 # Just for fun - PM

From CFAI text practice questions: Two assets have betas of 1.5 and 1.2, respectively. The residual standard deviation from the market model is 2 for the first asset and 4 for the second. The market standard deviation is 8. What is the correlation between the two assets?

Correction: (1.5)(1.2)(8^2) / (12.16 * 10.4) = .91 variance A = (1.5^2)(8^2) + 2^2 = 148 standard dev A = 12.16 variance B = (1.2^2)(8^2) + 4^2 = 108.2 standard dev B = 10.4

Can’t get this one. Correlation has to be between 0 and 1 but I keep getting the answer confusedbycfa is getting. Where are we going wrong?

I’ll give you a hint - residual standard deviation is not the same as total standard deviation.

Is correlation of 1 the answer?

Using the formulas of: Cov(1,2)=Beta(1)*Beta(2)*Market St. Dev squared St Dev Asset 1=SqRt[(Beta(1)^2*Mkt St Dev^2) + residual st. dev^2] and then plugging those results into: correlation=[Cov(1,2)]/[StDev(1)*StDev(2)] I’m coming up with 0.914

Good one. I start to recall theformular now. COV = 1.2 * 1.5 * (8) ^ 2 = 115.2 Var (A) = (1.5 * 8) ^2 + 4 = 148. Var(B) = (1.2 * 8 ) ^ 2 + 16 = 108.16 Got close to 0.91.

0.91 it is. Very impressive guys.

Covariance = 1.5 * 1.2 *8^2 = 115.2 Dev of asset 1: 1.5^2 * 8 ^2 + 2^2 = 148^.5 = 12.16 Dev of asset 2: 1.2^2 * 8 ^2 + 4^2 = 108^.5 = 10.4 115.2/(12.16*10.4) = 0.91052

Dwight, You are multiplying the individual asset standard devs. These should be squared and added to the product of Beta Squared*Mkt St Dev Sqrd.

Yeah figured it out. I knew the formula but messed it up royally. It’s been a long day Thanks though.