volatility adjustment on momentum

Question

I am trying to figure out what this text means any advice is greatly appreciated.

"volatility-adjusted crossover signal where momentum is measured by comparing a short-horizon (45 days) moving average of the total return index to a longer-horizon (90 days) moving average of the total return index" Momentum Investing in Fixed Income

say I have a returns series, i compute the cumulative return (ie the index) I then compute the average of the index over 45 days and 90 days. Do I then compute the volatility of the returns (std deviation over 45 days ) and (90 days)

So then the signal is: MA_45_Index/STDEV_RET_45 - MA_90_Index/STDEV_RET_90?

Answer 1

With the information given I would not expect that the denominators differ.

$MA_{90}$ tells you the long term price (the moving average should remove noise) while $MA_{45}$ gives you the more recent price (noise removed).

Then $M = MA_{45} - MA_{90}$ gives you momentum in terms of price level. You can downscale this momentum by using $M/\sigma$ and $\sigma$ is a measure of volatility. I would not use different $\sigma$ for $MA_{45}$ and $MA_{90}$. You would mainly look for future volatility. Due to volatiliy clustering you could use rather recent 45-days vol.