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Financial Economics and Capital Markets Seminar 1
发布时间：2022-01-10
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Financial Economics and Capital Markets
Seminar 1
Exercise 1
For a particular bond market, the following information is available on zero coupon bonds redeemable at a face value of £100:
|
Maturity |
Price |
Yield to maturity (YTM) |
|
1 year |
£95 |
? |
|
2 years |
£94 |
? |
|
3 years |
£88 |
4.35% |
Assume perfect capital markets, with no arbitrage opportunities and annual compounding.
a) Calculate the 1-year and 2-year yields to maturity.
b) Determine the equilibrium market price of a bond redeemable at a face value of £100 in three years that pays a coupon of 8% annually.
c) Show how to derive the yield to maturity of the bond studied in (b).
d) If the bond studied in (b) was trading in the market at a price of £115.76, what arbitrage opportunities would be available to investors? Devise a trading strategy that would generate risk-free profit.
Exercise 2
Bond X and Y are two corporate bonds, bond X pays 8% coupon rate semiannually. Bond Y pays 20% coupon rate semiannually. Both bonds have 8 years to maturity, a £100.00 par value and have an annual yield to maturity of 9%.
a) Compute the price of the two bonds
b) If the annual yield to maturity for the two bonds suddenly rises by 2%, what is the percentage price change of the two bonds?
c) What does this problem tell you about the interest rate risk (risk from unexpected changes of interest rates) of lower-coupon bonds?
d) Suppose Governor of the Bank of England announces that interest rates on short-term UK government bonds will rise next 8 years, and the market believes him. What will happen to today’s interest rate for these two 8-year corporate bonds?
Exercise 3
Assume that the annual interest rate on a one-year bond, y1, is 10% and the annual interest rate on a 2-year bond, y2, is 12%. Assume that those bonds do not pay coupons.
a) How much will you get if you invest £100 on the 2-year bond?
b) Today (Year 0) we agree that you will loan me £110 at Year 1 to be paid back with interest at Year 2. The interest rate at which I pay back the loan is called the forward rate (it is the interest rate today on a loan to be made at some future date which lasts some specified amount of time). You have £100 for a 2-year investment. Let f1,2 be the forward rate of the loan. Suppose that you invest £100 on the 1-year bond and then use the loan agreement for lending. Show how much will you get on the investment? (just give the expression, non computation)
c) What rate does the absence of arbitrage opportunities imply on the forward rate?
