Question

Suppose you are wondering whether to invest in the shares of Amazon (Security 1) or Southwest (Security 2). You decide that Security 1 offers an expected return of 10.0% and Security 2 offers an expected return of 15.0%. After looking back at the past variability of the two stocks, you also decide that the standard deviation of returns is 26.6% for Security 1 and 27.9% for Security 2.

Calculate the expected portfolio return and standard deviation for different values of x₁ and x₂, assuming the correlation coefficient ρ₁₂ = 0. Repeat the problem for ρ₁₂ = +0.25. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

For two securities, namely: Security 1 and Security 2, the expected portfolio return = Portfolio Weight of Security 1 x Expected Return of Security 1 + Portfolio Weight of Security 2 x Expected Return of Security 2

Standard Deviation of Portfolio = [(Portfolio Weight of Security 1 x Standard Deviation of Security 1)^(2) + (Portfolio Weight of Security 2 x Standard Deviation of Security 2)^(2) + (2 x Portfolio Weight of Security 1 x Portfolio Weight of Security 2 x Standard Deviation of Security 1 x Standard Deviation of Security 2 x Correlation Coefficient)]^(1/2)