Minimum Variance Hedge Ratio (Beta ) and Basis Risk

[Anonymous]

In the hedge constructed using minimum variance hedge ratio (eg: value of spot position / value of one futures contract * beta) which has the beta adjustment, does the beta correct the basis risk between spot and futures?

Related is Exam 1 Test Question 138, where the question states “When hedging an equity portfolio with index futures that carry no basis risk”, the number of futures contracts to hold is determined by:
and the answer is:
the equity portfolio’s beta, the value of the portfolio, and the notional value of one futures contract

[Nitin Iyer]

Minimum Variance Hedge Ratio (Beta ) and Basis Risk

[Anonymous]

The basis risk is the risk related to financing costs of the hedge, hence related to the risk free rate future moves (margin reinvestment rate or borrowing cost).

The beta does not take this risk into account, to do so you have to adjust your hedge ratio (see ‘Tailing the Hedge’ chapter in PRM Handbook I.B.3).
The question here is related to a ‘standard’ hedge ratio (not adjusted), in other words a hedge position in which you ignore any basis risk.

[Anonymous]

Thanks for the reply Kzg.

I just wondered as Basis Risk is the risk due to change in risk free rate, dividend etc changing between spot and futures, when you are estimating beta by a historical regression between spot and futures, wouldnt you pick up these risk free rate and dividend noise etc in the regression and account for it in the beta. So the beta (which tells you how much the spot will change if the futures changes by x) would implicitly account for Basis as well. I am not sure

Anyway, for the PRM exam, i’ll just assume, beta <>1 captures the non-unity move between spot and futures, and Basis is due to the change in risk free, dividends etc.

[Author]

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