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Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

EXPECTED RETURN A stock's returns have the following distribution:

Demand for the Company’s Products Probability of This Demand Occurring Rate of Return If This Demand Occurs
Weak 0.1 (50%)
Below average 0.2 (5)
Average 0.4 16
Above average 0.2 25
Strong 0.1 60
1.0

Calculate the stock’s expected return, standard deviation, and coefficient of variation.

Summary Introduction

To determine: The stocks expected return, standard deviation, and coefficient of variation.

Portfolio: It refers to a group of financial assets like bonds, stocks, and equivalents of cash. The portfolio is held by investors and financial users. A portfolio is constructed in accordance with the risk tolerance and the objectives of the company.

Expected Return on Stock: The expected return on stock refers to the weighted average of expected returns on those assets, which are held in the portfolio.

Standard Deviation: The standard deviation refers to the stand-alone risk associated with the securities. It measures how much a data is dispersed with its standard value. Sigma represents the standard deviation.

Coefficient variation: The coefficient of variation is a tool to determine the risk. It determines the risk per unit of return. It is used for measurement, when the expected returns are same for two data.

Explanation

Compute expected return.

Given,

The weights are 0.1, 0.2, 0.4, 0.2, and 0.1 for the different demands.

The rate of return is (50%), (5%), 16%, 25% and 60% for the different demands.

The formula to calculate the expected return is,

rp=i=1Nwiri=w1r1+w2r2+...+wNrN

Where,

  • rp is the expected rate of return.
  • wi is the weight of the stock.
  • ri is the estimated rate of return.
  • N is the number of stocks.

Substitute 0.1, 0.2, 0.4, 0.2 and 0.1 for the weights w1,w2,w3,w4,andw5 respectively and (50%), (5%), 16%, 25% and 60% for the rate r1,r2,r3,r4andr5 respectively.

rp=[((0.1)×(50%))+((0.2)×(5%))+((0.4)×(16%))+((0.2)×(25%))+((0.1)×(60%))]=(5%)+(1%)+6.4%+5%+6%=11.4%

The stock’s expected return is 11.4%.

Compute standard deviation.

Given,

The weights are 0.1, 0.2, 0.4, 0.2, and 0.1 for the different demands, and

The rate of return is (50%), (5%), 16%, 25% and 60% for the different demands.

Calculated,

The expected rate of return is 11.4%.

Calculation of standard deviation:

The formula to calculate the standard deviation is:

σ=i=1N(rir)2Pi

Where,

  • r is the expected rate of return,
  • wi is the weight of the stock,
  • ri is the estimated rate of return,
  • N is the number of stocks,
  • σ is the standard deviation

Substitute 0

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