Steve Jobs
Active Member
There is an illustration by formulas in the books showing how the Optimal Hedge Ratio(OHR) is equal to Beta. I found the idea very confusing because OHR is used for hedging and Beta is a symbol of systematic risk and risk should be reduced always unless the return is increasing.
Also, the formulas for the number of contracts to buy/sale for OHR, tailing, Beta and (even Duration Based hedging) are all almost the same. The total Asset value is divided by futures price and multiplied by x(which could be OHR , tailing, Beta and Duration Based hedging)
The Beta here is the same one we studied in econometrics/finance principles course which can be calculated manually or generated in excel by regressing one company stock prices against the market index. Right?
But in FRM book 3, or in banking course, instead of giving us the whole series of data (S and F prices for a specific period), the correlation and standard deviation are provided(which are calculated again by the author on excel based on data series) to students to calculate the OHR which is actually the same as Beta. So the OHR formula is the shortcut to Calculate Beta? Unless for historical reasons, why to introduce the Beta again in a different way?
Also the following observations:
Tailing: Since the used correlation and standard deviation are not updated to include the new prices, we somehow are updating them by multiplying them by the new prices. Right?
Duration based hedge: This is not the same as Beta, since it’s not being calculated based on historical data but rather on PV of future cash flow, so for sure it should be updated by time as cash flows are received/paid.
Also, the formulas for the number of contracts to buy/sale for OHR, tailing, Beta and (even Duration Based hedging) are all almost the same. The total Asset value is divided by futures price and multiplied by x(which could be OHR , tailing, Beta and Duration Based hedging)
The Beta here is the same one we studied in econometrics/finance principles course which can be calculated manually or generated in excel by regressing one company stock prices against the market index. Right?
But in FRM book 3, or in banking course, instead of giving us the whole series of data (S and F prices for a specific period), the correlation and standard deviation are provided(which are calculated again by the author on excel based on data series) to students to calculate the OHR which is actually the same as Beta. So the OHR formula is the shortcut to Calculate Beta? Unless for historical reasons, why to introduce the Beta again in a different way?
Also the following observations:
Tailing: Since the used correlation and standard deviation are not updated to include the new prices, we somehow are updating them by multiplying them by the new prices. Right?
Duration based hedge: This is not the same as Beta, since it’s not being calculated based on historical data but rather on PV of future cash flow, so for sure it should be updated by time as cash flows are received/paid.