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	0.03			0.05
Standard deviation of returns	0.02			0.07
Beta	1.40			0.70

Round your answers to two decimal places.

1. 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 +0.5, compute the following:

   1. The expected return from the portfolio: %

   2. The standard deviation of returns from the portfolio: %

2. 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?

   1. The expected return from the portfolio: %

   2. The standard deviation of returns from the portfolio: %

3. What happens to the expected return and standard deviation of returns of the portfolio in Part a if the following conditions exist?

   1. 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: %

   2. 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: %

   3. The correlation of returns between Securities X and Y is -0.7.
      The expected return from the portfolio: %

      The standard deviation of returns from the portfolio: %

Answer 1

a) Portfolio Returns = w1 x R1 + w2 x R2

Portfolio SD = [(w1 x SD1)^2 + (w2 x SD2)^2 + (2 x w1 x w2 x SD1 x SD2 x corr12)]^(1/2)

	X	Y	Portfolio
Return (R)	3.00%	5.00%	4.20%
SD	2.00%	7.00%	4.65%
Weight (w)	40%	60%

b)

	X	Y	Portfolio
Return	3.00%	5.00%	3.60%
SD	2.00%	7.00%	3.05%
Weight	70%	30%

c) With change in correlation, there is no change in expected returns, only standard deviation will vary. It will remain at 4.20%

i) If corr12 = 1, SD = 5.00%

ii) If corr12 = 0, SD = 4.28%

iii) If corr12 = -0.7, SD = 3.68%