Finance management cengage 2013 chapter 08

Chapter 8

Risk and Rates of Return
Stand-Alone Risk
Portfolio Risk
Risk and Return: CAPM/SML

8-1
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What is investment risk?

•

Two types of investment risk

•

Investment risk is related to the probability of
earning a low or negative actual return.

•

– Stand-alone risk
– Portfolio risk
The greater the chance of lower than expected, or
negative returns, the riskier the investment.

8-2
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Probability Distributions

•

A listing of all possible outcomes, and the
probability of each occurrence.

•

Can be shown graphically.
Firm X

Firm Y
-70

0

15

100

Rate of
Return (%)

Expected Rate of Return
8-3
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Selected Realized Returns, 1926-2010

Source: Based on Ibbotson Stocks, Bonds, Bills, and Inflation: 2011 Classic
Yearbook (Chicago: Morningstar, Inc., 2011), p. 32.
8-4
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Hypothetical Investment Alternatives
Economy
Recession

Prob T-Bills
HT
Coll
.
0.1 5.5% -27.0% 27.0%

USR

MP

6.0% -17.0%

Below avg

0.2

5.5%

-7.0%

13.0% -14.0% -3.0%

Average

0.4

5.5%

15.0%

0.0%

Above avg

0.2

5.5%

30.0% -11.0% 41.0% 25.0%

Boom

0.1

5.5%

45.0% -21.0% 26.0% 38.0%

3.0%

10.0%

8-5
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Why is the T-bill return independent of the economy?
Do T-bills promise a completely risk-free return?

•

T-bills will return the promised 5.5%, regardless of
the economy.

•

No, T-bills do not provide a completely risk-free
return, as they are still exposed to inflation.
Although, very little unexpected inflation is likely to
occur over such a short period of time.

•
•

T-bills are also risky in terms of reinvestment risk.
T-bills are risk-free in the default sense of the word.

8-6
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How do the returns of High Tech and Collections
behave in relation to the market?

•

High Tech: Moves with the economy, and has a
positive correlation. This is typical.

•

Collections: Is countercyclical with the economy,
and has a negative correlation. This is unusual.

8-7
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Calculating the Expected Return
rˆ = Expected rate of return
N

rˆ = ∑ Piri
i=1

rˆ = (0.1)(-27%) + (0.2)(-7%) + (0.4)(15%)
+ (0.2)(30%) + (0.1)(45%)

= 12.4%

8-8
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Summary of Expected Returns
Expected Return
High Tech
Market
US Rubber
T-bills 5.5%
Collections

12.4%
10.5%
9.8%
1.0%

High Tech has the highest expected return, and
appears to be the best investment alternative, but is it
really? Have we failed to account for risk?
8-9
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Calculating Standard Deviation
σ = Standard deviation
σ = Variance = σ2

σ=

N

2
ˆ
(
r
−
r
)
Pi
∑
i=1

8-10
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Standard Deviation for Each Investment
σ=

N

2
ˆ
(
r
−
r

)
Pi
∑
i=1

(5.5 − 5.5) (0.1) + (5.5 − 5.5) (0.2)


= (5.5 − 5.5)2 (0.4) + (5.5 − 5.5)2 (0.2)
2


+
(
5
.
5
−
5
.
5
)
(0.1)


= 0.0%
2

σ T -bills
σ T -bills

2

σHT = 20%

σColl = 13.2%

σM = 15.2%

σUSR = 18.8%

1/2

8-11

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.


Comparing Standard Deviations

Prob.

T-bills

USR
HT

0

5.5

9.8

12.4

Rate of Return (%)
8-12

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.


Comments on Standard Deviation as a Measure of
Risk

•

Standard deviation (σi) measures total, or standalone, risk.

•

The larger σi is, the lower the probability that actual
returns will be close to expected returns.

•

Larger σi is associated with a wider probability
distribution of returns.

8-13
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Comparing Risk and Return
Security
T-bills
High Tech
Collections*
US Rubber*
Market

Expected Return, rˆ
5.5%
12.4
1.0
9.8
10.5

Risk, σ
0.0%
20.0
13.2
18.8
15.2

*Seems out of place.

8-14
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Coefficient of Variation (CV)

•

A standardized measure of dispersion about the
expected value, that shows the risk per unit of
return.
Standard deviation σ
CV =
=
Expected return
rˆ

8-15
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Illustrating the CV as a Measure of Relative Risk
Prob.
A

B

0

Rate of Return (%)

σA = σB , but A is riskier because of a larger probability of
losses. In other words, the same amount of risk (as
measured by σ) for smaller returns.

8-16
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Risk Rankings by Coefficient of Variation

T-bills
High Tech
Collections
US Rubber
Market

CV
0.0
1.6
13.2
1.9
1.4

•

Collections has the highest degree of risk per
unit of return.

•

High Tech, despite having the highest standard
deviation of returns, has a relatively average CV.
8-17

© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.


Investor Attitude Towards Risk

•

Risk aversion: assumes investors dislike risk and
require higher rates of return to encourage them to
hold riskier securities.

•

Risk premium: the difference between the return
on a risky asset and a riskless asset, which serves as
compensation for investors to hold riskier
securities.

8-18
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Portfolio Construction: Risk and Return

•

Assume a two-stock portfolio is created with $50,000
invested in both High Tech and Collections.

•

A portfolio’s expected return is a weighted average of
the returns of the portfolio’s component assets.

•

Standard deviation is a little more tricky and requires
that a new probability distribution for the portfolio
returns be constructed.

8-19
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Calculating Portfolio Expected Return

rˆp is a weighted average :
N

rˆp = ∑ wirˆi
i=1

rˆp = 0.5(12.4%) + 0.5(1.0%) = 6.7%

8-20
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An Alternative Method for Determining
Portfolio Expected Return

Economy
Recession
Below avg
Average
Above avg
Boom

Prob
0.1
0.2
0.4
0.2
0.1

HT
-27.0%
-7.0%
15.0%
30.0%
45.0%

Coll
27.0%
13.0%
0.0%
-11.0%
-21.0%

Port
0.0%

3.0%
7.5%
9.5%
12.0%

rˆp = 0.10 (0.0%) + 0.20 (3.0%) + 0.40 (7.5%)
+ 0.20 (9.5%) + 0.10 (12.0%) = 6.7%
8-21
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Calculating Portfolio Standard Deviation and CV
 0.10 (0.0 - 6.7) 

2 
+ 0.20 (3.0 - 6.7) 
σp = + 0.40 (7.5 - 6.7)2 


+ 0.20 (9.5 - 6.7)2 


2
+ 0.10 (12.0 - 6.7) 
2

1

2

= 3.4%

3.4%
CVp =
= 0.51
6.7%
8-22
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Comments on Portfolio Risk Measures

•

σp = 3.4% is much lower than the σi of either stock
(σHT = 20.0%; σColl = 13.2%).

•

σp = 3.4% is lower than the weighted average of
High Tech and Collections’ σ (16.6%).

•

Therefore, the portfolio provides the average
return of component stocks, but lower than the
average risk.

•

Why? Negative correlation between stocks.

8-23
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General Comments about Risk

•
•

σ ≈ 35% for an average stock.

•

Combining stocks in a portfolio generally lowers
risk.

Most stocks are positively (though not perfectly)
correlated with the market (i.e., ρ between 0 and 1).

8-24
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Returns Distribution for Two Perfectly
Negatively Correlated Stocks (ρ = -1.0)

8-25
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