Hi, I have back-tested a strategy and the total return after 285 weeks is 24%. How would I annualize this? I would like the annualized rate of return in MATLAB.
Any help would be useful.
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r^285 = 1.24 so log(r^285) = log(1.24) so 285*log(r) = log(1.24) so log(r) = log(1.24) / 285 so r = exp( log(1.24) / 285) is the weekly interest rate.
Step 1 Time estimation
Years in 285 weeks....one year has 52 weeks. Then Y=285/52=5.48.
Step 2 Calculation interest rate
(1+x)^(5.48)-1=0.24, what you have to do is find x. In this case x is annual. The result is: x=0.04.
Step 3 "Prove"
If you have a 4% annual return during 5.48 years, the return is: (1.04)^(5.48)-1 = 0.24.
Hope it helps. Please grade if solve your question.