I have a question regaring the adjustments to the portfolio beta. I have not found the original formula in the CFAI books, from which the number of the contracts formula is derived, but from my perspective it should read something
Target Beta * Ptf Value = Current Beta * Ptf Value + Futures Beta * Futures Level * Price Multiplier * Number of Contracts, from which we derive Number of Contracts = [(Target Beta - Current Beta) * PtfValue] / [Futures Beta *Futures Level * Price Multiplier]
My question is, are not we mixing here the current value of the portfolio with the future price on futures,when we are trying to adjust the current beta exposure, not its future value.
P.S. The same question applies to adjustment of Bond PTF Duration with futures.
The reason that we use the future price on futures is that we don’t pay for them today; we pay in the future. So we’re not mixing current values and future values. You can think of it this way: whatever price we have on the futures contract, today we’re paying or receiving the present value of that price, so today we have a portfolio comprising today’s price on our equity holdings plus today’s price on the futures.
By the way, here are some articles I wrote on adjusting beta and duration that may be of some small help:
You better explain it on your site:“in both cases, what you’re really doing is adjusting the dollar beta of the portfolio.” That’s is correct, what your are looking for is to adjust the fluctuations of the dollar portfolio value. Instead of Futures/Forward you could take any other financial instrument, which can have its beta calculated, and add it to the portfolio. Delta Target Ptf will be equal to Delta Current Ptf plus Delta Financial Instrument.