Hedging portfolio with stock index future

[Deepak Chitnis]

Hi David,
p1.T3. Financial markets and products practice question page no.71 question no. 155.1,
I have calculated the hedge which is 250 contracts but how to decide that we should short the contracts or long the contracts? I have understand that while changing the beta to target beta, short the contract if reducing the beta and long the contracts when increasing the beta, but how to decide when there is only one beta given. also the question 155.3 on same page how to decide to long or short the contracts. (I think it is very dump question but struck in it) Little bit confused. Please help.
Thank you,

 

[David Harper CFA FRM]

Hi @Deepak Chitnis Please see the source at https://forum.bionicturtle.com/thre...portfolio-beta-with-stock-index-futures.4449/ which includes a related Q&A; i.e.,

Hi orit,
I have generally recommended that we use intuition rather than the +/- sign to determine the long/short. Adding long futures will increase the net beta of the position, while shorting them will subtract, so if the goal is to reduce the portfolio beta (which includes the special case of beta hedging altogether; i.e., to "hedge the beta" typically means reduce the net beta to zero), then you are going to short equity futures contracts.

You can rely on the formula:

Number of contracts = (target beta - current beta)*portfolio value/futures notional = (B* - B)*V(P)/V(F)

so for example, 155.2 would return:
N = (1.0 - 0.3)*10 MM/(1380*250) = +20.3, where + says go long,

and 155.3 would return (this has no target beta, the goal is to hedge, which implies NEUTRALIZE; i.e., target net beta = 0):
N = (0 - 1.14)*3.5 MM/(1343*250) = -11.9, where - says go short

but I really think relying on +/- is un-necessary and even less robust that just thinking about it after you get the number. I hope that helps, thanks,

So in the case of 155.3 where "An investor holds 10,000 shares of Apple (AAPL), each with a price of $350.00," the investor who owns shares is long beta. The hedge, in this context, seeks to neutralize beta, such that short futures contract ("short hedge") will be requires to neutralize beta. I hope that helps! Thanks,

 

[Deepak Chitnis]

Thank you David, appreciate your help thanks a lot