Question

An investor owns a portfolio consisting of $450,000 of IBM shares and $550,000 of Apple shares. Apple shares have a market index beta of 1.2 whereas IBM shares have a market index beta of 0.9. The investor wishes to take a risk-minimizing hedge for this portfolio using S&P 500 index futures. The current futures prices for the S&P500 index is $2600.00 and the futures contract is for 10 units of the index. What position should the investor take in the futures contract. Please state your answer as the fractional number of contracts, and whether his/her position should be long or short. 

 

Answer 1

Step 1
Hedging is a technique used to protect against the loss of Individual securities by trading in different instruments that offsets a loss. This hedging techniques are used to protect against unexpected losses occurring due to uncertain circumstances or events. Even though we have purchased quality stocks but that also needed to be hedged due to timing of purchase. Index futures is such an hedging technique where we can hedge our risk in individual securities by using market beta we can establish the number of contracts which we can either go long or short to protect our risk in securities.

 

Step 2

Here we have to first find out the value of the portfolio

Here Total Value of Portfolio is $450,000 + $550,000 = $11,00,000

Weighted average of Beta = ($450,000*0.9) + ($550,000*1.2)/$10,00,000
                                               = $405,000+$660,000/$10,00,000
     Weighted average Beta = 1.065

 

Here Current Future Price for S&P Index is $2600 and contract size is 10 Units hence the value of 1 future contract is $26,000.

 

We can derive the Number of contracts by dividing the value of portfolio by the value of future contract and multiplying the said result by weighted average beta.

 

Number of Contracts = ($11,00, 000 ÷ 26000) × 1.065

 

Number of Contract = 45 Approx

 

We can go short 45 Futures contract for hedging our securities.

We can go short 45 Futures contract for hedging our securities.