### CFA Practice Question

The correlation coefficient between the market and stock A is 0.33. The market has an expected return of 12% and a coefficient of variation of 1.4. The security has a variance of 0.03. Its beta with respect to the market equals ______.
A. 0.46
B. 0.34
C. 0.24
Explanation: The coefficient of variation equals the standard deviation divided by the mean. This gives the standard deviation of the return on the market equal to 1.4 * 12% = 16.8%. The standard deviation of the security equals square root(0.03) = 17.32%. Now, the beta of the security equals the covariance between the security and the market divided by the market variance. Also, the covariance equals the product of the correlation coefficient and the individual standard deviations. Hence, the covariance between the security and the market equals 0.33 * 0.1732 * 0.168 = 0.0096. Therefore, the beta of the security equals 0.0096/(0.16822) = 0.34.

### User Contributed Comments9

User Comment
KD101 Beta = Covariance(sec & Mkt)/Variance(Mkt)
chenyx coefficient of variation=SD/mean
julamo You'd better know your formulas like a computer if you want to solve this question within 1.5 minutes...
chantal I thought that the variance of the security was 0.03 and that covariance should equal the product of the variance of the market by the variance of the security ? what am I missing ? Can someone explain pls?
jpducros The formula above for the Beta was asked on last CFA 1 exam...so be prepared.
jonnyp May be a coincidence but I saw the correlation to the market was .33 which sounds very similar to beta. I picked the one closest to .33 and got it right.
achoi0 @chantal: COV = (correlation)x(standard dev. of security)x(standard dev. of market)
Shcote I always thought the beta WAS the correlation coefficient with the market by definition. I just picked 0.34
dwalasinski I'll be skipping that one on the exam day. 33% to win, zero time spent.
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