Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
1) A company has a $36 million portfolio with a beta of 1.2. The futures price for a
contract on the S&P index is 900. Futures contracts on $250 times the index can be
traded. What trade is necessary to achieve the following. (Indicate the number of
contracts that should be traded and whether the position is long or short.)
i. Eliminate all systematic risk in the portfolio
ii. Reduce the beta to 0.9
iii. Increase beta to 1.8
2) A trader enters into a long position in one Eurodollar futures contract. How much
does the trader gain when the futures price quote increases by 6 basis points?
3) On March 1 the price of gold is $1,000 and the December futures price is $1,015. On
November 1 the price of gold is $980 and the December futures price is $981. A gold
producer entered into a December futures contracts on March 1 to hedge the sale of
gold on November 1 . It closed out its position on November 1 . After taking account of
the cost of hedging, what is the effective price received by the company for the gold?
4) A portfolio of derivatives on a stock has a delta of 2400 and a gamma of 100. An
option on the stock with a delta of 0.6 and a gamma of 0.04 can be traded.
i. What position in the option creates a portfolio that is gamma neutral? Give size of
position and state whether it is long or short
ii. After this position has been taken what position in the stock is then necessary for
delta neutrality? Give size of position and state whether it is long or short
5) The volatility of an asset is 25% per year and there are 252 days per year.
i. What is the volatility per day?
ii. What is the volatility per 10 days?
6) The parameters in a GARCH (1,1) model are =0.000002, = 0.04, and =0.95. The
current volatility level is 1% per day.
i. What is the long run average variance rate?
ii. What is the expected variance in 20 days?
iii. What is the expected variance in 50 days?
iv. What is the expected variance in 20 days if the EWMA model is used with = 0.95?
