I have a set of annualized returns over 4 time periods: 10yr, 5yr, 3yr and 1yr.
Is there a way to weight each return to have a "more representative" return?
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Sign up to join this communityI have a set of annualized returns over 4 time periods: 10yr, 5yr, 3yr and 1yr.
Is there a way to weight each return to have a "more representative" return?
You can weight the returns and use them in calculations as shown below.
From this site:-
http://disc.sci.gsfc.nasa.gov/giovanni/additional/users-manual/G3_operation_time_series_stats.shtml
The weighted mean is
and the weighted standard deviation is
So, making up some annualised returns for time spans, 1 yr, 3 yrs, 5 yrs & 10 yrs:
r = {0.01, 0.02, 0.03, 0.04}
and some weights based on decaying relevance with, say τ = 2
a = {e^(-1/τ), e^(-3/τ), e^(-5/τ), e^(-10/τ)}
and fixing their total to be 1
w = a/Σa
{0.660361, 0.242933, 0.0893701, 0.00733595}
the weighted mean return is 0.0144 and weighted s.d. is 0.00972
Note, by using weights that sum to 1 the formulae are simplified, Σw and (Σw)^2 = 1.