Q1: Explain what is meant by basis risk when futures contracts are used for hedging. Next, make a comparative analysis between basis risk in futures contracts and credit risk in forward contracts. Last, compare the liquidity issue in futures and forward contracts.
Q2: A company has a USD 40 million portfolio with a beta of 1.5. It would like to use futures contracts on the S&P500 to hedge its risk. The index futures prices is currently 1,500 and each contract is for delivery of USD 250 times the index. If the company likes to minimize its risk, what is optimal hedge ratio? What is the optimal number of contracts? Last, what are the potential problems involved in the formula of optimal hedge ratio?
Q3: The following table gives the zero rates for different maturties:
|
Maturity (years)
|
Zero Rate (% cont. comp.)
|
Forward Rate (% cont. comp.)
|
|
0.5
|
5.0
|
|
|
1.0
|
5.8
|
|
|
1.5
|
6.4
|
|
|
2.0
|
6.8
|
|
a) Use the data to diagram the yield curve (i.e., zero rate curve) and explain the pattern of the yield curve using the liquidity preference theory.
b) Compute the forward rates and shows the results in the third column.
c) Describe how to determine zero rate using the data of bond price.
Q4: The S&P500 index is 2,000. The six-month risk-free rate is 2% per annum and the dividend yield over the next six months is 1.5% per annum. The nine-month risk-free rate is 5% per annum and the dividend yield over the next nine months is 1.2% per annum.
a) Estimate the futures price of the index for six-month and nine-month contracts. All interest rates and dividend yields are continuously compounded.
b) Describe how to do index arbitrage.