1. 1. Principles of Investment; Diversification

2. 1. Assume that an individual can either invest all of his resources in one of the two securities, A or B; or, alternatively, he can diversify his investment between the two. The distributions of the returns are as follows:

    

   Security A		Security B
   Return	Probability	Return	Probability
   -10%	0.5	-20%	0.5
   50%	0.5	60%	0.5

   Assume that the correlation between the returns from the two securities is zero, and answer the following questions:

   • Calculate each security’s expected return, variance and standard deviation.

   • Calculate the probability distribution of the returns on a mixed portfolio comprised of equal proportions of securities A and B, i.e. calculate all possible returns on this portfolio and the probability of each one.[1]

   • Also calculate the portfolio’s expected return, variance and standard deviation.

   • Calculate the expected return and the variance of a mixed portfolio comprised of 75% of security A and 25% of security B.

   1. The securities of companies Z and Y have the following expected returns and standard deviations:

   Company Z	15%	20%
   Company Y	35%	40%

   Assume that the correlation between the returns of the two securities is 0.25.

      (a)        Calculate the expected return and standard deviation for the following portfolios:

   (1) 100%Z

   (2) 75%Z + 25%Y

   (3) 50%Z + 50%Y

   (4) 25%X + 75%Y

   (5) 100%Y

   (b)     Graph your results (standard deviation on the X axis, Expected return on the Y axis).

   (c)     Which of the portfolios in part (a) is not optimal? Explain.

    

   Principles of Investment; Diversification

3. 2. Consider two assets A and B for which return distributions can be summarized as follows:

    

   Asset A	3%	1%
   Asset B	7%	2%
   Correlation Coefficient

    

   What is the risk of the minimum risk portfolio composed of these two Stocks? (Hint: Use the calculus to minimize s_p²). Is the risk of the minimum risk portfolio below that of every constituent asset? What is the expected ROR on the minimum risk portfolio?

    

   3. Consider two other assets A’ and B’, which are identical (in statistical summary), respectively, to A and B above except that r_AB = 1.

   4. Draw the graph of the efficient frontier in this case

   5. Write down the answers to the same questions as in problem 3.

    

   4. Assume N securities. The expected returns on all the securities are equal to 0.01 and the variances of their returns are all equal to 0.01. The covariances of the returns between two securities are all equal to 0.005.

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