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# Expected Returns and Deviation

Complete Problems 1, 2, and 3 from the Questions and Problems section of Chapter 11 (shown below). Remember to complete all parts of the questions, and report the results of your analysis.

1. Use the following information on states of the economy and stock returns to calculate the expected return for Dingaling Telephone.
2. Using the information in the previous question, calculate the standard deviation of returns.

3. Repeat Questions 1 & 2 assuming that all three states are equally likely.

Expected Returns and Deviation

Question 1

Basing on the probability of the states’ future economy and expected security returns, we can be able to calculate Expected returns, E(R). In the calculations, we sum up all the states after finding the product of the economy’s state probability and the returns projected (Fisher, Martin & Mueller, 1991). Such calculation is as shown below:

# The economy’s state

Probability (Ps) Security

return (Rs)

Product of

Ps andRs

## Recession

.30 -8% 0.3 (-0.08)
Normal .40 13% 0.4 (0.13)
Boom .30 23% 0.3 (0.23)

0.97    = 9.7%

Question 2: Standard deviation

1. The return within each state allows subtraction of its expected amount. The difference is then squared.
2. After squaring the differences, each is multiplied by the state of economy’s probability.
3. The summation on the weighted square terms are then done to get the variance. We then find the square root to obtain the standard deviation as shown below:

# Economys’State

Probability

(Ps)

Security return (Rs) Product of

Ps andRs

Product of (Rs – E(R))2and Ps
Recession

.30

-8%

.3(- .08)

.3(- .08 – .097)2

Normal

.40

13%

.4( .13)

.4(.13-.097)2

Boom

.30

23%

.3(.23)

.3(.23-.097)2

9.7% 1.514% 12.305%
Mean Variance Standard Deviation

Question 3

When each are equally likely, since they are three states, each of them equally likely will be 1/3 = 0.33. This is the new state of the economy. The procedure for calculating the expected return and standard deviation remains the same. Therefore, it follows that:

Expected returns when equally likely is

# The economy’s state

Probability (Ps) Security return (Rs) Ps * Rs

## Recession

.33 -8% 0.33(-0.08)
Normal .33 13% 0.33(0.13)
Boom .33 23% 0.33(0.23)

9.24%

Standard deviation when equally likely

# Economy’s State

Probability

(ps)

Security return (Rs) Product between

Ps and Rs

Multiplying

(Rs – E(R))2and Ps

Recession .33 -8% .33*(-.08)

(-.08 – .0924)2*(.33)

Normal .33 13% .33*(.13)

(.13 – .0924)2*(.33)

Boom .33 23% .33*(.23)

(.23 – .0924)2*(.33)

9.24% 1.65% 12.85%
Mean Variance Standard Deviation

Reference

Fisher, J. D., Martin, R. S., & Mueller, P. (1991). The language of real estate appraisal. Chicago, Ill: Real Estate Education Co.