Week 4 Fin 603

1. Week 4 Fin 603 U.S. Treasury Securities:Bills, STRIPS, Notes, Bonds, and TIPS

2. (13-week and 26-week) U.S. Treasury Bills • Short-term securities issued by the U.S. Treasury to finance the national debt • As good as cash for many purposes • Margin in brokerage accounts • Transfer of funds between corporations • Extremely liquid • Easy to purchase electronically • Easy to buy and sell through brokers & dealers • Easy to lend to others for short periods of time (repurchase agreements or repos) Professor Ross Miller • Fall 2005

3. Continuous T-Bill Quotes from Bloomberg(Free) Professor Ross Miller • Fall 2005

4. Daily T-Bill Quotes from eSpeed from the Wall Street Journal(subscription required) Market Close 9/9/2005 Professor Ross Miller • Fall 2005

5. Why T-Bills Can Pay Less Interest Than Eurodollars • Exempt from state and local taxes • The U.S. Treasury is considered the least risky financial institution in the world (the top credit rating is AAA, the U.S. Treasury is considered by some to be AAAA) Professor Ross Miller • Fall 2005

6. T-Bill Yields are Quoted Using the Same Method as Commercial Paper • At a discount from face value • Using a 360-day year Professor Ross Miller • Fall 2005

7. Let’s See What It Costs to Buy $10,000 Face Value of The T-Bill That Matures in 45 Days • The ask yield is 3.25% • Based on a 360-day year, 45 days is 1/8 of a year • The “discount” for the bond is 1/8 x 3.25% = 0.40625% • Applying the discount to $10,000 gives .0040625 x $10,000 = $40.625 (rounded up to $40.63) • The final cost is $10,000 – $40.63 = $9,959.37 Professor Ross Miller • Fall 2005

8. Microsoft Excel Note • Excel contains various T-Bill functions • TBILLYIELD (computes discount yield) • TBILLPRICE (compute T-bill price) • TBILLEQ (computes effective yield) • There are similar Excel function for other Treasury securities and bonds in general, you are free to explore them on your own • In practice, services like Bloomberg provide these automatically to professional Professor Ross Miller • Fall 2005

9. The TED (Treasury-Eurodollar) Spread • The difference in yield between the three-month Eurodollar (LIBOR) and the three-month T-bill • The TED spread is considered a credit-risk indicator and is easy to trade with futures • Example from 9/9/2005 • 3-month Eurodollar yield: 3.85% • 3-month (90-day) T-bill yield 3.48% • TED spread is 37 b.p. • Why? 3.85% – 3.48% = 0.37% (also known as 37 basis points—written 37 b.p. and pronounced “37 bips”) Professor Ross Miller • Fall 2005

10. Repurchase Agreement (Repo) • Deals with the problem that T-bills are only issued every 7 days • To create a “custom maturity” for a T-bill, a dealer will “rent it out” for the desired period of time, often just overnight • The actual mechanics are that the dealer sells the T-bill and agrees to “repurchase” it on a specified date at a higher price • The “renter” is said to have a reverse repurchase agreement and has the T-bill as collateral • T-bills are not the only securities that are “repoed,” but are the most popular Professor Ross Miller • Fall 2005

11. Anatomy of a 5-year Treasury Note with a 3.50% Coupon Rate $1,000 Principal Payable 8/15/09 $17.50CouponPayable2/15/07 $17.50CouponPayable2/15/05 $17.50CouponPayable8/15/05 $17.50CouponPayable2/15/06 $17.50CouponPayable8/15/06 $17.50CouponPayable8/15/08 $17.50CouponPayable2/15/09 $17.50CouponPayable8/15/09 $17.50CouponPayable8/15/07 $17.50CouponPayable2/15/08 Professor Ross Miller • Fall 2005

12. Treasury STRIPS • Stands for Separate Trading of Registered Interest and Principal of Securities and is an example of a “pure discount bond” • They are the principal and coupon payments “stripped” from U.S. Treasury notes and bonds • Treasury notes and bonds can be “reconstituted” from STRIPS • They generate cash flows like T-bills; however, they can have maturities out as far as 30 years Professor Ross Miller • Fall 2005

13. More on Treasury STRIPS • Two differences from Treasury bills • Quoted as a price rather than as an annualized discount • Even though payments are only made on maturity, taxes are assessed annually on the accrued interest • Often referred to as “Treasury zero-coupon bonds” or “Treasury zeroes” and treated like original-issue discount (OID) securities • Created in 1985 by U.S. Treasury in response to separate trading of treasury security principal and interest developed by securities firms, most notably Merrill Lynch Professor Ross Miller • Fall 2005

14. The Three Types of STRIPS • ci – Coupon Interest: Coupon payment from either a note or bond • np – Note Principal: Principal payment from a specific Treasury note (a Treasury security issued with a maturity of 2 to 10 years) • bp – Bond Principal: Principal payment from a specific Treasury bond (a Treasury security issued with a maturity of more than 10 years) Professor Ross Miller • Fall 2005

15. CUSIPs • They are lots of STRIPS, sometimes several with the same maturity date, so there has to be an easy way to tell them apart • CUSIPs are unique securities identifiers that not just Treasury STRIPS, but all securities are assigned • They are the industry standard way to identify fixed-income securities • Although stocks and mutual funds also have CUSIPs, ticker symbols (like GOOG for Google) are more commonly used to identify them Professor Ross Miller • Fall 2005

16. Getting Prices for STRIPS • Although easy to buy and sell from major brokers, they are difficult to get quotes on • Yahoo! Finance has quotes through its bond screener (simply check “Treasury Zero Coupon” and then click on the “Find Bonds” button); however, those prices are highly unreliable • The Wall Street Journal only prints those with maturities of ten years or less and has nothing online • STRIPS are usually quoted in 32nds Professor Ross Miller • Fall 2005

17. Quotes for 9/16/2005 from the Wall Street Journal Print Edition Professor Ross Miller • Fall 2005

18. A Detailed Look at a STRIPS Quote (Feb 06) Matures February 15, 2006 (ci) Is a coupon payment (Bid 98:19 and Ask 98:19) Has both a bid and ask price of 98 and 19/32, which is 98.59375 (Yld 3.50) Has a yield (calculated on a bond-equivalent basis) of 3.50% Note: The maturity price is 100 Professor Ross Miller • Fall 2005

19. Quotes From the Bottom of the 9/16/05 Table Professor Ross Miller • Fall 2005

20. Rule of 72 • For bonds with “normal” interest rates, the time it takes to double money is approximately 72 divided by the interest rate in percentage terms • Examples of this “rule”: • At a 10% APY, it takes about 7.2 years for money to double • Conversely, if you want your money to double in 10 years, you need to receive an APY of approximately 7.2% Professor Ross Miller • Fall 2005

21. General Formula for Valuing Pure Discount Bonds with T Years to Maturity • F is face value (same as the FV we used before) • T is time (in years) to maturity and can include fractional year—10 years and 2 months (the time until expiration for the Nov 2015 STRIPS would give T=10.1666… Professor Ross Miller • Fall 2005

22. Calculating the PV for a STRIP with r = 4.43% and T = 10.1666 PV = F/(1+r)T = 100/(1+0.0443)10.1666 = 100/1.5538 = 64.36 Notice that this does not match the ask price of 64:04, which is 64 4/32 or 64.125. This is because yields on STRIPS are quoted so that they are comparable to bonds that pay interest semi-annually Professor Ross Miller • Fall 2005

23. Yield to Maturity (Sneak Preview) • Since bonds trade based on prices, not yields, it is useful to be able to compute a bond’s yield from its price, time to maturity, and par (or redemption) value • For simple values of T (1 year or 2 years) the yield can be found directly from the pure discount bond formula (or using logarithms for less simple values) • For bonds with coupon payments, no direct formula is available Professor Ross Miller • Fall 2005

24. The “Gotcha” with STRIPS • STRIPS would appear to be an ideal tax shelter—no taxable interest, just a giant capital gain at maturity • The IRS figured this angle out some time ago • All OIDs (original-issue discount bonds) have their discount amortized over the life of the bond • This is the worst of both worlds, the only cash flow you get is at maturity, but you are taxed on annual basis for cash you do not receive • STRIPS are mainly useful for tax-sheltered or foreign investments Professor Ross Miller • Fall 2005

25. Why STRIPS are So Important • Using STRIPS financial institutions can create risk-free securities with any sequence of cash flows that they or their clients desire • There are other ways to approximate securities using duration and convexity analysis (we will get to this), but STRIPS replicate risk-free cash flows exactly Professor Ross Miller • Fall 2005

26. The Sensitivity of STRIPS Prices to Changes in Interest Rates • Like all bonds, the value of a STRIP goes down when interest rates increase and goes up when they decrease • As the time to maturity (T) of a STRIP increase, so does its sensitivity to changes in interest rates • This is a direct consequence of the formula for the pure discount bond formula—higher values of T means bigger changes in PV for the same change in r Professor Ross Miller • Fall 2005

27. An Overview of the Bond Markets • A bond is a promise to make periodic coupon payments and to repay principal at maturity—breech of this promise is an event of default • Bonds carry original maturities greater than one year, so bonds are instruments of the capital markets • Bonds issued with maturities of 10 years or less are sometimes called notes • Issuers are corporations and government units Professor Ross Miller • Fall 2005

28. Bonds are Bundles of Cash Flows • Bonds can be viewed as a “bundle” of zero-coupon securities—Treasury bonds are literally bundles of STRIPS • New cash flow scheme • Cash flows out now to buy the security • Cash flows in several times until the security matures • Later, we will incorporate options that can accelerate the payments at the borrower’s discretion Professor Ross Miller • Fall 2005

29. Treasury Notes and Bonds • T-notes and T-bonds issued by the U.S. Treasury to finance the national debt and other federal government expenditures • Backed by the full faith and credit of the U.S. government and are essentially default risk free • Have significant interest-rate risk due to their longer maturities • Pay interest twice a yield (interest payments are at half the “coupon rate”) Professor Ross Miller • Fall 2005

30. Anatomy of a 5-year Treasury Note with a 3.50% Coupon Rate $1,000 Principal Payable 8/15/09 $17.50CouponPayable2/15/07 $17.50CouponPayable2/15/05 $17.50CouponPayable8/15/05 $17.50CouponPayable2/15/06 $17.50CouponPayable8/15/06 $17.50CouponPayable8/15/08 $17.50CouponPayable2/15/09 $17.50CouponPayable8/15/09 $17.50CouponPayable8/15/07 $17.50CouponPayable2/15/08 Professor Ross Miller • Fall 2005

31. “On-the-Run” (Most Recently Issued)Treasury Notes and Bonds on 9/21/2005 Professor Ross Miller • Fall 2005

32. Bond Complications • Bond prices are given using a par value of 100 • Bonds are traded in multiples of $1,000, so “one bond” typically represents a principal amount of $1,000 • While Treasury securities do routinely trade in multiples of $1,000, many corporate bonds only trade in multiples of $1,000,000 or $5,000,000 • Like STRIPS, quotes are normally in 32nds Professor Ross Miller • Fall 2005

33. What Is Easy and What Is Difficult about Bonds • Finding a present value (PV) is easy • The present value of the bond is just the sum of the present values of every cash flow it generates • With regular coupon payments, annuity factors make this a snap to do • Finding the future value (FV) is difficult • The obvious point in time to seek an FV for the bond is at its maturity • The problem is what happens to all the cash flows received before then • This problem is known as “reinvestment risk” and certain assumptions (often unrealistic) are used to attempt to deal with it Professor Ross Miller • Fall 2005

34. Why Care About This? Does It Matter? Professor Ross Miller • Fall 2005

35. Another Difficulty: Bond Yield • For a zero-coupon bond, one can find an APY (annual percentage yield) by solving FV=PV(1+r)T for r, which gives: r = (FV/PV)(1/T)– 1 • With multiple cash flows, there is no general formula • One can use Excel’s (or a financial calculator’s) IRR or YIELD function to compute a yield to maturity (and this is standard practice), but yield to maturity assumes that all cash flows can be reinvested at that yield Professor Ross Miller • Fall 2005

36. Current Yield vs. Yield to Maturity • Current Yield = Annual Coupon Payment/Price • Example in BKM, Chapter 14 • 8% coupon, 30-year bond, price=$1,276.76 • Current yield = $80/$1,276.76 = 6.2659% • The problem is that in 30 years the bond matures at $1,000, so $276.76 is being lost over the 30 years and should be reflected in the yield Professor Ross Miller • Fall 2005

37. Current Yield vs. Yield to Maturity (continued) • Yield to maturity is a way of adjusting yield to account for the expected gain or loss in the bond over its lifetime • In the case of the textbook 30-year bond example, the yield to maturity is the value of r that solves: Professor Ross Miller • Fall 2005

38. Realized Compound Yield • BKM shows how to compute the realized compound yield, which takes into account the projected reinvestment rates for the bond • This computation is not frequently used in practice because no one knows what those reinvestment rates are ahead of time with any accuracy Professor Ross Miller • Fall 2005

39. Par, Premium, and Discount Bonds • Bonds that trade at 100 are trading at par • Their yield to maturity is the same as their coupon rate • Bonds that trade above 100 are trading at a premium to par • Their yield to maturity is less than their coupon rate because receiving less than the bond’s price at maturity diminishes the interest payments • Bonds that trade below 100 are trading at a discount to par • Their yield to maturity is more than their coupon rate because receiving more than the bond’s price at maturity supplements the interest payments Professor Ross Miller • Fall 2005

40. Computing a Bond’s Price from Its YieldStep 1: Listing the Cash Flows • We will assume (for now) that the first interest payment occurs in ½ year from now • An easy example: 4% coupon rate that matures in 1 year • Just two cash flows: • $2 in ½ year (all interest) • $102 in 1 year ($2 interest + $100 principal) Professor Ross Miller • Fall 2005

41. Computing a Bond’s Price from Its Yield:Step 2: Get An Interest Rate • Bond payment periods are at ½-year intervals, so use a ½-year (or semiannual) interest rate (but it is usually stated as an annual rate, that is then halved) • Suppose the rate is quoted as 5.00% annually, but is really 2.50% semi-annually Professor Ross Miller • Fall 2005

42. Computing a Bond’s Price from Its Yield:Step 3: Discount the Cash Flow and Add Up • The first cash flow is $2, so discounted at 2.5%, it is worth $2/(1.025) = $1.9512 • The second cash flow is $102, so discounted at 2.5% (twice), it is worth $102/(1.025)2 = $97.0851 • Add them together to get the bond’s value:$1.9512 + $97.0851 = $99.0363 or about $99.04 • Notice that because the yield is above the coupon rate, the bond trades at a discount Professor Ross Miller • Fall 2005

43. The General Bond Valuation Formula Annuity Factor PV Factor Professor Ross Miller • Fall 2005

44. Comments on the Bond Pricing Formula • Reminder: r is semiannual rate • The second term is simply the pure discount bond formula where T is measuring in half-years • The first term can be derived using a trick that is explained in the textbook • If the coupon payment is received forever (in perpetuity), the present value of that perpetual stream of cash flows is Coupon. r • We then subtract off the present value of a perpetuity that begins in T periods Professor Ross Miller • Fall 2005

45. Standard Treasury Bonds are Fixed-Rate Bonds • The price of Treasury bonds and other bonds with fixed coupon rates moves inversely with interest rates • Rates up, bonds down • Rates down, bonds up • If the coupon rate were to adjust itself to prevailing interest rates, the price of the bond would remain relatively stable • We will cover such “floating-rate” bonds next time Professor Ross Miller • Fall 2005

46. Wait! There’s More! • Quoted bond prices (such as those on Bloomberg on in the Wall Street Journal) do not include accrued interest since the last coupon payment • This is known as the “clean price” • Adding in the accrued interest gives the “dirty price” (also known as the sale or invoice price), which is what is really paid for the bond Professor Ross Miller • Fall 2005

47. Computing Accrued Interest Accrued Interest = INT x Actual days since last coupon payment 2 Actual days in coupon period • An example: 5.875% coupon rate,81 days since last coupon payment and 184 days in coupon period:Accrued interest = (5.875%/2) x (81/184) = 1.29314% Professor Ross Miller • Fall 2005

48. Getting the Dirty Price Dirty Price = Clean Price + Accrued Interest • Suppose the bond with the 5.875% coupon rate trades at 101-11, which is 101.34375% of face value, so Dirty price = 101.34375% + 1.29314% = 102.63689% Professor Ross Miller • Fall 2005

49. TIPS(Treasury Inflation-Protected Securities) • Treasury securities with a guaranteed coupon payment and a floating coupon payment tied to the CPI-U (Urban Consumer Price Index) • These the securities indicated with an “i” in the Wall Street Journal notes and bonds table • The difference between the yield to maturity of a regular Treasury securities and the TIPS with approximately the same maturity provides an indication of expected inflation Professor Ross Miller • Fall 2005

50. TIPS from Bloomberg Professor Ross Miller • Fall 2005