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23-08-2018

Product code: Accounts-AW408

 

1. Bond prices and durations (10 p): Use the information for the Finland 2001 5% 04/07/07 government bond found in the lecture  notes, except that assume that the settlement date is 21.3.2005 (use this date as "today", t = 0). That is, there are 105 days to the next coupon payment. For simplicity, assume there are no leap years

(assume a 365 day year), and that all payments are paid on weekdays such that there is exactly 1 year between all payments.

 

Also assume that the yield has remained unchanged at 3.017%

 

a. Calculate the gross price (PV) and market price for the bond.

 

b. Compare your calculated gross price as of 21.3.2005 with the gross price as of 22.1.2004 (data printed 19.1.2004, but settlement is T+3, so all numbers shown are as of 22.1.2004) and explain the difference. Note that you have used the same yield in both cases.

 

c. Calculate the duration (Macaulay duration) and modified

duration.

 

d. Explain in words what your numerical answers in c. mean to an investor.

 

2. Yield, returns, zeroes and forwards (10 p): The current yield curve for default-free zero-coupon bonds is as follows:

Maturity (Years) YTM

1 4.0

2 4.5

3 5.0

a. What are the implied 1-year forward rates?

 

b. Assume the pure expectations hypothesis (also called the unbiased expectations hypothesis, UEH) of the term structure is correct. If market expectations are accurate, what will the pure yield curve (that is, the yield to maturity on 1- and 2-year

zero-coupon bonds) be next year?

 

c. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (Hint: compute the current and expected future prices for a bond with 100 nominal value).

 

Index futures pricing & arbitrage (10 p^: The S&P portfolio pays a dividend of 1% annually. Its current value is 900. The riskfree rate is 4%. Suppose the S&P futures price for delivery in 1 year is 930. Construct an arbitrage strategy to exploit the mispricing and show that your profits 1 year hence will equal the mispricing in the futures market.

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Since future price is more than what is calculated. Hence an investor can exploit the arbitrage opportunity by borrowing 900 and enter into cureent future so as to sell it at 930 next year.

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