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# Year Bond Semiannual Coupon Annum

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2) An airline knows that it will need to purchase 20,000 metric tons of jet fuel in three
months. It wants some protection against an upturn in prices using futures
contracts. The company can hedge using heating oil futures contracts traded on
NYMEX. The notional for one contract is 42,000 gallons. There is no futures
contract on jet fuel, the risk manager wants to check if heating oil could provide an
efficient hedge. The current price of jet fuel is \$300/metric ton. The futures price
of heating oil is \$0.7/gallon. The standard deviation of the rate of change in jet
fuel prices over three months is 20%, that of futures is 15%, and the correlation is
0.8.
a) You decide to hedge your price exposure. What is your optimal strategy?
Explain.
b) What are the payoffs of hedging?

3) Assume today is September 9, 2009. Today's close price of the MSFT share is
\$35. The risk-free interest rate is 5% per annum, continuously compounded.
Consider a six-month forward contract to purchase the stock.
a) What is the forward price, assuming zero dividends?
[Hint. To calculate the forward price, set up two strategies and then make
use of the arbitrage principle].
b) If the 6-month forward price is \$35.5, what is the implied continuously
compounded dividend yield? What is the forward and annualized forward
c) One month later, the price of the stock is \$40 and the risk-free interest rate
declined to 4.0% per annum. What is the forward price? [Hint. Once
again, to calculate the forward price, set up two strategies and then make
use of the arbitrage principle].
d) What is the value of a long position in the original forward contract?

4) Compute Macaulay and modified durations for the followings bond?
a) A 5-year bond paying annual coupons of 4.432% and selling at par?
b) An 8-year bond paying semiannual coupons with a coupon rate of 8% and a
yield of 7%.
c) A 10 year bond paying annual coupons of 6% with a price of \$92 and face
value of \$100.

8) Suppose that in order to hedge interest rate risk on your borrowing, you enter into
an FRA that will guarantee a 6% effective annual interest rate for 1 year on
\$500,000,000.00. On the date you borrow the \$500,000,000.00, the actual interest
rate is 5%. Determine the dollar settlement of the FRA assuming
a) Settlement occurs on the date the loan initiated
b) Settlement occurs on the date the loan is paid.

9) Suppose the September Eurodollar futures contract has a price of 96.4. You plan to
borrow \$50m for 3 months in September at LIBOR, and you intend to use the
Eurodollar contract to hedge your borrowing rate.
a) What rate you can secure?
b) Will you be long or short the futures contract?
c) How many contracts will you enter into?
d) Assuming the true 3-month LIBOR is 1% in September, what is the settlement
in dollars at expiration of the futures contract?

10) The current price of oil is \$83.27 per barrel. Forward prices for 3, 6, 9, and 12
months are \$87.24, \$88.82, \$89.70 and \$90.66. Assuming 2% compounded annual
risk-free rate, what is annualized lease rate for each maturity? Is this an example of
contango or backwardation? (Lease rate can be considered as the negative of
storage cost)

5) The following table gives the price of bonds
The following table gives the price of bonds
a) Calculate the zero rates for maturities 0.5, 1.0, 1.5 and 2.0 years. Comment on
b) What are the forwards rates for the periods: 6 months to 12 months, 12 months to
18 months, 18 months to 24 months? Comment on your results.
c) Estimate the price and yield of a 2-years bond providing a semiannual coupon of
7% per annum.
d) Assume that the zero rates you computed in part a) are bond yields. Describe and
discuss the shape of the yield curve.

Bond Principal Time to Maturity (years) Annual Coupon (\$) Bond Price (\$)
100 0.5 0 98
100 1 0 95
100 1.5 6.2 101
100 2 8 104

#### Solution Preview

Hi,

2. We have,
Amount of jet fuel to be purchased=20,000 metric ton
Notional for one contract of heating oil=42,000 gallon
Current price of Jet fuel=\$300 metric ton
Future price of heating oil=\$0.7 gallon
Standard deviation of jet fuel price=20%
Standard deviation of future price=15%
Correlation=0.8
So hedge ratio is:

Or,

(a) As per the optimal strategy the number of contracts to be purchased is:
As we know that,

So,

So the Airlines have to purchase 156 ...

#### Solution Summary

The expert estimates the price and yield of a 2 year bond providing a semiannual coupon. Zero rates are also computed.

\$2.19