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Hedge ratio

D

didster

Member
First of all, I don't mean to be overly critical of the markers but I am just interested in the right answers for the exam which is what matters.

The hedge ratio for futures is a ratio of standard deviations and a correlation coefficient.

The marker for my X3.7 script had the opinion that it should be the standard deviation of the CHANGE in price and not the price itself, eg the SD of the change in future price instead of the SD of the future price.

Is there a difference? Surely taking differences of prices has the same standard deviation as the price itself, unless I am misinterpreting something.
 
As it states on page 28 in Chapter 11 of the Course Notes, the standard deviations and correlations are based on changes in spot and future prices (i.e. delta S and delta F). (See also the derivation of the hedge ratio in Question 11.22.)

This is important because the standard deviation of the differences will generally be quite different to the standard deviation of the prices
themselves.

For example, suppose the spot prices were: 7, 9, 11, 8, 7, 6, 4, 8, 10, 9

The differences would then be: +2, +2, -3, -1, -1, -2, +4, +2, -1

The standard deviations of these two sets of numbers are 2.02 and 2.33, which are materially different.
 
Thank you Simon for your prompt response.

However I am still confused. While I know to include "change in price" for the exam, I don't really understand what to do.

My line of thinking (which seems to be wrong) was that the price in one years time should have the same SD as the change in price over the next year (because the price today is known).

Say I wanted to hedge the value of an equity portfolio in 3 months time, how would I go about calculating the standard deviation to use.
  • Would I calculate the standard deviations of the differences in prices over 3 month periods (non overlapping)
  • calculate the Sd of changes in prices over some other period eg daily changes over a 3-month period
  • Use Black scholes (or other method) to estimate implied volatility (rather than using past values) which gives volatility of prices (or is it "changes in prices"?)
If the implied volatility is the volatility of prices, how do I convert this to SD of changes in price?
 
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