Convert monthly Geometric asset returns into arithmetic returns
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I've been given monthly geometric Returns (new-old)/(old) for exactly 10 years.
I need to convert this to monthly aritmetic returns.
If I do it through the 'matlab' way in [ma, Ca] = geom2arith(m, C, 12). I do ..
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returns=xlsread('returns.xls','blad1','B2:I188')
%The Sample Covariance Matrix
C=cov(returns)*12;
%The Sample Mean Vector
m=mean(returns)';
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And thus do [ma, Ca]=geom2arith(m, C, 1);
However, when I do that, my means really look utterly crap and I think something is going wrong here. I wanna know the step in between.
I was told that I can calculate my monthly 'arithmetic' returns in Matlab (while being provided monthly geometric returns) numerically by calculating the covariance matrix of the returns ( to take the diagonal for the returns as variances) multiply that by 12 and add that for every geometric monthly return you obtain the monthly arithmetic return.
Since the formula is;
Arithmetic_returns_i = Geometric_returns_i + 1/2*VaR_i
I only wonder how I do this in Matlab and wonder if this is the best way to obtain monthly arithmetic returns. I can read in the returns, calculate the covariance matrix, take the variances and annualize them by multiplying 12 but I doubt thats getting anywhere near the estimate through the geo2arith method :X
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