Question

Analyzing portfolio risk and return involve the understanding of expected returns from a portfolio. Consider the following case: Andre is an amateur investor who holds a small portfolio consisting of only four stocks.The stock holdings in his portfolio are shown in the following table: Artemis (20% of portfolio, 6.00% expected return, 34.00% standard deviation) Babish & Co. (30% of portfolio, 14.00% expected return, 38.00% standard deviation) Cornell Industries (35% of portfolio, 12.00% expected return, 41.00 standard deviation) Danforth Motors (15% of portfolio, 3.00% expected return, 43.00% standard deviation) What is the expected return of Andre's stock portfolio? a. 15.08, b. 13.57, c. 10.05 d. 7.54 Suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (p=0.4) with each of the other stocks. If the weighted average of the risk (standard deviation) of the individual securities in the partially diversified portfolio of four stocks is 39%, the portfolio's standard deviation most likely is ________ 39%.
a. equal to.
b. more than.
c. less than.

Answer 1

Answer:

In order to find expected portfolio return we multiply the weight of each security by its expected return and then add all the values.

Artemis = 0.2*0.06=0.012= 1.2%

Babish= 0.3*0.14=0.042= 4.2%

Cornell = 0.35*0.12= 0.042= 4.2%

Danforth Motors = 0.15*0.03=0.0045= 0.45%

1.2+4.2 + 4.2 +0.45=10.05%

Then in order to find the portfolio variance  the formula is

Variance = (w(1)^2 * SD(1)^2) + (w(2)^2 * SD(2)^2) + (2 * (w(1)*(1)*w(2)*o(2)*q(1,2)))

and we can under root this to find the standard deviation

Variance = (w(1)^2 * SD(1)^2) + (w(2)^2 * SD(2)^2) + (2 * (w(1)*SD(1)*w(2)*SD(2)*CR(1,2)))

W (1): Weight of one stock in the portfolio squared.

SD (1): The standard deviation of one asset in the portfolio squared.

W (2): Weight of second stock in the portfolio squared.

O (2): The standard deviation of the second asset in the portfolio squared.

CR(1,2): The correlation between the two assets in the portfolio has been denoted as q (1,2).

When we use this formula whenever the co relation is less than 1 the portfolio standard deviation is less than the weighted average standard deviation of all the individual stocks.

So in this case as the co relation is less than 1 portfolios standard deviation is less than 39%

Explanation: