 # calculating variance/standard deviation of portfolio

When calculating the covariance of two stocks, should you convert the return to a decimal first? eg. return = 5%, do you use 5 or .05 in the formula? Does it matter as long as you stay consistent? In the CFAI end of chapter questions, sometimes they convert it to decimal sometimes they don’t. In Q12B reading 8: they use covariance calculated from the decimal notation. However in Q14: they do not convert return to decimal notation first. The problem I have with this is, the answer to Q12B is 0.121346(variance of portfolio). In Q12C they ask you to calculate standard deviation of portfolio, which should be the square root of variance. The answer they give is square root of 0.121346, which is 0.348348. Why is the standard deviation of portfolio bigger than the variance of the portfolio? It doesn’t make much sense if the variance of the portfolio is 12.13% and the standard deviation is 34.83%. I think it should be square root of 12.1346, which would end up with 3.48348 as the standard deviation. So I guess I have 2 questions. 1. As long as you stay consistent with your % or decimal notation, will everything work out ok? 2. When calculating standard deviation from variance in a portfolio context. Should the variance be converted to % notation first before taking the square root?

I like to keep everything in decimal when working with % returns. Yes, a little cumbersome but it doesn’t go wrong. I ignore % signs only when I am taking ratios and know for sure that there is a denominator with a % too so that the 100s will get canceled.

Ah I figured it out after working through a whole problem for both cases. From covariance -> variance -> standard deviation. I can answer my own question now. 1. Yes stay consistent and all will work out. 2. No, do not change conventions during the calculation. Just take the root.

If you calculate standard deviation either approach is going to give you the same answer if you stay consistent. If you calculate variance, you would be better off using decimals to avoid possible mistakes similar to 1%*1% = 1%. Using decimals, you will clearly see that 0.01*0.01 = 0.0001.

I find that decimals work better. To answer your question the standard dievation is the square root of the “mean” which is the expected return * the probability and then sumed up (“added” ) Example: Return Probability 10% 0.1 0.10 * 0.1 = 0.01 15% 0.3 0.15* 0.3 = 0.05 20% 0.4 0.20 *0.4 = 0.08 25% 0.2 0.25 *0.2 = 0.05 _______ 18.50% is the mean or expected return STD is the square root of the mean 18.50 squared is 4.30% Correct me if this doesnt sound correct