Asked by Deneatra Caesar on May 26, 2024

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Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%. The risk-free portfolio that can be formed with the two securities will earn a(n) _____ rate of return.

A) 8.5%
B) 9.0%
C) 8.9%
D) 9.9%

Perfectly Negatively Correlated

A relationship between two variables in which one variable increases as the other decreases with a correlation coefficient of -1.

Risk-free Portfolio

A portfolio consisting of investments that are considered to have zero risk, often associated with government securities.

Standard Deviation

A statistical measure of the dispersion or variability of a set of values, indicating how much the values differ from the mean.

  • Understand the concept of systematic and unsystematic risk and their implications for portfolio management.
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TH
Tanner HearneJun 02, 2024
Final Answer :
C
Explanation :
Given two perfectly negatively correlated securities, the risk-free portfolio's return is calculated as the weighted average of the two securities' returns. Since they are perfectly negatively correlated, we can form a risk-free portfolio by appropriately weighting the securities to eliminate risk. The exact rate can be determined through calculations that involve the expected returns and the weights of the securities in the portfolio. However, without performing these calculations directly (as the question does not provide specific weights or a formula to calculate the exact risk-free rate), we can infer that the risk-free rate should lie between the two given expected rates of return, 10% and 8%. Among the provided options, 8.9% is the only rate that falls between these two rates, making it the correct choice by process of elimination and understanding of the concept.