Question

Question 8

Generous Dynamics maintains an inventory of 4000 ounces of gold. The company is interested in protecting the inventory against daily price changes. The correlation of the daily change in the spot and futures price is 0.4, the standard deviation of the daily spot price change is 26 percent, and the standard deviation of the daily change in the futures price is 14 percent. The futures contract size is 1000 ounces. How many contracts should GD buy or sell to hedge its inventory?

Sell 0.86154

Buy 2.9714

Sell 2.9714

Buy 0.86154

Question 9

Modern Portfolio Managers (MPM) hold a 19 million dollar portfolio of stocks with a beta of 1.25 measured with respect to the S&P 500 index. The current value of the index is 955 and the current value of a futures contract on the index is 1018.0. The multiplier on the futures equals $250. If MPM wishes to hedge the systematic risk in its portfolio, how many contracts must it buy or sell?

Buy 93.317

Buy 99.476

Sell 99.476

Sell 93.317

Question 10

Modern Portfolio Managers (MPM) hold a 7 million dollar portfolio of stocks with a beta of 0.85 measured with respect to the S&P 500 index. The current value of the index is 1039 and the current value of a futures contract on the index is 1084.7. The multiplier on the futures equals $250. If MPM wishes to increase its systematic risk in its portfolio to 1.65, how many contracts must it buy or sell?

Buy 5389.8

Sell 20.651

Sell 21.559

Buy 20.651

Answer 1

Q 8) The hedge ratio compares the value of a position protected through the use of a hedge with the size of the entire position itself. A hedge ratio may also be a comparison of the value of futures contracts purchased or sold to the value of the cash commodity being hedged.

Now correlation × sd of future price ÷sd of cash price

0.4×14÷26=0.215384 is hedge ratio

For 1000 ounce of gold futures to be sold is 0.215384

For 4000 ounce of gold 4×0.215384 = 0.86154 ct needed to be sold

Q9 perfectly hedge this portfolio we need to sell futures equivalent to Beta times portfolio value. Here is how to go about it!

Value of future cont need to be sold 19000000×1.25= 23750000

Now value of one future cont

1018 ×250=254500

No of future cont 23750000÷254500= 93.3 cont to be sold

Q10. By 20.651 cont

Now to increase the beta upto 1.65

Add up the value (number of shares x share price) of each stock you own and your entire portfolio.

Based on these values, determine how much you have of each stock as a percentage of the overall portfolio.

Multiply those percentage figures by the appropriate beta for each stock. (Thus, if Amazon comprises 25% of your portfolio and has a beta of 1.43, it has a weighted beta of 0.3575.)

Add up the weighted beta figures.

Value of future cont 1084.7*250=271000