Question

Correlation, risk, and return Matt Peters wishes to evaluate the risk and return behaviors associated with various combinations of assets V and W under three assumed degrees of correlation: perfectly positive, uncorrelated, and perfectly negative. The expected return and risk values calculated for each of the assets are shown in the following table,囲

a. If the returns of assets V and W are perfectly positively correlated (correlation coefficient = +1), describe the range of (1) expected return and (2) risk associated with all possible portfolio combinations
b. If the returns of assets V and W are uncorrelated (correlation coefficient = 0), describe the approximate range of (1) expected return and (2) risk associated with all possible portfolio combinations.
c. If the returns of assets V and w are perfectly negatively correlated (correlation coefficient =-1), describe the range of (1) expected return and (2) risk associated with all possible portfolio combinations

Answer 1

The range of expected return and risk in a portfolio depends on the degree of correlation between the assets. Positive correlation limits the range, while negative correlation and no correlation widen the range.

Step-by-step explanation:

The risk and return behaviors associated with different combinations of assets are influenced by the degree of correlation between those assets. In perfectly positive correlation (correlation coefficient = +1), the expected return and risk of the portfolio will vary within the range of the individual assets' expected return and risk.

This means that the portfolio's expected return and risk will be a linear combination of the individual assets' expected return and risk.

In uncorrelated assets (correlation coefficient = 0), the range of expected return and risk for all possible portfolio combinations will be wider. This means that the portfolio's expected return and risk will not be limited by the individual assets' expected return and risk.

In perfectly negative correlation (correlation coefficient = -1), the range of expected return and risk for all possible portfolio combinations will be even wider. This means that the portfolio's expected return and risk will be a combination of the individual assets' expected return and risk but in an inverse relationship.