Question

Consider the following:

A.Asset A has an expected return of 12.5% and a standard deviation in expected returns of 7.5%.
B.Asset B has an expected return of 13.33% and a standard deviation in expected returns of 4%
Suppose a portfolio is invested 50% in Asset A and 50% in Asset B.The standard deviation of the portfolio = 5.75%.
What is the correlation coefficient in expected returns between Asset A and Asset B?

Answer 1

To calculate the correlation coefficient between Asset A and B, use the formula for the portfolio standard deviation and the given weights, standard deviations, and portfolio standard deviation. After computations, this will yield the correlation coefficient necessary for portfolio analysis.

Step-by-step explanation:

To calculate the correlation coefficient between the returns of Asset A and Asset B, we can use the formula of the standard deviation of a two-asset portfolio:
σp = √(wA2σA2 + wB2σB2 + 2wAwBσAσBρAB), where ρAB is the correlation coefficient, wA and wB are the portfolio weights of Asset A and B, and σA and σB are the standard deviations of Asset A and B.

Given that the standard deviation of the portfolio (σp) is 5.75%, and the investment is equally distributed between the two assets (wA = wB = 0.5), we can compute ρAB as follows:

After performing these calculations, you would find the correlation coefficient between Asset A and Asset B's returns to assist you in portfolio diversification and risk management decisions.