- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 7. Expected Value, Variance, Standard Deviation, Covariances, and Correlations of Portfolio Returns

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**CFA Practice Question**

Assume a portfolio is composed of 25% stocks (S) and 75% bonds (B). The expected return from stocks is 7.9% and the expected return from bonds is 4.5%. The incomplete covariance matrix for the returns of this portfolio is as follows:

B. 18.06

C. 44.5

We know that p(S,B) = -0.125. What is the variance of return on this portfolio?

A. 16.19

B. 18.06

C. 44.5

Correct Answer: A

p(S,B) = -5 / [64

V(R

First compute the variance for bonds:

p(S,B) = -5 / [64

^{1/2}x Var(B)^{1/2}] = -0.125 ==> Var(B) = 25Then proceed to calculate the variance of return on the portfolio:

V(R

_{P}) = V(0.25 x R_{S}+ 0.75 x R_{B}) = 0.25^{2}V(R_{S}) + 0.75^{2}V(R_{B}) + 2 x 0.25 x 0.75 x Cov(R_{S}, R_{B}) = 16.1875###
**User Contributed Comments**
9

User |
Comment |
---|---|

commandos |
Can somebody explain to me the first step,please? |

alallstar |
p(s, b) = COV(s,b)/ (standard deviation(s) * standard deviation(b)) Standard deviation = sqrt(variance) Variance for S is given, from which the standard deviation can be found, as is Covariance, so you plug these numbers these numbers into the formula for p(s, b) to calculate standard deviation of b and then square it to get variance(b) |

ddodoo |
V(Rp)...i get the first step but what about the 2nd step? |

jpducros |
It is important to know the formula of the portfolio variance; to have in mind that you need : - the weight of each component, - the variance of each component - the correlation of the components and the St Dev of each components.....or the covariance of the components. Here weights are given, one variance is missing...so focus on calculating it and covariance is given...so just apply the formula. |

carst |
so the key is: CORR (A,B) = COV (A,B) / STD (A)*STD (B) and the key formulas VAR(P)=w1^2*VAR(1)+w2^2*VAR(2)+2w1w2COV(1,2) |

cfaajay |
from the given data ,cov(s,s) = 64 , cov(s,b) = -5 ,we need to calculate cov(b,b) ,which will be calculated as per below cov(s,b) = corr(s,b)*corr(s,s)*corr(b,b) corr(b,b) = cov(s,b)/(corr(s,b)*corr(s,s)) corr(s,s) = square root of 64 i.e 8 (from given data) corr(b,b) = -5/(-1.25 * 8) corr(b,b) = 5 therefore cov(b,b) = square of 5 i.e 5^2 = 25 now the variance of portfolio (.25^2)*64 +(.75^2)*25+2*.25*.75*(-5) = 16.1875. Hope this helps. |

DCPWS |
Don't forget - they're asking for VAR, not SD. |

ashish100 |
@cfaajay i dont get why you're using -1.25 instead of .125 on the step corr(b,b) = -5/(-1.25*8) |

Huricane74 |
@ashish100: The (-1.25) is given to us in the question above. On a side note, I got 16.25 for the portfolio variance and I can not figure out why my answer is difference from 16.1875. |