1. 60 futures contracts are used to hedge an exposure to the price of silver. Each futures contract has a unit size of 5,000 ounces. At the time the hedge is closed out, the basis is $0.20 per ounce. What is the effect of the basis on the hedger’s financial position if (a) the trader is hedging the purchase of silver, and (b) the trader is hedging the sale of silver.
2. The standard deviation of monthly changes in the spot price of live cattle is (in cents per pounds) 1.2. The standard deviation of monthly changes in the futures price of live cattle for the nearby contract is 1.4. The correlation between the futures price changes and thee spot price changes is 0.7. It is now January 15. A beef producer plans to purchase 200,000 pounds of live cattle on February 15. The producer wants to use the March live cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle.
a) What strategy should the beef producer follow?
b) What proportion of the variance of monthly price changes can be eliminated by hedging?
3. An investor holds 50,000 shares of a stock, which has a market price of $30 per share. The investor wants to hedge the market risk of the stock over the next month, and decides to use the March S&P E-mini futures contract. The futures price if currently 1,500 and the multiplier the contract is $50. The beta of the stock is 1.3. What strategy should the investor follow?
4. Briefly, what are the advantages and disadvantages of a futures-contract hedge compared to a forward-contract hedge?
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5. You own 100,000 shares of the Vanguard Small Cap ETF (ticker symbol VB). The Excel file “Assignment 3 data” on the D2L Web page contains the adjusted daily closing values. The file also contains S&P 500 adjusted closing prices. We will pretend that these represent closing futures prices (the 1/29/16 closing price is $1,940.24).
Compute the optimal (minimum variance) number of futures to sell using the two methods we discussed: 1) regress returns on returns and scale by market values (the traditional approach to stock-index futures hedging); and 2) regress price changes on price changes and scale by units.
Assume that you are hedging with E-mini March S&P 500 futures, which has a $50 multiplier (i.e., a unit size of 50). Please attach the regression output and graph of the fitted regression line to your homework.
6. Suppose a 6.5-month zero coupon bond is priced at $97.625 (per $100 par) and a
9.5-month zero is priced at $96.50.
a) Find the 6.5 and 9.5 month c.c. spot yields, and the c.c. forward rate from 6.5 to
9.5 months.
b) What trading strategy would lock in the above forward rate for a three-month investment on a $50 million cash inflow expected in 6.5 months? (Be precise.)
7. Suppose the following discount bond prices (per $100 par):
maturity Price
1 year $99.005
2 years 97.824
3 years 96.464
4 years 94.933
a) What is the price of a forward contract on the 4-year discount bond with delivery in 1 year?
b) Given the forward price in (1) and the spot price, what is the implied repo rate?
c) Find the forward rate f(1,4) from the end of year 1 to the end of year 4.
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8. Find the par yield of an annual coupon bond maturing in 4 years, using the discount bond prices given in problem 7.
9. A zero coupon bond maturing in 6 months is priced at $99.005. A 3% semiannual note maturing in 1 year is priced at $100.479. A 4% semiannual note maturing in 1.5 years is priced at $101.4425. Use the bootstrap method to find the prices of discount bonds maturing in 1 year and 1.5 years.
10. Suppose that on February 15 a firm enters a (short) FRA to lend $100m for the three month period beginning on September 1 at the FRA rate of 1.5% (actual/360 day). Suppose 3-month LIBOR rate on September 1 (the settlement date) is 1.7%.
Assuming settlement in advance, what is the cash flow and when does it occur? (Note that there are 91 days from September 1 to December 1.)
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