# CAPM question

Someone emailed me this question. The slope of the SML in an economy is 8.9%. The risk free rate prevailing in the economy is 4.9%. A security has a corelation coeff. of 0.23 with the market. The market’s std dev is 15% while that of the security is 19%. The expected return on the portfolio equals ______. A. 14.19% B. 7.49% C. 13.66% D. 12.39% I don’t know what the right answer should be, my calculation gives B. Using Beta = covariance(market, security)/variance(market) and covariance = correlaction coefficient * std dev(market) * std dev(security) I get Beta = correlation coefficient * std dev (security) / std dev (market). = 0.291 Now use E(portfolio) = Risk Free Rate + SML slope * Beta = 7.49%.

I am not sure too but I guess while calculating Beta You take only Std Dev (market) in denominator and covariance in Numerator.

stratus’ looks good to me. (use variance in denominator)

beta = correl*stdev(security)/stdev(market) = .23*19/15 slope = E(M) - RFR E(portfolio) = RFR + beta*(E(M)-RFR) = 4.9% + .23*19/15*8.9% = 7.49%

I got a wrong ans but what puzzles me is the formular in use here from my understanding correlation = cov1,2/stdev1*stdev2 cov = correlation*stdev1*stdev2 and beta = cov/variance(mkt) so, beta = correlation*stddev(mkt)*stddev(security)/variance(mkt) beta = 0.23*0.19*0.15/sqrt 0.15 Please help with clarification

webtwister1 Wrote: ------------------------------------------------------- > I got a wrong ans but what puzzles me is the > formular in use here > > from my understanding > > correlation = cov1,2/stdev1*stdev2 > cov = correlation*stdev1*stdev2 > and beta = cov/variance(mkt) > so, > > beta = > correlation*stddev(mkt)*stddev(security)/variance( > mkt) > beta = 0.23*0.19*0.15/sqrt 0.15 > > Please help with clarification beta in this case would be (.23*.19*.15)/(.15^2).

Thanks budfox427, but still not correct…If the answer is there could we be missing something? slope? slope = (R(M) - RFR) ?

They give you the slope in the first sentence 8.9% So the answer is 4.9% + beta*8.9% Beta = .291 answer 7.49%