Use the formulas in the first picture to derive the following formulas in picture two and three.

Hedging an equity portfolio by stock index future o Va: Current value of the portfolio o Ve: Current value of one future contracts How many index future contracts should be used? Value change of the portfolio: AV=VARA NVERE RA= R+ BA(RM R) RE=R+ BF(RM-R) The optimal number of contracts: N=COCO The optimal number of contracts: N=COCO Changing the Beta of a portfolio: a short position in (B B*) A Hedging an equity portfolio by stock index future o Va: Current value of the portfolio o Ve: Current value of one future contracts How many index future contracts should be used? Value change of the portfolio: AV=VARA NVERE RA= R+ BA(RM R) RE=R+ BF(RM-R) The optimal number of contracts: N=COCO The optimal number of contracts: N=COCO Changing the Beta of a portfolio: a short position in (B B*) A