Question

The standard deviation of a two asset portfolio with a correlation coefficient of .35 will be _______________ the weighted average standard deviation of the portfolio.

Answer 1

The answer will be equal to!

Answer 2

Answer:

The standard deviation of a two asset portfolio with a correlation coefficient of .35 will be lower than the weighted average standard deviation of the portfolio

Explanation:

The bone of contention here is whether the standard deviation formula for a two-asset portfolio produces a higher, equal, or lower standard deviation compared to the weighted average standard deviation of the portfolio when the correlation between the two assets is 0.35.

Let us assume random numbers:

σP = √(wA2 * σA2 + wB2 * σB2 + 2 * wA * wB * σA * σB * ρAB)

wA=proportion of the portfolio invested A=45%

σA=standard deviation of return of A=15%

wB=proportion of the portfolio invested B=55%

σB=standard deviation of return of B=20%

ρAB= correlation between both= 0.35

square root=^(1/2)

Note the formula above without the square root gives variance of the portfolio

standard deviation

=(45%^2*15%^2+55%^2*20%^2+2*45%*55%*15%*20%*0.35)^(1/2)

standard deviation= 14.78%

weighted average standard deviation of the portfolio=(45%*15%)+(55%*20%)

the weighted average standard deviation of the portfolio=17.75%

The standard deviation using the two-asset formula is lower