Convert monthly Geometric asset returns into arithmetic returns

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