Question

You are considering investing in two securities, X and Y. The following data are available for the two securities: Security X Security Y Expected return 0.09 0.02 Standard deviation of returns 0.04 0.06 Beta 1.00 0.85

Round your answers to two decimal places.

If you invest 40 percent of your funds in Security X and 60 percent in Security Y and if the correlation of returns between X and Y is +0.45, compute the following: The expected return from the portfolio: %

The standard deviation of returns from the portfolio: %

What happens to the expected return and standard deviation of returns of the portfolio in Part a if 70 percent of your funds are invested in Security X and 30 percent of your funds are invested in Security Y? The expected return from the portfolio: %

The standard deviation of returns from the portfolio: %

What happens to the expected return and standard deviation of returns of the portfolio in Part a if the following conditions exist? The correlation of returns between Securities X and Y is +1. The expected return from the portfolio: %

The standard deviation of returns from the portfolio: %

The correlation of returns between Securities X and Y is 0. The expected return from the portfolio: %

The standard deviation of returns from the portfolio: %

The correlation of returns between Securities X and Y is -0.9. The expected return from the portfolio: %

The standard deviation of returns from the portfolio: %

Answer 1

Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)

Standard deviation of portfolio =

(wxox)2 + (wyoy)2 + 2 * 0x *0x *W, * Wy* P1,2

where x and y are the securities

If you invest 40 percent of your funds in Security X and 60 percent in Security Y and if the correlation of returns between X and Y is +0.45

Expected return = 0.4*0.09+0.6*0.02= 0.048 = 4.80%

Standard deviation = ((0.4*0.04)^2 + (0.6*0.06)^2 + 2*0.4*0.6*0.04*0.06*0.45)^0.5 = 4.55%

What happens to the expected return and standard deviation of returns of the portfolio in Part a if 70 percent of your funds are invested in Security X and 30 percent of your funds are invested in Security Y?

Expected return = 0.7*0.09+0.3*0.02 = 0.069 = 6.90%

Standard deviation = ((0.7*0.04)^2 + (0.3*0.06)^2 + 2*0.7*0.3*0.04*0.06*0.45)^0.5 = 3.95%

What happens to the expected return and standard deviation of returns of the portfolio in Part a if the following conditions exist? The correlation of returns between Securities X and Y is +1.

Expected return = 0.4*0.09+0.6*0.02= 0.048 = 4.80%

Standard deviation = ((0.4*0.04)^2 + (0.6*0.06)^2 + 2*0.4*0.6*0.04*0.06*1)^0.5 = 5.20%

The correlation of returns between Securities X and Y is 0

Expected return = 0.4*0.09+0.6*0.02= 0.048 = 4.80%

Standard deviation = ((0.4*0.04)^2 + (0.6*0.06)^2 + 2*0.4*0.6*0.04*0.06*0)^0.5 = 3.94%

The correlation of returns between Securities X and Y is -0.9

Expected return = 0.4*0.09+0.6*0.02= 0.048 = 4.80%

Standard deviation = ((0.4*0.04)^2 + (0.6*0.06)^2 + 2*0.4*0.6*0.04*0.06*(-0.9))^0.5 = 2.27%