) – Steepening – Flattening Andrei Simonov - debt and money markets 54 Yield curve When we want to calculate the price of a bond, which interest rate should we use? – Say there are two bonds, both having the same maturity of 2 years. One has coupon rate of 8% and the yield is 7%. The other has coupon rate of 5% and the yield is 6.5%. Should we use the 7% or 6.5% as the interest rate to calculate the price of other bonds? – Bond yield is a function of coupon rate, and thus is bond specific. The bottom line: the yield curve should not be used to price a bond The appropriate interest rate must be independent of coupon rate – The yield on zero-coupon bond (or more precisely the bond with a single future cash flow) » Called spot rate – The yield curve that consists of spot rates is called the spot rate curve – How to create the spot rate curve? Andrei Simonov - debt and money markets 55 Bootstrapping The method to create the spot rate curve, called bootstrapping, is to calculate the spot rates through the present value formula. Example of boot strapping: Suppose you observe the following list of bond prices. Calculate the spot rates. Maturity annual coupon bond price 0.25 0 97.5 0.50 0 94.9 1.00 0 90.0 1.5 8% 96.0 2.00 12% 101.6 Andrei Simonov - debt and money markets 56 Bootstrapping Denote Z t PV of $1 that will be paid after t years. With semi - annual compoundin g, 100 1 94.9 100 Z 0.5 94.9 Z 0.5 0.949, R 0.5 10.75% (1 R 0.5 / 2) (1 R 0.5 / 2) 100 1 90.0 100 Z1 90.0 Z1 0.9, R 1 10.82% 2 (1 R 1 / 2) (1 R 1 / 2) 2 4 4 104 96.0 4 Z 0.5 4Z1 104 Z1.5 96 (1 R 0.5 / 2) (1 R 1 / 2) 2 (1 R 1.5 / 2) 3 Z1.5 0.8520, R1.5 10.97%. 6 6 6 106 101.6 2 3 4 (1 R 0.5 / 2) (1 R 1 / 2) (1 R 1.5 / 2) (1 R 2 / 2) 6 Z 0.5 6 Z1 6 Z1.5 106 Z 2 101.6 Z 2 0.8055, R2 11.11% The zero rates maturity 0.50 1.00 1.50 2.00 zero rates (%) 10.75 10.82 10.97 11.11 Andrei Simonov - debt and money markets 57 Arbitrage free pricing of Treasuries Example: Suppose you observe the following bond prices. Calculate the spot rates and the price of the zero with 1-year to mature. Bond maturity coupon price A 0.5 8.00 100.97 B 1.00 6.00 99.96 104 Z 0.5 100.97 Z 0.5 0.9709 3 Z 0.5 103 Z1 99.96 Z1 0.9422 zero1 100 Z1 $94.22 Arbitrage opportunity: a possibility to make some positive cash flow with no possibility of a negative cash flow – A free lunch! Arbitrage free pricing principle: the bond markets are efficient enough to eliminate arbitrage opportunities – This implies that identical cash flows must have the same price. If not, someone could buy the cheaper flow and short sell the more expensive one. This is an arbitrage opportunity Andrei Simonov - debt and money markets 58 Arbitrage free pricing of Treasuries Q: What will happen if the one year zero is selling at $96.00 now? This means there is an arbitrage opportunity that we can explore. We want to find a combination of security Bond A and B such that we can replicate the cash flow of a one year zero. We will then buy this synthetic security and short the zero. w1 104 w2 3 0 w1 0 w2 103 100 w2 0.9709, w1 0.0280 In other words we can short sell 0.028 of bond A and buy 0.9709 of bond B. In the meantime we short sell one year zero. Trade short 0.028 of A buy 0.9709 of B short 1 of 1-year zero total Cash Flow now 2.83 -97.05 96 1.78 6 mo. -2.91 2.91 0 0 Andrei Simonov - debt and money markets 12 mo. 0 100 -100 0 59 Arbitrage free pricing of Treasuries Q: What will happen if the one year zero is selling at $90.00 now? This means there is an arbitrage opportunity that we can explore. We want to find a combination of security Bond A and B such that we can replicate the cash flow of a one year zero. We will then short this synthetic security and buy the zero. w1 104 w2 3 0 w1 0 w2 103 100 w2 0.9709, w1 0.0280 In other words we can buy 0.028 of bond A and short 0.9709 of bond B. In the meantime we buy one year zero. Trade buy 0.028 of A short 0.9709 of B buy 1 of 1-year zero total Cash Flow now -2.83 97.05 -90 4.22 6 mo. 2.91 -2.91 0 0 Andrei Simonov - debt and money markets 12 mo. 0 -100 100 0 60 Bootstrapping Bonds that can be used for bootstrapping are – On-the-run Treasury issues » Include the 3-month, 6-month, and 1-year Treasury bills, the 2-year, 5year, 10-year notes, and 20-year bonds. » Bonds that are not on-the-run are called off-the-run. – On-the-run Treasury issues and selected off-the-run Treasury issues » Do not have enough on-the-run securities » Problem of on-the-run securities Sometimes too expensive (yields too low because of high liquidity). – All Treasury issues – Treasury strips » Easy Par yield curve – Easy, but cannot be used to price other securities Only zero rate curve is usually used to price bonds. Andrei Simonov - debt and money markets 61 Term structure of interest rate If we have the term structure of spot rates, we can calculate the price of any treasury securities. But why do we go through this trouble of bootstrapping? Why not just use STRIP prices? – STRIPs are not as liquid » There is a liquidity spread – The demand varies for different maturity of STRIPs – STRIPs are taxed differently from the coupon bonds – All of these might work to distort the relationship between STRIP and bonds Andrei Simonov - debt and money markets 62