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EASY QUESTION: Is futures / cash hedge dynamic or static?

February 8th, 2019, 5:46 pm

Assume a very simple asset, a stock with no dividends.  Assume constant interest rates over life of the hedge. Assume 0 costs for storage and the only cost is the interest rates cost.  Let's say you are long this stock and want to completely hedge it with futures by selling futures.

The price of a future is:
F = S * (1 + r * days/365)

The hedge ratio is not 1 to 1 (because of interest rates) correct?  It would be:
S / S * (1 + r * days/365), which simplifies to 1 / (1 + r * days/365)

For example, if the stock price today is 100, rates are 10%, and we want to hedge the position for 2 years.  Your hedge ratio would be 1/1.2 = 0.8333.  Thus for every stock you are long, you must sell 0.8333 futures.

Therefore, even though futures are linear instrument, if you were to hedge cash completely, you would still need to dynamically adjust your position as time changes.  Not to mention interest rate could change too.  If we add in dividends/coupons and storage costs that change, you would have to adjust your hedge even more.

Is my understanding of hedging spot correct?  Or am I just over complicating it and that a 1 to 1 hedge suffices?
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: EASY QUESTION: Is futures / cash hedge dynamic or static?

February 9th, 2019, 2:18 am

Your understanding is basically correct, although I would not refer to a trading strategy that is a deterministic function of known variables (in this case time and a constant interest rate) as being dynamic. From this perspective, a forward hedge is cleaner, simpler, and more robust to assumptions than a futures hedge, but as you move toward a real world perspective you run into the reasons why futures markets usually dominate forward markets. As a practical matter, you tend to see most of the market liquidity (and thus, presumably, most hedging action) in the first couple of contracts, where interest rate effects are pretty much neglible. 
 
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DavidJN
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Joined: July 14th, 2002, 3:00 am

Re: EASY QUESTION: Is futures / cash hedge dynamic or static?

February 10th, 2019, 4:49 pm

Google "tailing a hedge" or "tailing a futures hedge".
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