 # covariance in std deviation formula

In the Q below, why do you use numbers in percentages rather than decimals for the std dev. (i.e. 16 rather than 0.16)? Does it have something to do with covariance being in squared units? I wasn’t able to get the answer using 0.16 but when i divided covariance by std dev of both assets and used correlation it worked fine: Which of the following is closest to the expected standard deviation of the client’s portfolio if 10% of the portfolio is invested in the Quality Commodity Fund? A) 9.6%. B) 16.0%. C) 14.2%. Your answer: B was incorrect. The correct answer was C) 14.2%. The market model offers a simple way to estimate the covariance between two assets, using the beta of each asset and the variance of the market return. Here, covariance is -51.84 = 0.8 × (-0.2) × 324. The variance of the new client portfolio is 200.59 = (0.9 × 0.9 × 16 × 16) + (0.1 × 0.1 × 16 × 16) + (2 × 0.9 × 0.1 × (-51.84)). The square root of the variance of the new client portfolio is approximately 14.2%. (Study Session 18, LOS 64.a,g)

I don’t think so. I think if you are consistent throughout it should work.

consistent about what? it seems that if you are inputting covariance in the formula, you use the percentage (i.e. 16). if you divide covariance by (stddev1 x stddev 2 x corr), you use the decimal (i.e. 0.16). this is how you obtain the same answer.

if 16 is your variance - 16 should also be your covariance (same units, same type… etc. etc.) if .16 is your variance - make sure .16 (or some such decimal #) is your covariance as well

yah, I posted a problem similar to this. Someone responded that covariance is +/- infiniti and I agree, so how does one make the assumption that the covariance is from, say… .530 to 5.3? As 530 doesn’t mean 530%

using correlation makes more sense to me, i’ll prob just take the cov and divide by (stddev1 x stddev2) so that that i can use correlation, decimals in the stddev, and sleep easy