a.
To determine: The cost of restriction in terms of Sharpe’s measure
Introduction: The Sharpe ratio is used to measure the accumulated performance of an aggregate investment portfolio or an individual stock. It evaluates the performance of equity investment to the
a.
Answer to Problem 18PS
The cost of restriction in terms of Sharpe’s measure is in the cost
Explanation of Solution
Given Information:
Sharpe ratio is mostly used to measure the risk return. For this, first compute the expected return on investment or individual stock and then subtract it from the risk free rate of return. Generally, when the ratio is greater than 1, it is considered as acceptable by the investors.
If the manager would not sell the securities he would consider only the stock A and C
A | 1.6 | 3,364 | 0.00048 | 0.3352 |
C | 3.4 | 3,600 | 0.00094 | 0.6648 |
Total | 0.001420 | 1 |
The alpha of active portfolios,
The beta of active portfolio
So, the standard deviation of portfolio is,
The active risky portfolio,
The adjustment of beta,
The information ratio for the active portfolio,
The Sharpe ratio for the optimal portfolio,
Calculation of Beta,
The expected return,
The variance,
As, A = 2.8, the optimal position is calculated as,
So, the share per each asset is,
BILLS | 1-0.5455 | 45.45% |
MARKET | 0.5455x(1-0.0931) | 49.47% |
A | 0.5455x (0.0931)x (0.3352) | 1.70% |
C | 0.5455 x (0.0931)x (0.6648) | 3.38% |
100.00% |
b.
To determine: The utility loss to the investor in new complete portfolio
Introduction: The Sharpe ratio is used to measure the accumulated performance of an aggregate investment portfolio or an individual stock. It evaluates the performance of equity investment to the rate of return.
b.
Answer to Problem 18PS
The utility levels for the unconstrained, constrained and passive strategy are 10.40%, 10.23% and 10.16% respectively.
Explanation of Solution
Given Information:
Forecast returns, standard deviations and the beta values are given.
Sharpe ratio is mostly used to measure the risk return. For this, first compute the expected return on investment or individual stock, then subtract it from the risk free rate of return. Generally, when the ratio is greater than 1, it is considered as acceptable by the investors.
The variance and for passive strategy, the calculations are
E ( R) | ||
UNCONSRAINED STRATEGY | 4.79 | 170.95 |
CONSTRAINED STRATEGY | 4.46 | 159.36 |
PASSIVE STRATEGY | 4.32 | 154.31 |
By using the utility level formula,
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Chapter 8 Solutions
INVESTMENTS(LL)W/CONNECT
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