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PROJECT Principles of Investments Learning Exercise 2 Bond Concepts N. Gershun Part 1: Theoretical Problems 1. Suppose that the price of discount (zero coupon) bonds maturing in years 1, 2, 3, 4, and 5 are given (respectively) by Price Time to Maturity 940 1 870 2 800 3 715 4 630 5 Consider the following risk-free investments. Which is best? T=0 1 2 3 4 5 Investment A -40 20 15 10 5 1 Investment B -10 1 5 10 15 20 2. Three zero coupon risk-free discount bonds of one, two and three year term to maturity are selling for, respectively, $950, $890 and $800. What would be the selling price today of a 10% coupon bond of 3 year maturity (maturity value $1,000)? 3. Consider a coupon bond, with the current period t = 0 market price $900, with payments: 1 2 3 50 50 1050 Discount (zero coupon) bonds of 1, 2 and 3 years maturity (all with maturity value of $1000) sell for respectively, 960, 900, 820 dollars. Is this coupon bond properly priced? If not, design an arbitrage argument to profit by the mispricing. 4. The prices of discount bonds (all with maturity value of $1,000) maturing in years 1, 2, 3, 4, 5 are given below. Price Time to Maturity 920 1 860 2 790 3 700 4 600 5 What is the yield to maturity on a risk-free 5% bond due in 5 years (also with maturity value of $1,000)? Part 2 – Empirical Investigation of the Term Structure of Interest Rates Prior to working on this part of LE 2, you need to: a. Study lectures 2A and 2B b. Study a Review file c. Watch a video with the Excel example of Bootstrapping d. Explore the Excel file used in this video Step 1: Data Download data on prices, times to maturity and coupon rates for SIX government bonds maturing in consecutive six-month intervals. Make sure that the accrued interest on the bonds, which you select, is as small as possible. Recall that Treasury bonds pay coupons either on the 15th of the month or on the last day of the month every six months. For example, if today’s date is June 5, 2020 and you decide to download data for your bonds today, the first bond on your list should mature on November 30, 2020, the second bond --on May 31, 2021, the third bond on November 30, 2021, etc. These bonds paid their coupons on May 31st, i.e. just five days ago. The accrued interest on these bonds is negligible and you can ignore it in your calculations. If you choose bonds that mature either on June 15th of any year or December 15th of any year, these bonds will pay their next coupon on June 15, 2020, i.e. in ten days. The accrued interest on these bonds is very large and cannot be ignored. The best source of data for this project is Bloomberg. If you are unable to use Bloomberg, use Wall Street Journal data: https://www.wsj.com/market-data/bonds/treasuries Step 2: Calculations Using the bootstrapping method, calculate the first six elements of the term structure of interest rates. Remember, that US Treasury bonds pay semi-annual coupons and you need to adjust your calculations to take semi-annual coupons into account. The technique is exactly the same as with annual coupons, but your time period is six months. You will find semi-annual rates. Annualize the rates. In your report for this part of the LE. You essentially need to replicate the example in the video and the corresponding Excel file, posted on Bb. Step 3: Deliverables: For all deliverables you need to show formulas in symbols (not Excel formulas) as is done in lectures. Then show how you plug your data into these formulas. Write short verbal comments at the end of each step. a. Show how you convert annual coupon rates into semi-annual coupon payments in dollars. b. Show how to convert the ask price (you need to use the ask price for this project) from ticks into the dollar price. c. Create a time line (it will be a triangular table with each row showing cash flows of one bond). d. Show all your calculations for each of the six rates; include formulas and show how you plugged in your data into these formulas. You can use Equation Editor in Word to type any formula. e. Attach printouts with your data from Bloomberg or WSJ to your report as an Appendix. 1. Using Excel Chart menu, draw the graph of the term structure, with time periods on the horizontal axis and term structure rates on the vertical axis. Is the term structure currently increasing or decreasing? Discuss briefly. 2. Briefly comment on the information that the observed term structure implies for economic conditions, as perceived by market participants. Show all your calculations, including all regular (not Excel) formulas, graph and explanations. Report (including all the equations) should be typed. Corporate Finance Introduction to Fixed Income Securities Lecture 2A https://www.google.com/url?sa=i&source=images&cd=&ved=2ahUKEwj2t7722v_mAhUJU98KHWP8B24QjRx6BAgBEAQ&url=http%3A%2F%2Fglobalwealthpartnersinc.com%2Fwealth-management%2Ffixed-income%2F&psig=AOvVaw376XLNR8JW_HA548uSMwZ4&ust=1578974896400273 Plan for This Part of the Lecture I. Introduction to the terminology and conventions surrounding bonds, especially U.S. Treasury securities. II. Zero coupon bonds and coupon bonds III. Strips IV. Bond quotes https://www.google.com/url?sa=i&source=images&cd=&ved=2ahUKEwjQ04q2pe7mAhVNTd8KHff3DLEQjRx6BAgBEAQ&url=https%3A%2F%2Fwww.treasurydirect.gov%2Ftimeline.htm&psig=AOvVaw2Wp5JAa7oQ3joL7kZCj_U3&ust=1578376438798617 https://www.google.com/url?sa=i&source=images&cd=&ved=2ahUKEwiLqIz0pu7mAhWBhOAKHSshDBsQjRx6BAgBEAQ&url=https%3A%2F%2Fwww.amazon.com%2FBoeing-Company-Bond%2Fdp%2FB074B5NWDW&psig=AOvVaw20pcKRj8fMY3d3SfG2lo0L&ust=1578376885653130 https://www.google.com/url?sa=i&source=images&cd=&ved=2ahUKEwjz_s3U3v_mAhWFneAKHV8WATYQjRx6BAgBEAQ&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DSWN2Y3xx7yo&psig=AOvVaw3dj4Zy-_F7E8QZg9vh74Je&ust=1578975996364338 What Are “Fixed Income Securities”? These are securities or agreements that generate contractually guaranteed (legally enforceable to at least some extent) future payments More typically, “Fixed Income” represents the market for borrowing and lending. It includes: Bank loans and deposits Bonds Derivatives written on these instruments. What Are Bonds (Fixed Income Securities)? Bonds are securities that promise to pay: Regular fixed coupon payments (every six months, or every year, or every quarter) The principal value or face value at maturity Cash flows are all contracted (but not always riskless) Different type of issuers Governments (U.S., Germany, France, etc…) Corporations (GE, Ford, etc …) Agencies (Fannie Mae, Freddie Mac…) Municipalities (New York City, etc…) Why Understanding Bonds and Their Pricing is Useful for Valuation Data on Government bonds are used to determine risk-free rates, yield curve, the effects of inflation expectations and growth. Firms often issue corporate bonds to fund their own investments. The return on corporate bonds is one of determinants of Cost of Capital Who Issues Bonds in the U.S.A.? Type of Bonds Issuer Municipal States and localities Agencies and GSE’s (Government Sponsored Enterprises) Fannie Mae, Freddie Mac, Farm Credit System, Tennessee Valley Authority Treasury U.S. Federal Debt Corporate U.S. and foreign corporate issuers Money Market Commercial paper Asset Backed Mortgages, credit card balances, student loans, airplane loans, etc., are aggregated into portfolios. Fractions of these portfolios are then sold to investors. “Fannie Mae” and “Freddie Mac” issue most mortgage backed securities although, until recently, the big investment banks did so as well. The individual securities in the portfolios would not otherwise trade because the informational requirements are too great. But when packaged together in large numbers statistical averages dominate to reduce risk. Insurance Companies 18% Mutual funds 15% Foreign Investors 15% Pension Funds 12% Financial Institutions 12% Households 12% Other (industrial companies) 16% Who Owns Bonds? Cash Flow Pattern of a Typical Bond Units of time (∆?) ∆? = 0.5 year (6 months) pretty much everywhere, but Europe. ∆? = 1 year for Euro-denominated bonds (especially France, Germany) ? = ? 1 2 3 …. T −?0 ? ? ? ? +??? Price Today Coupons Maturity Value or Face Value or Par Value U.S. Treasury Securities: Terminology Maturity: T- Bills: Maturity less than 1 year, zero coupon (discount) bonds, only face value T- Notes: Maturity 1 – 10 years, coupons and face value T- Bonds: Maturity 10 – 30 years, coupons and face value Some T-Bonds are callable – can be bought at pre- fixed price and a pre-specified date Face value (maturity value or par value): amount the bond will pay back at its maturity date (in addition to final coupon) Think of this as repayment of principal Bond prices are quoted per $100 of face value U.S. Treasury Securities: Terminology Coupon and coupon rate: Yield to Maturity (YTM): is the IRR of the bond, annualized. To find YTM for U.S. Treasury bonds, which pay semi-annual coupons solve the following equation: 10 ?????? ???? = ??????? ???? ??? ???? (?? $) ???? ????? ?? ?ℎ? ???? ?0 = ???? − ?????? ?????? ൗ??? 2 1 − 1 1 + ൗ??? 2 2×? + ???? ????? 1 + ൗ??? 2 2×? Bond Yields: An Example US Treasury Bond with a coupon rate 3.875% due in exactly two years from now The coupons are paid semi-annually The current market price of this bond is 99 11/32 (bond prices are expressed per $100 of face value) What is its YTM? ???? − ?????? ?????? = 0.03875 × 100 2 = $1.9375 Time 0 (now) 1 2 3 4 -99.3438 1.9375 1.9375 1.9375 101.9375 Bond Yields: Examples To find the bond’s YTM, solve: for Τ??? 2 You can use the Goalseek in Excel to find Τ??? 2 = 2.11% Convert to an annual rate: ??? = 4.22% Concept Check: What happens to the price of a bond if interest rates increase? 99.3438 = 1.9375 ൗ??? 2 1 − 1 1 + ൗ??? 2 4 + 100 1 + ൗ??? 2 4 YTM Calculation: An Example 13 You can also use the IRR function in Excel to find the semi- annual rate Τ??? 2 and then annualize the rate by multiplying it by 2. We always report the annualized return YTM as a Measure of Return on a Bond 14 Under what circumstances is the yield-to-maturity a good measure of the returns on a bond earned by the investor? This will be so only provided: i. Coupons are paid on time ii. All coupons are reinvested at YTM until the bond matures iii. You hold the bond to maturity. Yields, in general, will not represent the rate of return an investor will actually earn. Other names for the yield to maturity: “yield on a semiannual basis” “yield compounded semiannually” “bond equivalent yield” Bond Prices: Relationship Between Coupon and Yield If ??? = ?????? ???? the bond price is equal to the par value of the bond and