Finance

1. 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

2. 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

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5. Not the whole picture… Andrei Simonov - debt and money markets

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7. Euro Area interest rates Andrei Simonov - debt and money markets

8. 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

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12. 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.

13. 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%.

14. 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

15. 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.

16. 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 bond-equivalent yield so that their rates can be compared to each other on a common basis.

17. 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.

18. 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.

19. 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%:

20. 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%: • Thus, the yield for a portfolio of bonds is not simply the average of the YTMs of the bonds making up the portfolio.

21. Federal Marketable Debt: July 31, 10 Source: Board of Governors of the Federal Reserve System, to http://www.treasurydirect.gov/govt/reports/pd/mspd/2010/opds072010.pdf

22. 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

23. 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

24. List of primary dealers as of Sept 2010 Federal Reserve Bank of New York: www.newyorkfed.org/markets/pridealers_listing.html BNP Paribas Securities Corp.Banc of America Securities LLCBarclays Capital Inc.Cantor Fitzgerald & Co.Citigroup Global Markets Inc.Credit Suisse Securities (USA) LLCDaiwa Capital Markets America Inc.Deutsche Bank Securities Inc.Goldman, Sachs & Co.HSBC Securities (USA) Inc.Jefferies & Company, Inc.J.P. Morgan Securities LLCMizuho Securities USA Inc.Morgan Stanley & Co. IncorporatedNomura Securities International, Inc.RBC Capital Markets CorporationRBS Securities Inc.UBS Securities LLC. Andrei Simonov - debt and money markets

25. 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

26. 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’ Mozeradmitted 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

27. 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

28. Price yield relationship Assume the coupon rate is a constant 10 percent. Andrei Simonov - debt and money markets

29. 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

30. Price Path of Premium or Discount Bonds over Time Price Premium Bond Par Bond Par value Discount Bond Time to Maturity 0

31. 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: • Default Risk • Call Risk • Market Risk

32. 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)

33. Highest Default Probabilities Entity Name Mid Spread CPD (%) Venezuela 1338.03 59.50 Greece 876.62 51.45 Pakistan 840.30 43.21 Argentina 850.28 42.91 Ukraine 547.63 31.24 Ireland 364.86 26.48 Dubai/Emirate of 449.51 26.26 Iraq 422.20 25.14 Portugal 323.43 23.92 California/State of 289.14 22.13 Andrei Simonov - debt and money markets

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37. 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.

38. 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

39. US Treasury bonds calls since 20000 Andrei Simonov - debt and money markets

40. Call Risk Premium Call Risk Premium:

41. Valuation of Callable Bonds • When valuing a callable bond, one needs to take into account the possibility that interest rates could decrease, leading to the bond being called. If called, the bond's cash flow patterns would be different than if rates increased and the bond was not called. • Given the uncertainty of the bond's cash flows, valuing callable bonds and other bonds with embedded option features is more difficult than valuing option-free bonds.

42. Valuation of Callable Bonds • One approach to valuing callable bonds is to incorporate interest rate volatility by using a binomial interest rate tree. • Another valuation approach is to determine the value of the call feature. Conceptually, when an investor buys a callable bond, she implicitly sells a call option to the bond issuer, giving the issuer the right to buy the bond from the bondholder at a specified price before maturity.

43. Valuation of Callable Bonds • Theoretically, the price of a callable bond, PC, should therefore be equal to the price of an identical, but noncallable bond, PNC, minus the value of the call feature or call premium, VC. • The value of the call feature can be estimated using the option pricing model developed by Black and Scholes.

44. 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.

45. 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.

47. Market Risk

48. 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.

49. Reinvestment risk • Suppose you are an investor that is willing to hold bonds for 5 years, and try to choose among the following bonds: • 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? • Step 1: the future value of coupons 3 years later is • Step 2: the price of the bond 3 years later is • Step 3: The total return is Andrei Simonov - debt and money markets