(a) To calculate: The expected profit and standard deviation where ten stocks have an positive alpha of 3 % and ten have negative alpha of − 3 % when 20 stocks data studied by analyst and beta of all the stock in the economy is 1 . Firms have a standard deviation of 30 % . Introduction: Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return . Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Question

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Answer 1

Question

Chapter 7, Problem 29PS

Summary Introduction

(a)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 20 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation of $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$1,34,164.08$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $10$ stock is $3%$

Alpha of $10$ stock is $−3%$

Investors invest $$1$ million for buying and selling positive and negative alpha stock respectively.

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation for return as follows

$Standard Deviation=No. of stocksTotal invest10Std. deviation2=20$10,00,00010×0.302=20$30,0002=$18,00,00,00,000=$1,34,164.08$

The risk exposure on positive and negative alpha will be eliminated but the variance is not zero. So the portfolio is not diversified.

Summary Introduction

(b)

To calculate:

The Expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst. And beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$84,852.81$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $25$ stock is $3%$

Alpha of $25$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=50$10,00,00025×0.302=50$12,0002=$7,20,00,00,000=$84,852.81$

Summary Introduction

(c)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$60,000$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $50$ stock is $3%$

Alpha of $50$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=100$10,00,00050×0.302=100$6,0002=$3,60,00,00,000=$60,000$

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Answer 2

Question

Chapter 7, Problem 29PS

Summary Introduction

(a)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 20 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation of $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$1,34,164.08$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $10$ stock is $3%$

Alpha of $10$ stock is $−3%$

Investors invest $$1$ million for buying and selling positive and negative alpha stock respectively.

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation for return as follows

$Standard Deviation=No. of stocksTotal invest10Std. deviation2=20$10,00,00010×0.302=20$30,0002=$18,00,00,00,000=$1,34,164.08$

The risk exposure on positive and negative alpha will be eliminated but the variance is not zero. So the portfolio is not diversified.

Summary Introduction

(b)

To calculate:

The Expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst. And beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$84,852.81$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $25$ stock is $3%$

Alpha of $25$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=50$10,00,00025×0.302=50$12,0002=$7,20,00,00,000=$84,852.81$

Summary Introduction

(c)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$60,000$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $50$ stock is $3%$

Alpha of $50$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=100$10,00,00050×0.302=100$6,0002=$3,60,00,00,000=$60,000$

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Answer 3

Question

Chapter 7, Problem 29PS

Summary Introduction

(a)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 20 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation of $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$1,34,164.08$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $10$ stock is $3%$

Alpha of $10$ stock is $−3%$

Investors invest $$1$ million for buying and selling positive and negative alpha stock respectively.

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation for return as follows

$Standard Deviation=No. of stocksTotal invest10Std. deviation2=20$10,00,00010×0.302=20$30,0002=$18,00,00,00,000=$1,34,164.08$

The risk exposure on positive and negative alpha will be eliminated but the variance is not zero. So the portfolio is not diversified.

Summary Introduction

(b)

To calculate:

The Expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst. And beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$84,852.81$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $25$ stock is $3%$

Alpha of $25$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=50$10,00,00025×0.302=50$12,0002=$7,20,00,00,000=$84,852.81$

Summary Introduction

(c)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$60,000$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $50$ stock is $3%$

Alpha of $50$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=100$10,00,00050×0.302=100$6,0002=$3,60,00,00,000=$60,000$

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Answer 4

Question

Chapter 7, Problem 29PS

Summary Introduction

(a)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 20 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation of $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$1,34,164.08$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $10$ stock is $3%$

Alpha of $10$ stock is $−3%$

Investors invest $$1$ million for buying and selling positive and negative alpha stock respectively.

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation for return as follows

$Standard Deviation=No. of stocksTotal invest10Std. deviation2=20$10,00,00010×0.302=20$30,0002=$18,00,00,00,000=$1,34,164.08$

The risk exposure on positive and negative alpha will be eliminated but the variance is not zero. So the portfolio is not diversified.

Summary Introduction

(b)

To calculate:

The Expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst. And beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$84,852.81$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $25$ stock is $3%$

Alpha of $25$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=50$10,00,00025×0.302=50$12,0002=$7,20,00,00,000=$84,852.81$

Summary Introduction

(c)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$60,000$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $50$ stock is $3%$

Alpha of $50$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=100$10,00,00050×0.302=100$6,0002=$3,60,00,00,000=$60,000$

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Answer 5

Chapter 7, Problem 29PS

Summary Introduction

(a)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 20 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation of $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$1,34,164.08$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $10$ stock is $3%$

Alpha of $10$ stock is $−3%$

Investors invest $$1$ million for buying and selling positive and negative alpha stock respectively.

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation for return as follows

$Standard Deviation=No. of stocksTotal invest10Std. deviation2=20$10,00,00010×0.302=20$30,0002=$18,00,00,00,000=$1,34,164.08$

The risk exposure on positive and negative alpha will be eliminated but the variance is not zero. So the portfolio is not diversified.

Summary Introduction

(b)

To calculate:

The Expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst. And beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$84,852.81$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $25$ stock is $3%$

Alpha of $25$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=50$10,00,00025×0.302=50$12,0002=$7,20,00,00,000=$84,852.81$

Summary Introduction

(c)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$60,000$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $50$ stock is $3%$

Alpha of $50$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=100$10,00,00050×0.302=100$6,0002=$3,60,00,00,000=$60,000$

Answer 6

Chapter 7, Problem 29PS

Summary Introduction

(a)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 20 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation of $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$1,34,164.08$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $10$ stock is $3%$

Alpha of $10$ stock is $−3%$

Investors invest $$1$ million for buying and selling positive and negative alpha stock respectively.

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation for return as follows

$Standard Deviation=No. of stocksTotal invest10Std. deviation2=20$10,00,00010×0.302=20$30,0002=$18,00,00,00,000=$1,34,164.08$

The risk exposure on positive and negative alpha will be eliminated but the variance is not zero. So the portfolio is not diversified.

Answer 7

Chapter 7, Problem 29PS

Summary Introduction

(a)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 20 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation of $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Answer 8

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$1,34,164.08$

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $10$ stock is $3%$

Alpha of $10$ stock is $−3%$

Investors invest $$1$ million for buying and selling positive and negative alpha stock respectively.

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation for return as follows

$Standard Deviation=No. of stocksTotal invest10Std. deviation2=20$10,00,00010×0.302=20$30,0002=$18,00,00,00,000=$1,34,164.08$

The risk exposure on positive and negative alpha will be eliminated but the variance is not zero. So the portfolio is not diversified.

Answer 13

Summary Introduction

(b)

To calculate:

The Expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst. And beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$84,852.81$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $25$ stock is $3%$

Alpha of $25$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=50$10,00,00025×0.302=50$12,0002=$7,20,00,00,000=$84,852.81$

Answer 14

Summary Introduction

(b)

To calculate:

The Expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst. And beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Answer 15

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$84,852.81$

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $25$ stock is $3%$

Alpha of $25$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=50$10,00,00025×0.302=50$12,0002=$7,20,00,00,000=$84,852.81$

Answer 20

Summary Introduction

(c)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$60,000$

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $50$ stock is $3%$

Alpha of $50$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=100$10,00,00050×0.302=100$6,0002=$3,60,00,00,000=$60,000$

Answer 21

Summary Introduction

(c)

To calculate:

The expected profit and standard deviation where ten stocks have an positive alpha of $3%$ and ten have negative alpha of $−3%$ when 50 stocks data studied by analyst and beta of all the stock in the economy is $1$ . Firms have a standard deviation is $30%$ .

Introduction:

Expected return: It is the gain or loss to an investor which is expected on an investment and known as expected rate of return.

Standard deviation: It is historical volatility. It's applied to the annual rate of return to quantify the investment volatility.

Answer 22

Expert Solution

Answer to Problem 29PS

Expected profit is $$60,000$

Standard deviation of return is $$60,000$

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

Beta of all stock is $1$

Alpha of $50$ stock is $3%$

Alpha of $50$ stock is $−3%$

$Expected return=Inva1+w×Rm-Inva2+w×Rm$

Where:

$a1$ is first 10 stock's positive alpha i.e. $3%$

$a2$ is next 10 stock's negative alpha i.e. $−3%$

w is weight measurement of each stock i.e. $1$

$Rm$ is Market return.

So expected return by using above formula

$Expected Return=$10,00,0000.03+1×Rm−$10,00,000−0.03+1×Rm=$10,00,0000.03+Rm−$10,00,000−0.03−Rm=$10,00,0000.03+Rm+0.03−Rm=$10,00,000×0.06=$60,000$

Standard deviation is calculated as under:

$Standard Deviation=No. of stocksTotal invest25Std. deviation2=100$10,00,00050×0.302=100$6,0002=$3,60,00,00,000=$60,000$

Answer 27

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Answer to Problem 29PS

Explanation of Solution

Answer to Problem 29PS

Explanation of Solution

Answer to Problem 29PS

Explanation of Solution

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