(a)
To calculate:
By using a misestimated beta of
Introduction:
Standard deviation is a measure to calculate the deviation from the mean which is also called as a measure of dispersion. It helps in analyzing the performance of the fund.

Answer to Problem 18C
The standard deviation for the (imperfect) hedge portfolio is
Explanation of Solution
Given:
For calculating the standard deviation, the following formula is to be used:
By using the formula, the standard deviation is:
(b)
To calculate:
By taking the expected market return value of
Introduction:
Standard deviation is a measure to calculate the deviation from the mean which is also called as a measure of dispersion. It helps in analyzing the performance of the fund.

Answer to Problem 18C
The probability for getting a negative return is
Explanation of Solution
Given:
Based on the previous problem i.e
The expected return for zero beta market was calculated by following formula:
So the
The monthly returns are distributed normally given in the question. So the rate of return for zero beta is
Thus, the probability of getting a negative return is:
Now, in the present problem,
Number of contracts to be calculated which is as follows:
As the portfolio is unhedged, the rate of return should be computed fresh by adding the dolar value and future position.
The computation of dollar value of the stock portfolio:
Now, the value of future position:
The total value of dollar plus future is as follows:
Now, the new rate of return for the imperfect hedge portfolio is:
The monthly returns are distributed normally given in the question. So the rate of return for zero beta is
Thus, the probability for negative return is to be:
Thus, it can be said that it almost same to the probability computed before for the previous problem.
(c)
To calculate:
By taking the data of problem
Introduction:
Standard deviation is a measure to calculate the deviation from the mean which is also called as a measure of dispersion. It helps in analyzing the performance of the fund.

Answer to Problem 18C
The probability for getting a negative return is
Explanation of Solution
Given:
For calculating the standard deviation, the following formula is to be used:
By using the formula, the standard deviation is:
Now, the new rate of return for the imperfect hedge portfolio is:
The monthly returns are distributed normally given in the question. So the rate of return for zero beta is
Thus, the probability for negative return is to be:
(d)
To determine:
The reason for explaining the fact that the misestimated beta affects more to
Introduction:
Standard deviation is a measure to calculate the deviation from the mean which is also called as a measure of dispersion. It helps in analyzing the performance of the fund.

Explanation of Solution
The reason is the level of volatility to the portfolio. The more there is stock in portfolio with improper hedging, the more it contains volatility.
Thus, the reason that misestimated beta affects
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Chapter 20 Solutions
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