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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

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

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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.

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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

CP

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