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

Beta of Our Portfolio = 1.3 that means if the market moves by 1% our portfolio moves by 1.3%

In order to Hedge our portfolio with S&P 500 contracts we have to purchase such number of portfolio such that it will immunise our portfolio's return taking into consideration its extra movement.

1- No. of Contrcats we need to Sell

Value of portfolio = 250,000,000 $

Beta of Portfolio = 1.3

Amount to be Shorted = 250,000,000*1.3 = 325000000 $

S&P Futures with a 6 month expiration has a price of 3100$

Therefore No. of Contracts to be Sold = 325000000/3100 = 104838.7 = 104839

2- Gain on the Futures Contract if Nifty declines to 2790$

Since we have sold the contracts 6 month in advance at a price of 3100$, in order to square off the transaction we have to purchase the contracts 6 month into the future.

Since the price now has declined, we will have to pay a lesser amount to purchase which will allow us to have a profit.

Profit = No. of Contracts Sold * (Price at which it is sold - Price in current Market )

Profit = 104839 * (3100-2790) = $ 32500090

3- Loss on the Portfolio if S&P 500 declines to $2790

If the S&P500 declined 10% then because our portfolio has a beta of 1.3 our portfolio should decline by 10*1.3 = 13%

Therefore 13% of our Portfolio = 250000000*13% = 32500000

Since the market has gone down our portfolio will go down too.

So Loss on our portfolio = $32500000

4- How did the hedge Work

As you saw when the market declined 10% we had a profit on our future contract to the tune of $32500090 and on the other hand due to markets decline our portfolio lost its value to the tune of 13% which is also valued at $32500000.

So if we calculate our ultimate Profit/Loss on the movement

Profit/Loss = Profit from Futures Contract - Loss from Portfolio

Profit/Loss= 32500090-32500000 = $90

This is a minimal amount which is coming due to rounding off. So we can see how the changes in the market have been immunised and our portfolio value stays protected.