Estimating Quarterly Jensen's Alpha from Monthly Returns

Summary

The document considers how to convert monthly Jensen's alpha estimates for individual stocks into quarterly or yearly measures. It describes two approaches: aggregate returns to the desired observation period and rerun the regression, or combine the monthly returns across the period to form a compounded return. This addresses why simply averaging monthly alpha estimates may not produce the alpha associated with a longer measurement interval.

The response gives a quarterly compounding relationship for three monthly returns and recommends regression on quarterly returns as the direct estimation route. It does not provide a parallel explicit calculation for yearly alpha, nor discuss changes in benchmark specification, risk-free rates, or beta estimation when the return frequency changes. Thus, the advice is useful as a starting point, but researchers should align the regression inputs and benchmark with the target period.

Key ideas

• Quarterly Jensen's alpha can be estimated by running the regression on quarterly returns.
• Quarterly returns are formed by compounding the returns for the months in the quarter.
• Averaging monthly alpha estimates is not established as equivalent to estimating alpha at a quarterly frequency.
• The document does not specify how benchmark inputs or beta estimation should change for yearly estimates.

Tags

# How to convert Jensen's Alpha from monthly to quarterly observations


# How to convert Jensen's Alpha from monthly to quarterly observations












I am being puzzled while calculating jensen's alpha for single stocks. I have monthly returns data and have calculated alpha for each stock on a monthly basis (used 36-month rolling window for beta estimation). Now, I need to convert my monthly alphas into quarterly and yearly observations. What is the best way to do it?

I thought of averaging over 3 and 12 months, respectively, but not sure if it's correct.

Would be glad if anyone could help!

## Answer by QuantK (score 1)

https://quant.stackexchange.com/a/27733

You can do a couple of things:

The easiest way to calculate your quarterly Jensen's alphas is achieved by calculating quarterly returns and then applying the regression method you have done before.

Alternatively, your Jensen's alpha represents the abnormal monthly return over a benchmark. Therefore, your quarterly Jensen's alpha can be calculated by annualizing your returns : $r_q = (1+r_{m1})\cdot(1+r_{m2})\cdot(1+r_{m3})-1$.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.