3. To calculate the variance of a three-stock portfolio, you need to add nine bo

Question

3. To calculate the variance of a three-stock portfolio, you need to add nine boxes:




Use the same symbols that we used in chapter 7; for example, x1=proportion invested in stock 1 and s12=covariance between stock 1 and stock 2. Now complete the nine boxes.

4. Suppose the standard deviation of market return is 15%.
a. What is the standard deviation of returns on a well-diversified portfolio with a beta of 1.4%?
b. What is the standard deviation of returns on a well-diversified portfolio with a beta of 0%?
c. A well diversified portfolio has a standard deviation of 10%. What is its beta?
d. A poorly diversified portfolio has a standard deviation of 15%. What can you say about its beta?




5. Here are returns and standard deviations for four investments.

Return Standard Deviation
T-bills 1.5% 0%
Stock X 9 10
Stock Y 15.5 25
Stock Z 20 22
Calculate the standard deviation of the following portfolios.
a. 60% in T-bills, 40% in stock X.
b. 50% in each Y and Z, assuming the shares have
- perfect positive correlation
-perfect negative correlation
-no correlation
c. Stock Y has a lower return than Z but a higher standard deviation. Does that mean that Y’s price is too high or that Z’s price is too low?

Explanation / Answer

3. Stock Proportion of funds invested in Stock 1 Probability Expected return on stock Deviation Diviation square Squared deviation*probability Stock Proportion of funds invested in Stock 1 Probability Expected return on stock Deviation Diviation square Squared deviation*probability
4.          Beta   = Relative Volatility/Market Volatility         (a)   Beta is 1.4%.                       1.4%      = Relative Volatility/15%                  Relative Volatility      = 1.4%*15%                                                  =21%          Standard deviation on well diversified portfolio is 21% (b)Beta is 0%                             0%      = Relative Volatility/15%                      Relative Volatility   = 0%             Standard deviation on well diversified portfolio is 0 (c)                Beta      = 10%/15%                             = 0.67 (d)          Beta      = 15%/15%                       = 1       Beta is 1. There is no risk and return. 5. Calculation of S.D: (a) Stock Proportion Expected return Deviation Deviation Squared Squared deivaion*Prop T-bill 0.6 1.50% -3.75% 0.001406 0.000844 x 0.4 9% 3.75% 0.001406 0.000563 0.001406 Standard deviation is 1.4% (b) Stock Proportion Expected return Deviation Deviation Squared Squared deivaion*Prop Y 0.5 15.50% -2.25% 0.000506 0.000253 Z 0.5 20% 2.25% 0.000506 0.000253 0.000506       Standard deviation is 0.5% (c)       Y's stock prices are too high                              Stock Proportion of funds invested in Stock 1 Probability Expected return on stock Deviation Diviation square Squared deviation*probability

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