Gujarati’s regression is applied in Hull’s 3.3 example of an airline that cross-hedges jet fuel costs with heating oil futures. For the FRM candidate, I have three key points here:

• the minimum variance hedge ratio is the slope of the regression line (beta)
• Therefore, both (MV hedge ratio and beta) can be expressed as: correlation multiplied by relative volatility!
• Mathematically, you must be very facile with (i) COV = correlation*volatility*volatility and (ii) generic beta = COV()/VAR()

Briefcast:

Comments

1. James 18 Apr 2009

   Which of these is the dependent variable—spot or futures?  I thought spot was the basis for futures prices.  That is, spot prices are predictive of future prices (and not the other way). In other words, should the labels on the X and Y axis be flipped? 

   If correct, then the beta slope definition needs the spot beta in the denominator, not the futures.

2. David Harper, CFA, FRM, CIPM 18 Apr 2009

   Hi James - That’s an really interesting point i never considered. My approach above, stealing from Hull Chapter 4 is pretty safely conventional, but…I see no reason your approach wouldn’t work (i.e., it’s a different regressional line, and a new definition for “hedge ratio”). I do see what you are saying, it defies they dependence of the futures price on the spot price that is implied by cost of carry. But, first, I think ultimately it would not matter: I didn’t check but I’d imagine the newly defined optimal hedge ratio would produce that same number of contracts; so, ultimately this hedge exercise is leaning on the “mere association” of a correlation. Second, I think it’s ultimately because of a definitional convention: the hedge ratio (h) is based on the starting assumption: let’s minimize the variance of change spot - (hedge ratio)*(change in futures). Only because that’s the starting point, do we end up with a hedge ratio = correl*spot vol/futures vol. And, I *think* that the only reason we run the regression this way; i.e., to correspond. I think the hedge ratio could easily be redefined (unconventionally) to match your more intuitive view of independent-dependent. David

3. Jibran Anjum 06 Aug 2009

   OLS technique is simple and easy to use and you explained this quite well. According to my knowledge the can be two issues with OLS regression. 1) In many cases OLS regression does not completely satisfy that the error term in the regression is heteroscedastic. In this case how will you resolve this problem.
   2) Another problem with OLS method is the fact that it uses unconditional sample moments instead of conditional sample moments, which use currently available information. Under this condition how will you relsove this matter.
   I have gathered this information from the S S Chen et al / The Quarterly Review of Economics and Finance 43 (2003) 433 - 465.

   Kind Regards
   Jibran Anjum

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