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?

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.

• does it matter though that you are doing the volatility adjustment using a different window ? in your example you are using the same window as the short term moving average – qfd Dec 14 '17 at 16:33
• also the volatility measure that you mention above at is the vol of the returns not the price right? – qfd Dec 14 '17 at 16:35
• @qfd this is my point. I would use the same volatility and I would use a recent one. And vol in percentage terms is ok . If you do the same calculation for other assets or other points in time comparisons are still possible. And the aim is not the precise form of your momentum indicator but possibility to compare it. – Ric Dec 14 '17 at 17:12