Exam 1:How do you determine if it’s long or short?

[Anonymous]

This is the 49th question from the practice exam:
An investor has a portfolio with a value of $1,000,000 and a beta of 2.5. He believes the portfolio carries more market risk than he desires and wishes to reduce the beta to 1. How many futures contracts should be buy or sell to reduce the beta if the futures contracts have a beta of 1.2 and the notional value of each contract is $240,000?

And the answer is : SELL 5 contracts.

I know how to get the 5, but I don’t understand why it’s sell.

Can anyone help me out please

[Anonymous]

beta_P = Net beta of the portfolio (Here, this is the desired beta that we want to construct)
beta_S = beta of stock
beta_F = beta of futures

Total number of Futures N_F = (beta_P -beta_S)/beta_F *(V_s/V_f) = (1 – 2.5)/1.2 *(10^6/2.4×10^5) = -5.2

If N_F > 0 : long position in futures .
N_F < 0 : short position in futures . Therefore short 5 futures. Generally if we want to reduce the effective beta (beta_P < beta_S) of a portfolio then a short position in futures will be needed.

[Anonymous]

Usually, if you hold it is assumed that you are long the stock/index/portfolio and to hedge, you should take a short position in the futures market. That is why most times you find that you are always short the futures, Although you may have to check what position he has in his portfolio sometimes. If you also notice, the formula usually has a minus in front to indicate a short position.

[Author]

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