Hrm 531 Week 3 Derivatives Assignment

Derivatives Assignment

‘Option, Futures and Forwards’

October 2015

Instructor: Jacques Bernard

Done by: Zainab Yehia Bakr

i. Explain the difference between selling a call option and buying a put option.

Selling a call option is when you give the other party the right to buy an underlying asset at an agreed upon price ‘strike price’ on an agreed upon date. When you write a call option, you have the obligation to sell the underlying asset to the counterparty, and the counterparty chooses whether to exercise the contract or not, your payoff would be either negative or zero, in other words, It gives you a payoff of:

-Max(St –K,0) = Min(K -St,0)

Buying a put option is when you buy the right to sell an underlying asset

Trader A enters into a forward contract to buy gold for $1000 an ounce in one year. Trader B buys a call option to buy gold for $1000 an ounce in one year. The cost of the option is $100 an ounce. What is the difference between the positions of the traders? Show the profit per ounce as a function of the price of gold in one year for the two traders.

Assuming ST is the price of gold in one year. Trader A makes a profit of ST ̶ 1000 and Trader B makes a profit of max (ST ̶ 1000, 0) –100. Trader A does better if the price is above $900, while trader B starts making actual profit above $1100, when the amount exceeds the price of gold plus premium.

iv. A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on the S&P 500 to hedge its risk. The index futures are currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfolio to 0.6?

A hedge that minimizes risk is:

1.2 x (20,000,000 / 1080x250) =

1.2 x (20,000,000 / 270,000) = 88.888 = 89 Contracts

To reduce beta to 0.6:

0.6 x (20,000,000 / 1080x250) =

0.6 x (20,000,000 / 270,000) = 44.444 = 44