Leveraged Decay: how to calculate it
Brexit and currency hedging has thrown up the need for products such as SUP3 however there is danger in holding such leveraged products as SUP3 (3X Long GBP Short EUR). As path dependency of the currency picks up in volatility the arithmetic mean drifts below the geometrical mean.
This is most easily realised in the following example of an up and down fluctuation of 10%:
100 +10% = 110
110 - 10% = 99
We have lost 1% due to the path dependency having only moved up and down 10%
We can approximate the volatility drag using the following:
Volatility Drag = 0.5 * (Leverage) * (Standard Deviation) ^2
This comes from the formula for the geom mean:
Geom Mean = Arith Mean - 0.5 * SD^2
It is not precise but allows a proxy to be formed!
This is most easily realised in the following example of an up and down fluctuation of 10%:
100 +10% = 110
110 - 10% = 99
We have lost 1% due to the path dependency having only moved up and down 10%
We can approximate the volatility drag using the following:
Volatility Drag = 0.5 * (Leverage) * (Standard Deviation) ^2
This comes from the formula for the geom mean:
Geom Mean = Arith Mean - 0.5 * SD^2
It is not precise but allows a proxy to be formed!