6. risk return

Chapter 6
The Meaning
and
Measurement of
Risk and Return

Copyright © 2011 Pearson Prentice Hall.
All rights reserved.

Learning Objectives

1. Define and measure the expected rate
of return of an individual investment.
2. Define and measure the riskiness of
an individual investment.
3. Compare the historical relationship
between risk and rates of return in the
capital markets.
© 2011 Pearson Prentice Hall. All rights
reserved. 6-2

Learning Objectives

4. Explain how diversifying investments
affects the riskiness and expected rate
of return of a portfolio or combination
of assets.
5. Explain the relationship between an
investor’s required rate of return on an
investment and the riskiness of the
investment.
reserved. 6-3

Slide Contents

Principles used in this chapter
1. Expected return
2. Risk Defined and Measured
3. Rates of Return: The Investor’s Experience
4. Risk and Diversification
5. The Investor’s Required Rate of Return

reserved. 6-4

Principles Applied
in this Chapter

 Principle 3:
Risk requires a reward.
 Principle 1:
Cash flow is what matters.

reserved. 6-5

1. Expected Return

1.1 Historical or holding-period or realized
rate of return
Holding period return = payoff during the
“holding” period. Holding period could be
one day, few weeks or few years.

reserved. 6-6

Expected Return

 You bought 1 share of HPD for $19.70 in May
2008 and sold it for $32.32 in May 2009. The
company paid divided of 8 cents every
quarter during the last two years.
 Holding Period dollar gain, DG
= 32.32 + .08*4 – 19.70
= $12.94

reserved. 6-7

Expected Return

Holding Period rate of return

= 12.94/19.70
= .6568 or 65.68%

reserved. 6-8

Expected Return

1.2 Expected Cash Flows and Expected
Return
 The expected benefits or returns, an
investment generates come in the form of
cash flows.
 Cash flows are used to measure returns (not
accounting profits).

reserved. 6-9

Expected Return

 The expected cash flow is the weighted
average of the possible cash flows outcomes
such that the weights are the probabilities of
the occurrence of the various states of the
economy.
 Expected Cash flow (X) = ΣPbi*CFi
 Where Pbi = probabilities of outcome i
 CFi = cash flows in outcome i
reserved. 6-10

Measuring the Expected Cash
Flow and Expected Return

State of the Probability Cash flow % Return (Cash
economy of the states from the Flow/Inv. Cost)
investment

Economic 20% $1,000 10%
Recession ($1,000/$10,000)

Moderate 30% 1,200 12%
Economic ($1,200/$10,000)
Growth

Strong 50% 1,400 14%
Economic ($1,400/$10,000)
Growth
reserved. 6-11

Expected Cash flow equation

reserved. 6-12

Expected Cash Flow

 Expected Cash flow = ΣPbi*CFi

= .2*1000 + .3*1200 + .5*1400
= $1,260 on $1,000 investment

reserved. 6-13

Expected Rate of Return

 We can also determine the % expected return
on $1,000 investment. Expected Return is the
weighted average of all the possible returns,
weighted by the probability that each return
will occur.
 Expected Return (%) = ΣPbi*ri
 Where Pbi = probabilities of outcome i
 ri = expected % return in outcome i
reserved. 6-14


reserved. 6-15


 Expected Return (%) = ΣPbi*ri
 Where Pi = probabilities of outcome i
 ki = expected % return in outcome i

= .2(10%) + .3(12%) + .5(14%)
= 12.6%

reserved. 6-16

2. Risk
Defined and Measured

Three important questions:
1. What is risk?
2. How do we measure risk?
3. Will diversification reduce the risk of
portfolio?

reserved. 6-17

2. Risk

2.1 Risk Defined
 Risk refers to potential variability in future
cash flows.
 The wider the range of possible future events
that can occur, the greater the risk.
 Thus the returns on common stock is more
risky than returns from investing in savings
account in a bank.
reserved. 6-18

2. Risk

2.2 Risk Measurement
Example
Two Investment Options:
1. Invest in Treasury bill that offers a 3% annual
return.
2. Invest in stock of a local publishing company with
an expected return of 15% based on the payoffs
(given on next slide).
reserved. 6-19

Probability of Payoffs

Probability Rate of Return
Treasury Bill
100% 3%
Stock
10% 0%
20% 5%
40% 15%
20% 25%
10% 30%
reserved. 6-20

Probability of Payoffs

Expected return
 T. Bill = 1*3% =3%
 Stock
= .1*0 + .2*5% + .4*15% + .2*25% + .1*30%
= 15%

reserved. 6-21

Figure 6-1
Treasury bill versus Stock

reserved. 6-22

Figure 6-1
Treasury bill versus Stock

 We observe from Figure 6-1 that the
stock of publishing company is more
risky but it also offers the potential of a
higher payoff.

reserved. 6-23

Standard deviation (S.D.)

 Standard deviation (S.D.) is one way to
measure risk. It measures the volatility or
riskiness of portfolio returns.
 S.D. = square root of the weighted average
squared deviation of each possible return
from the expected return.

reserved. 6-24

Equation 6-5

reserved. 6-25

Table 6-2

reserved. 6-26

Comments on S.D.
 There is 66.67% probability that the actual returns will
fall between 5.78% and 24.22% (= 15% ± 9.22%). So
actual returns are far from certain!
 Risk is relative; thus whether 9.22% is high or low
risk, we need to compare the S.D. of this stock to the
S.D. of other investment alternatives.
 To get the full picture, we need to consider not only
the S.D. but also the expected return.
 The choice of particular investment depends on
investor’s attitude to risk.
reserved. 6-27

3. Rates of Return: The Investor’s
experience (1926–2008)

Figure 6-2 shows:
A. The direct relationship between risk and return
B. Only common stocks provide a reasonable
hedge against inflation.

The study also observed that between 1926–
2008, large stocks had negative returns in 23
out of 83 years, while treasury bills generated
negative returns in only 1 year.
reserved. 6-28

Figure 6-2

reserved. 6-29


4.1 Portfolio
 Portfolio refers to combining several assets.
 Examples of portfolio:
 Investing in multiple financial assets
(stocks – $6000, bonds – $3000, T-bills – $1000)
 Investing in multiple items from single market
(example – investing in 30 different stocks)

reserved. 6-30


4.2 Diversifying away the risk in a Portfolio
 Total risk of Portfolio is due to two types of Risk:
 Systematic (or Market risk) is risk that affects all firms
(ex. Tax rate changes, war)
 Unsystematic (or company unique risk) is risk that affects
only a specific firm (ex. Labor strikes, CEO change)

 Only non-systematic risk can be reduced or
eliminated through effective diversification
(Figure 6-3)
reserved. 6-31

Total Risk & unsystematic risk
decline as securities are added

reserved. 6-32


 The main motive for holding multiple assets
or creating a portfolio of stocks (called
diversification) is to reduce the overall risk
exposure. The degree of reduction depends
on the correlation among the assets.
 If two stocks are perfectly positively correlated,
diversification has no effect on risk.
 If two stocks are perfectly negatively correlated,
the portfolio is perfectly diversified.

reserved. 6-33


 Thus while building a portfolio, we
should pick securities/assets that have
negative or low positive correlation to
attain diversification benefits.

reserved. 6-34


4.3 Measuring Market Risk:
Google versus S&P 500
Table 6-3 and Figure 6-4 displays the
monthly returns for Google and S&P500
for the 12 months ending May 2009.

reserved. 6-35

Table 6-3

reserved. 6-36

Figure 6-4

reserved. 6-37

Equation 6-6

reserved. 6-38

Equations 6-7 and 6-8

reserved. 6-39

Total Risk & unsystematic risk decline
as securities are added (cont).

 Both Google and overall market declined
during 2008 and 2009. The average monthly
return for Google and S&P500 index was
–1.3% and –2.2% respectively.
 Google has relatively higher risk compared to
S&P500 (SD of 9.9% versus 8.3%).
 There is a moderate positive relationship
between the returns of Google and S&P500
(See Figure 6-5).
reserved. 6-40

Total Risk & unsystematic risk decline
as securities are added (cont).

 The relationship between Google and S&P500 is
captured in Figure 6-5.
 Characteristic line is the “line of best fit” for all the
stock returns relative to returns of S&P500.
 The slope of the characteristic line (= .68) measures
the average relationship between a stock’s returns
and those of the S&P 500 Index Returns. This slope
(called beta) is a measure of the firm’s market risk
i.e. Google’s returns are .68 times as volatile on
average as those of the overall market.
reserved. 6-41

Interpreting Beta

 Beta is the risk that remains for a company even after
we have diversified our portfolio.
 A stock with a Beta of 0 has no systematic risk
 A stock with a Beta of 1 has systematic risk equal to the
“typical” stock in the marketplace
 A stock with a Beta exceeding 1 has systematic risk greater
than the “typical” stock

 Most stocks have betas between .60 and 1.60. Note,
the value of beta is highly dependent on the
methodology and data used.
reserved. 6-42

Portfolio Beta

 Portfolio beta indicates the percentage
change on average of the portfolio for every
1 percent change in the general market.
βportfolio= Σ wj*βj
Where wj = % invested in stock j
βi= Beta of stock j

reserved. 6-43

Equation 6-10

reserved. 6-44

Figure 6-7
Portfolio Beta

reserved. 6-45

4.4 Risk and Diversification
Demonstrated

 The market rewards diversification.
 Through effective diversification, we can
lower risk without sacrificing expected
returns and we can increase expected
returns without having to assume more
risk.

reserved. 6-46

Asset Allocation

 Asset allocation refers to diversifying among
different kinds of asset types (such as
treasury bills, corporate bonds, common
stocks).
 Asset allocation decision has to be made
today – the payoff in the future will depend on
the mix chosen before, which cannot be
changed. Hence asset allocation decision is
considered the “most important decision”
while managing an investment portfolio.
reserved. 6-47

Asset Allocation

Example
 In 2002, $1,000 invested in stock market will have
earned less than $1,000 invested in banks
 In 2003, $1,000 in stocks will have earned higher
returns
 History shows asset allocation matters and that taking
high risk does not always pay off!!!

 Of course, decision has to be made today for
the future and that is why “asset allocation”
decision determines who will be the “winners”
in the financial market!!!
reserved. 6-48

Historical Returns in the
US Market: 1926–2000

 Treasury Bills 3.9%
 Government Bonds 5.6%
 Corporate Bonds 6.0%
 Common Stocks 13.0% (S&P 500)
 Small company stocks 17.3%

reserved. 6-49

Asset allocation example

 Determine the final value of the portfolio based on the
following two portfolios with a 75-year time horizon.
Use the average returns from the previous slide and
$1m initial investment.
 Conservative investor– invests 20% in Tbills, 40% in
Govt. bonds and 40% in Corporate Bonds
 Aggressive investor – invests 10% in Tbills, 50% in
small company stocks and 40% in common stocks

reserved. 6-50

Asset allocation matters!

 Return = Σ Weightj*Return%j
 Conservative investor = 5.42%
 Aggressive investor = 14.24%

 Final Value = $1m(1 + i)75
 Conservative = $52,387,284.93
 Aggressive = $21,695,246,174.70
reserved. 6-51

Figure 6-8

reserved. 6-52

Asset allocation matters!

 We observe the following from Figure 6-8:
 Direct relationship between risk and return:
As we move from an all-stock portfolio to a
mix of stocks and bonds to an all bond-
portfolio, both risk and return decline.
 Holding period matters: As we increase the
holding period, risk declines.

reserved. 6-53

5. The Investor’s Required Rate
Return

5.1 Required Rate of Return
 Investor’s required rate of returns is the
minimum rate of return necessary to
attract an investor to purchase or hold a
security.
 This definition considers the opportunity
cost of funds i.e. the foregone return on
the next best investment.
reserved. 6-54

Investor’s Required Rate of
Return

reserved. 6-55

Risk-Free Rate

 This is the required rate of return or
discount rate for risk-less investments.
 Risk-free rate is typically measured by
U.S. Treasury bill rate.

reserved. 6-56

Risk Premium

 Additional return we must expect to
receive for assuming risk.
 As the level of risk increases, we will
demand additional expected returns.

reserved. 6-57

Measuring the Required
Rate of Return

reserved. 6-58

Capital Asset Pricing Model

 CAPM equation equates the expected rate of
return on a stock to the risk-free rate plus a
risk premium for the systematic risk.
 CAPM provides for an intuitive approach for
thinking about the return that an investor
should require on an investment, given the
asset’s systematic or market risk.

reserved. 6-59

Capital Asset Pricing Model

 If the required rate of return for the market
portfolio rm is 12%, and the rf is 5%, the risk
premium for the market would be 7%.
 This 7% risk premium would apply to any
security having systematic (nondiversifiable)
risk equivalent to the general market, or beta
of 1.
 In the same market, a security with Beta of 2
would provide a risk premium of 14%.
reserved. 6-60

CAPM

CAPM suggests that Beta is a factor in
determining the required returns.

reserved. 6-61

CAPM example

Market risk = 12%
Risk-free rate = 5%
Required return = 5% + Beta * (12% - 5%)

If Beta = 0 Required return = 5%
reserved. 6-62

The Security Market Line (SML)

 SML is a graphic representation of the
CAPM, where the line shows the
appropriate required rate of return for a
given stock’s systematic risk.

reserved. 6-63

The Security Market Line

reserved. 6-64

Figure 6-5

reserved. 6-65

Figure 6-6

reserved. 6-66

Table 6-1

reserved. 6-67

Key Terms
 Asset allocation  Portfolio beta
 Beta  Required rate of return
 Capital Asset Pricing Model  Risk
(CAPM)
 Risk-free rate of return
 Characteristics line
 Company-unique risk  Risk premium

 Diversifiable risk  Security market line

 Expected rate of return  Standard deviation
 Holding-period return  Systematic risk
 Market risk  Unsystematic risk
 Nondiversifiable risk
reserved. 6-68

6. risk return

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