Question

1) You want to protect the value of a $250,000,000 portfolio over next 6 months;   the beta of your portfolio is 1.3.   Currently the S&P futures contract with six months to expiration has a price of $3100.

Questions:

1. How many contracts you need to sell?
2. Calculate the gain on the future contracts if S&P 500 index price declines 10% to $2790 six months later.
3. Calculate the loss on the portfolio if S&P 500 index price declines 10% to $2790 six months later.
4. Explains how the hedge has worked.

Answer 1

a. To find out number of contracts required to buy or sell, we will use the following formula :-

(Target Beta - Portfolio beta) / (Beta of futures contract) * (Current Value of Portfolio / Price of the Futures Contract * Contract Multipler or lot size of futures contract)

Let us assume the lot size or contract multiplier to be 250

= (0 - 1.3) / (1.0) * 250,000,000 / (3,100 * 250) = -419.35 contracts = -420 contracts (Rounded off)

Hence, we need to short sell 420 S&P futures contracts to completely hedge the portfolio

b.

Gain if price declines to $2790 = (2,790 - 3,100) * 420 * 250 = $32,550,000

c. There will be no loss. Instead as demonstrated in Pert B, it will result into a gain of $32,550,000

d.

To effectively hedge the portfolio, we have reduced the portfolio beta into 0, by short-selling equal number of S&P future contracts.

In case market declines by 10%, loss on portfolio = (250,000,000 * 1.3 * 10% ) = $32,500,000

Gain be selling S&P futures = $32,550,000

Netting off will result in = ( $32,550,000 - $32,500,000) = $50,000 gain which is due to rounding off the contract

Hence, this hedge is working perfectly