# 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!

• Can you please define Jensen's alpha, in a mathematical formula? – Gordon Jun 17 '16 at 20:14
• @Gordon yes, sure, it's an excess return over a benchmark: Ri-Rf-beta*(Rm-Rf), where Ri, Rf, Rm are stock return, risk-free rate and market return, respectively. – Daria Diachenko Jun 22 '16 at 13:12
• Thanks for clarification. Is the answer below helpful for you? – Gordon Jun 22 '16 at 13:14
• @Gordon yes, it is, I used the same approach, however it causes further questions – Daria Diachenko Jun 22 '16 at 13:20

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 : $$r_q = (1+r_{m1})\cdot(1+r_{m2})\cdot(1+r_{m3})-1$$.