Chapter 5:
The Trade-off between
Risk and Return
Corporate Finance, 3e
Graham, Smart, and Megginson
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Introduction to Risk and Return
Valuing risky assets:
A task fundamental to financial management
Three-step procedure for valuing a risky asset
1. Determine the asset’s expected cash flows.
2. Choose discount rate that reflects asset’s risk.
3. Calculate present value (PV cash inflows  PV
outflows).
This three-step procedure is called
discounted cash flow (DCF) analysis.
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Risk and Return
The return earned on investments
represents the marginal benefit of
investing.
Risk represents the marginal cost of
investing.
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Three Basic Steps for Valuing a
Risky Asset
1. Determine the asset’s expected cash flows.
2. Choose a discount rate that reflect’s the asset’s risk.
3. Calculate the present value.
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Historical Return and Risk
Decisions must be based on expected return and risk.
One simple way to estimate expected return and
risk…
Assume that expected return and risk going
forward will be similar to past values.
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Equity Risk Premium

The difference in equity returns and
returns on safe investments

Implies that stocks are riskier than bonds
or bills

Volatility of stocks relative to bonds or
bills depends on the time horizon over
which investment returns are measured

Trade-off always arises between risk
and expected return
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Risk Aversion
Risk Neutral
• Investors seek the highest return without
regard to risk.
Risk Seeking
• Investors have a taste for risk and will
take risk even if they cannot expect a
reward for doing so.
Risk Averse
• Investors do not like risk and must be
compensated for taking it.
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Return on a Single Asset
Return - The total gain or loss experienced on an
investment over a given period of time
Pt 1  Pt  Ct 1
Rt 1 
Pt
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Arithmetic Versus Geometric
Returns
• Arithmetic average return: The simple average of
annual returns
(R1 + R2 + R3 + … + Rt) / t
Best estimate of expected return over a single year
• Geometric average return: The compound annual
return to an investor who bought and held a stock t
years
[(1+R1)(1+R2)(1+R3)….(1+Rt)]1/t – 1
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Arithmetic Versus Geometric
Returns
An example....
Year
Return
2007
-10%
2008
+13%
2009
+17%
2010
+ 8%
AAR = 7.00%
GAR = 6.47%
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Probability Distribution
A
probability distribution tells us
what outcomes are possible and how
likely each outcome is.
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Risk of a Single Asset
How Do We Measure Risk?
A reasonable way to define risk is to focus on the
dispersion of returns.
• Most common measure is the variance, or its
square root, the standard deviation.
• Variance equals the expected value of squared
deviations from the mean.
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Risk of a Single Asset
Example:
Year
Return
2007
-10%
2008
+13%
2009
+17%
2010
+8%
Average annual return = 7%
N
2 
2
(
R

R
)
i
 it
t 1
N 1
(10%  7%) 2  (13%  7%) 2  (17%  7%) 2  (8%  7%) 2

4 1
 142% 2
  2  142%2  11.9%
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Expected Return for a Portfolio
 Most
investors hold multiple-asset
portfolios.
 Key
insight of portfolio theory: Asset
return adds linearly, but risk is almost
always reduced in a portfolio.
E ( R p )  w E ( R )  w E ( R )  w E ( R )  w E ( R )
N
N
1 1
2
2
3
3
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The Importance of Covariance

Risk reduction is achieved in portfolios because
fluctuations in one asset partially off set
fluctuations in the other

Risk of a portfolio depends crucially on whether
the returns on the portfolio’s components move
together or in opposite directions

Covariance: statistical measurement of the comovements of two random variables
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Two-Asset Portfolio Standard
Deviation
  w   w   2w1w21212
2
p
2 2
1 1
2
2
2
2
Standard Deviation 
2
p
Correlation between stocks influences portfolio
volatility.
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Portfolios of More Than Two Assets
 Five-Asset
Portfolio
E ( R p )  w1E ( R1 )  w2 E ( R2 )  w3 E ( R3 )
 w4 E ( R4 )  w5 E ( R5 )
Expected return of portfolio is still the average of
expected returns of the two stocks.
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Portfolio Risk
 Variance
cannot fall below the average
covariance of securities in the portfolio.
 Undiversifiable
risk (systematic risk, market
risk)
 Diversifiable risk (unsystematic risk,
idiosyncratic risk, or unique risk)
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What is a stock’s beta?
Beta is a measure of systematic risk.
 im
i 
m
What if
Beta = 1?
•
What if
Beta > 1 or
Beta < 1?
•
•
•
The stock moves 1% on average when the
market moves 1%.
An “average” level of risk
The stock moves more than 1% on average
when the market moves 1%. (Beta > 1)
The stock moves less than 1% on average
when the market moves 1%. (Beta < 1)
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Diversifiable and
Non-Diversifiable Risk
 As
number of assets increases,
diversification reduces the importance of
a stock’s own variance
an asset’s covariance with all other
assets contributes measurably to overall
portfolio return variance.
 Only
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How risky is an individual asset?
One Approach: Asset’s Variance or Standard Deviation
but…
What really matters is systematic risk… how an
asset covaries with everything else.
Use asset’s beta.
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