This is from the first item set of the Capital Market Expectation questions on the CFAI website.
Question 1 asks to calculate Beta for the Real Estate market segment and gives various data points to work with, including:
Correlation of RE to market .39
Cov .0075
St dev of RE .14
Sharpe ratio of market .36
What I did was use the correlation of RE,M and backsolved for the st deviation of M
So:
Cov=correlation * st dev M * st dev of RE
.0075 = .39(st dev of M)(.14)
= .137 st dev of M
Used st dev of m to solve for Beta.
The answer I calculated wasn’t an option in the item set. The answer actually used the sharpe ratio to solve for st dev of M and then used that figure to calculate Beta which makes sense to me but gave a different answer.
Is there anything i’m missing from this? I should be able to use Co-variance to solve for st dev of M if given st dev of RE right to calculate Beta right?
If your calculations are right, the only factor that would make a difference is the RFR value in the Sharpe ratio. They might have chosen an arbitrary RFR for the sake of the question.
In real life statistics, this shouldnt happen and the numbers should match.
just to be sure: in your calculation, Beta= Correlation X (SD.RE/SD.M); or B= Covariance/(SD.M)squared; right?
^ thanks and yep I used B = Covariance / variance.m
That’s what i’m concerned with, should I just bank on the idea that the CFAI will choose statistics that work from multiple angles? I’m probably worrying too much…
Well, the grand majority of CFA questions are clear and clean; might be tricky; but not ambigious.
If my answer is not in the list. I’ll recalculate it fast. If still is not there, I would think fast of an alternative solution. Or i would make an educated guess and return to it if there’s enough time.
If I were you i wouldnt worry much. You understand the concepts.