CFA CFA Level 1 Portfolio Variance Equation (Expected Return vs no Expected Return)

# Portfolio Variance Equation (Expected Return vs no Expected Return)

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• mvibs
Participant
• CFA Level 1
3

I am trying to understand why the solution for the following problem does not include expected return:

Betsy Minor is considering the diversification benefits of a two stock portfolio. The expected return of stock A is 14 percent with a standard deviation of 18 percent and the expected return of stock B is 18 percent with a standard deviation of 24 percent. Minor intends to invest 40 percent of her money in stock A, and 60 percent in stock B. The correlation coefficient between the two stocks is 0.6. What is the variance and standard deviation of the two stock portfolio?

Answer given is: (0.40)^2 (0.18)^2 + (0.60)^2 (0.24)^2 + 2(0.4)(0.6)(0.18)(0.24)(0.6) = 0.03836. 0.038360.5 = 0.1959 or 19.59%.

The portfolio variance formula also has expected return in most places, why did they leave it out in this question (From portfolio management part 1)?

Why the difference between Portfolio Variance in the Statistical book and Schweser QuickSheet?

I thought portfolio variance was:

Weight of Asset A Squared x Variance of Asset A X Expected Return Asset A +Weight of Asset B Squared x Variance of Asset B X Expected Return Asset B + 2(weight AxWeightB)(Correlation x Std Dev A x Std Dev B)

• Stuj79
Participant
• CFA Charterholder
5

Ah right, yes I see how that notation could be missinterpreted…glad to help ðŸ™‚

• Stuj79
Participant
• CFA Charterholder
4

Nope, no expected return variables are included in the portfolio variance equation. It is:

(weight of asset A squared x variance of asset A) + (weight of asset B squared x variance of asset B) + 2 x (weight of asset A) x (weight of asset B) x (correlationAB) x (stand dev A) x (stand dev B)

the expected return of a two asset portfolio uses weighted expected return of individual assets….but not the variance/standard dev of portfolio equation.

• rsparks
Participant
• CFA Level 2
4

The B) has made my morning!

• Stuj79
Participant
• CFA Charterholder
0

Good god, it’s converted the “B )” in my post above into bloody smiley faces with sunglasses!!

• mvibs
Participant
• CFA Level 1
0

Thank you, here’s what I realized:

Solution, I’m an idiot. I’ve started memorizing formulas on flash cards this week, and the difference in presentation made me think in the Quicksheet one the “(Ra)” figure was a separate factor of the equation instead of a more complete way of saying “variance OF return on asset A” vs. “variance TIMES return of asset A”

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Thanks for the help.