Index Futures

Question 5: Index Futures

An equity mutual fund holds $2M in TELUS stock as of November 2, 2005. It is expected that the stock market would fall. In order to protect the value of investment in TELUS stock, we would short some S&P/TSX 20 December, 2005 index futures.

Current S&P/TSX 60 Index = 597.13

1 index point = $200

Futures price = $585.1

# of contracts to be shorted= (2,000,000 * beta)/(futures price *200)

= (2,000,000*1.3)/ (585.1*200)

= 22.218 contracts

Beta of TELUS = 1.3

(b)

Now the market drops by 12%

S&P/TSX Index drops from 597.13 to 525.4744.

And Futures Index drops from 585.1 to 514.888.

Loss in long position = .12* 2,000,000 *1.3

= $312,000

Gain in futures =

= (Initial futures price – futures price after 12% drop) * # of contracts shorted

= (585.1 – 514.888) * 22.218*200

=$311,995

Thus, the loss in long position will almost be perfectly offset by the gain in shorting futures index.

(c) Now if we partially hedge the long position in stock by shorting five contracts less than the number of contracts needed for full hedge.

So, total number of contracts hedged = full hedge -5

= 22.218-5 = 17.218

Loss in long position in stock = .12*2,000,000*1.3

= $312,000

Gain in futures= 17.218* (585.1-514.888)*200

= $241,782.1

We observe that when we partial hedge, or we don’t hedge the risk fully we incur a loss in this situation.

Implication of partial hedging is that even though we pay less initial capital but we are still exposed to some residual risk.