7. Bonds and Interest rates

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1 7. Bonds and Interest rates 1 2 Yields and rates I m thinking of buying a bond that has a face value of $1000, pays semiannual coupons of $40 and has 7 years to maturity. The market price is $943. Fixed income may seem boring, but it s not. It s a huge and very dynamic market. Much larger than equities. Bond traders can take on similar levels of risk and earn similar returns to equities by using leverage. Derivatives are very important in fixed income markets (used to manage risk and take on leverage). What is the coupon rate? What is the yield to maturity? what is the current yield? Par 3 Risk-free rate 4 What does it mean if I say a bond is trading at par? What is a discount bond? What is a premium bond? What is a pure discount bond? What does the term riskfree rate refer to and what does it have to do with the intertemporal rate of substitution? At a single point in time, is there only one or are there many risk-free rates? Explain.

2 Price dynamics 5 Term structure 6 Suppose I own a discount bond with 5 years to maturity. Suppose that I expect the yield to maturity to stay about the same for the near future. Would I expect the price of this bond to increase, decrease, or remain about the same over time? What is the term structure of interest rates and how does it differ from the yield curve? What is meant by an on-the-run bond? Why might US Treasury bonds with the same time to maturity but different issue dates have different yields to maturity? (How is it even possible for Treasury bonds to have the same time to maturity but different issue dates?) What is the spot rate? Forward rate 7 Pricing coupon bonds 8 What is a forward rate? Given the following prices for riskfree zero coupon bonds with face value $1000 Years to maturity price What would I expect the price to be for a riskfree bond with face value $1000, paying annual coupons of $100, and 4 years to maturity? Why?

3 Computing term structure from yield curve 9 yield curve 10 Can you compute the yields of zero coupon bonds from a collection of coupon bonds? What is an inverted yield curve? Can you compute the forward rate curve from the term structure? What does it signal about the market s expectations for future interest rates? Is it generally regarded as a bullish or bearish signal for financial markets? Why? Pricing financial assets 11 Opportunity cost of capital 12 Generally, what determines the price of any financial asset? What does the term opportunity cost of capital refer to?

4 Fed policy 13 Treasury bills, bonds and notes 14 Why does it make sense for the Fed to try to manipulate interest rates as a tool to stimulate or cool down the economy? What is the difference between a Treasury bill, bond and note? Is it possible to have a Treasury bond with seven years to maturity? Treasury bonds 15 Risk-free investing 16 Is a 30 year treasury bond risk-free? What are the main components of risk for any bond? Suppose that I want to invest some money for one month and I want to do it in the least risky way. I have the option to invest in 30 day Treasury bills, 5 year Treasury notes and 30 year Treasury bonds. Which is least risky? Which is most risky?

5 Risk-free investing 17 Total holding period return 18 Suppose I don t have quite enough cash to buy the yacht of my dreams, so I want to invest my funds in a riskfree security for two years, at which time I expect to have enough to complete my purchase. What kind of security should I use? Explain the difference in risk between investing in short term Treasury bills and rolling them over at maturity versus investing in a long-term bond. I paid $943 for a bond with 8 years to maturity paying semiannual coupons, face value of $1000 and coupon rate of 6%. I held it for one year and sold it for $970 just after it made a coupon payment. What was my total holding period return? Yields and prices 19 Interest rate risk 20 If the price of a bond increases, what happens to the yield? Between a 30 year pure discount bond and a 30 year bond with 10% coupons, if both have the same coupon rate which is riskier (assume both have no default risk)? How does this change if there is a risk of default?

6 Duration 21 Duration 22 What is meant by the duration of a bond? Why might one care? What is the duration of a bond with face value $1000, semiannual coupons of $40, YTM of 9%, and 5 years to maturity? Unequal cash flows 23 Default risk 24 An investment has an IRR of 8% and pays cash flows as follows A bond with face value $1000 and coupon rate 8% (annual coupons) has a time to maturity of 1 year, market price of $620, a 50% chance of default, and an expected collection rate of 30%. What is the expected return of this bond? Compute the NPV (can you do this without using the NPV function on your calculator?).

7 Bond pricing 25 Clean versus dirty price 26 What are the main determinants of a bond s price? What is the difference between a clean price and dirty price? Clean vs dirty (and discount vs premium) 27 Clean vs dirty price 28 The quoted price for a bond is $920. The bond pays $80 coupons. There are 180 days between the previous coupon payment and the next coupon payment. It has been 63 days since the last coupon was paid. If I buy this bond, what will the invoice price be?

8 Bond prices and stock prices 29 Yield spread 30 Stocks pay out periodic dividends, much as bonds pay out periodic coupons. Do we differentiate between clean and dirty prices for stocks? Why or why not? What is a yield spread? Yield spread 31 Yield spread 32

9 Sovereign debt 33 Investment grade 34 Suppose that a country is in danger of not being able to meet their payments on sovereign debt. What alternative do they have to going into default? What is the drawback of this? In what situation is this strategy not possible? What is the lowest rating for investment grade bonds? What is a junk bond? Why might one want to hold a junk bond??? Which are generally more volatile, investment grade or junk bonds? Bonds with very high default probabilities behave much like equity. Why is this?

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