Answer to Question #196613 in Management for Qmmath

Question

Assume that we have five assets. first one has expected return μ1 = 20% and standard deviation of return equal to σ1 = 10%. The second has expected return μ2 = 40% and standard deviation of return equal to σ2 =20%. Next we want to determine the range of μ4 and σ4 such that Asset 4 dominates Asset 2, but does not dominate Asset 1. After careful calculation, and checking our result by drawing a graph .we know that Asset 4 dominates Asset 2 and not Asset 1 if the standard deviation of the return of Asset 4 is __________ and the pair (μ4 , σ4) is not equal to the pair (μ2 , σ2).

larger than that of Asset 1.

larger than or equal to that of Asset 1.

smaller than or equal to that of Asset 2.

smaller than that of Asset 2.

is larger than that of Asset 1 and smaller than to that of Asset 2.

smaller than or equal to that of Asset 1.

smaller than that of Asset 1.

larger than that of Asset 2.

larger than or equal to that of Asset 2.

Answer 1

The language / jargon associated with the CAPM has become ubiquitous in finance. E[RA] = E[RB] = µ Var(RA) = σ2 Var(RB) = σ2/n. The two portfolios therefore have the same expected return but very different return variances.

The covariance between the two stock returns is 0.665.

...

Using our example of ABC and XYZ above, the covariance is calculated as:

1. = [(1.1 - 1.30) x (3 - 3.74)] + [(1.7 - 1.30) x (4.2 - 3.74)] + [(2.1 - 1.30) x (4.9 - 3.74)] + …
2. = [0.148] + [0.184] + [0.928] + [0.036] + [1.364]
3. = 2.66 / (5 - 1)
4. = 0.665

Standard deviation allows a fund's performance swings to be captured into a single number. For most funds, future monthly returns will fall within one standard deviation of its average return 68% of the time and within two standard deviations 95% of the time.