Question

What is the variance of a portfolio formed by 50% stocks and 50% bonds if the standard deviation of the stocks is 10%, the std. dev of bonds is 5% and there is no correlation between the two (Choose the closest answer)? Group of answer choices

a) 0.003

b) 0.002

c) 0.001

d) 0.004

Answer 1

The variance of a portfolio with 50% stocks and 50% bonds, and no correlation between them, is calculated to be 0.003125. The closest answer choice provided is 0.003 (option a).

Step-by-step explanation:

The question asks about calculating the variance of a portfolio consisting of two assets - stocks and bonds - with given standard deviations and with zero correlation. Since the two assets are not correlated, the variance of the portfolio can be calculated by simply squaring the standard deviations of the individual assets, multiplying by the squared weights, and adding them.

The weights for stocks and bonds are both 0.5, and their standard deviations are 0.10 and 0.05, respectively. Using the formula for the portfolio variance:

Variance = (weight of stocks2 × std. dev of stocks2) + (weight of bonds2 × std. dev of bonds2)

Therefore:

Variance = (0.52 × 0.102) + (0.52 × 0.052)

= (0.25 × 0.01) + (0.25 × 0.0025)

= 0.0025 + 0.000625

= 0.003125

Since we need to choose the closest answer from the multiple-choice options, the best choice would be 0.003 (option a).