Beta and Hedge Ratio

[cillianmccotter]

Hi all,

I couldn't find a relevant thread on this, but apologies if this has been asked before - I've got myself in to a bit of a quandary around the calculation of "beta", or as we know, the slope of the regression line, for instance between an asset and the hedge. The typical methodology I guess is to run linear regression on the asset's returns versus the hedge's returns. Using the formula from Kaplan in the Introduction section for Part I, this is confirmed. To note, when it say's return, I would take that to mean change in price / previous day's price, NOT simply change in price (which would go without saying I guess).



I was then watching David's video on Minimum Variance Hedge (using the Jet Fuel/Heating Oil example), and notice it's the change in price of one asset against another which are being regressed to produce Beta (with correlation * cross-rate of s.deviation).



With that said, it would seem that for two set's of asset prices, there are three feasible regressions:

• Regress asset price of one against another
• Regress change in asset price against change in the other
• Regress return in asset price against the return of the other

I tried playing around in Excel with some mock numbers - naturally the standard deviation would be in a different format in each case, and I'm not certain the three methods would ever produce a consistent value of Beta i.e. correlation * std dev asset * std dev hedge. Is there a one-size fits all methodology here? Any clarification would be great.

 

[cillianmccotter]

It intuitively would make sense to obviously always use returns, as it scales both asset price series into a comparable format, and once exposure of the asset and hedge are matched off, a negative return in the asset will then produce an equal and opposite positive return on the hedge. Went back to double check the video and it is indeed ST.DEV of the price change series, not the return series, being used...