investment portfolio management ans
1. Suppose that you have $1 million and the following two opportunities from which to construct a portfolio:
a. Risk-free asset earning 12% per year.
b. Risky asset with expected return 30% per year and standard deviation of 40%.
If you construct a portfolio with a standard deviation of 30%, what is its expected rate of return?
Ans:
P = 30 = yy y = 0.75
E(rP) = 12 + 0.75(30 12) = 25.5%
2. Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows: Stock Expected Return Standard Deviation A 10% 5% B 15 10 Correlation = -1 Suppose that it is possible to borrow at the risk-free rate . What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from Stocks A and B.)
Ans:
Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio, in equilibrium, will be the risk-free rate. To find the proportions of this portfolio [with the proportion wA invested in Stock A and wB = (1 – wA ) invested in Stock B], set the standard deviation equal to zero. With perfect negative correlation, the portfolio standard deviation is:
P = Absolute value [wAA wBB]
0 = 5wA [10 (1 – wA )] wA = 0.6667
The expected rate of return for this risk-free portfolio is:
E(r) = (0.6667 10) + (0.3333 15) = 11.667%
Therefore, the risk-free rate is 11.667%.
3. Abigail Grace has a $900,000 fully diversified portfolio. She subsequently inherits Euro Co common stock worth $100,000. Her financial adviser provided her with the following forecast information:
Risk and Return Characteristics Expected Monthly Standard Deviation of Returns Monthly Returns Original Portfolio 0.67% 2.37% Euro Co 1.25 2.95 The correlation coefficient of Euro Co stock returns with the original portfolio returns is 0.40.
The inheritance changes Grace’s
a. Risk-free asset earning 12% per year.
b. Risky asset with expected return 30% per year and standard deviation of 40%.
If you construct a portfolio with a standard deviation of 30%, what is its expected rate of return?
Ans:
P = 30 = yy y = 0.75
E(rP) = 12 + 0.75(30 12) = 25.5%
2. Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows: Stock Expected Return Standard Deviation A 10% 5% B 15 10 Correlation = -1 Suppose that it is possible to borrow at the risk-free rate . What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from Stocks A and B.)
Ans:
Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio, in equilibrium, will be the risk-free rate. To find the proportions of this portfolio [with the proportion wA invested in Stock A and wB = (1 – wA ) invested in Stock B], set the standard deviation equal to zero. With perfect negative correlation, the portfolio standard deviation is:
P = Absolute value [wAA wBB]
0 = 5wA [10 (1 – wA )] wA = 0.6667
The expected rate of return for this risk-free portfolio is:
E(r) = (0.6667 10) + (0.3333 15) = 11.667%
Therefore, the risk-free rate is 11.667%.
3. Abigail Grace has a $900,000 fully diversified portfolio. She subsequently inherits Euro Co common stock worth $100,000. Her financial adviser provided her with the following forecast information:
Risk and Return Characteristics Expected Monthly Standard Deviation of Returns Monthly Returns Original Portfolio 0.67% 2.37% Euro Co 1.25 2.95 The correlation coefficient of Euro Co stock returns with the original portfolio returns is 0.40.
The inheritance changes Grace’s