This chapter discusses risk and return, and their relationship to the cost of capital. It defines different types of returns, such as dividend yield and capital gain yield, and provides an example calculation. The chapter then discusses measuring risk through variance and standard deviation, and how diversification can help reduce overall portfolio risk by spreading investments across different asset classes. The key relationship discussed is that higher expected returns generally correspond to higher risks.

1. McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Risk and Return
Risk and Return are related.
How?
This chapter will focus on risk and return and their
relationship to the opportunity cost of capital.

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Equity Rates of Return:
A Review
Capital Gain + Dividend
Initial Share Price Percentage Return =
Dividend Yield =
Dividend
Initial Share Price Capital Gain
Initial Share Price Capital Gain Yield =

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Rates of Return: Example
Example: You purchase shares of GE stock at $15.13 on December 31, 2009. You
sell them exactly one year later for $18.29. During this time GE paid $.46 in
dividends per share. Ignoring transaction costs, what is your rate of return,
dividend yield and capital gain yield?
Percentage Return = $18.29 - $15.13 + +
$.46
=
23.93% $15.13
Dividend Yield = $.46 3.04%
$15.13
=
Capital Gain Yield = $18.29 - $15.13
=
$15.13 20.89%

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Real Rates of Return
Recall the relationship between real rates and nominal rates:
1+ real rate of return =
1 + nominal rate of return
1 + inflation rate Example: Suppose inflation from December 2009 to December 2010 was
1.5%. What was GE stock’s real rate of return, if its nominal rate of return
was 23.93%?

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Capital Market History:
Market Indexes
• Market Index - Measure of the investment performance of the
overall market.
• Dow Jones Industrial Average (The Dow)
• Standard & Poor’s Composite Index (S&P 500)
Other Market Indexes?

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Total Returns for Different
Asset Classes
The Value of an Investment of $1 in 1900

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What Drives the Difference in
Total Returns?
Maturity Premium: Extra average return from investing in
long- versus short-term Treasury securities.
Risk Premium: Expected return in excess of risk-free return
as compensation for risk.

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Risk Premium: Example
Interest Rate on Normal Risk
Expected Market Return = +
Treasury Bills Premium
1981: 21.4% = 14% + 7.4%
2008: 9.6% = 2.2% + 7.4%

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Returns and Risk
How are the expected returns and
the risk of a security related?

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Measuring Risk
Variance: Average value of squared deviations from
mean. A measure of volatility.
Standard Deviation: Square root of variance. Also a
measure of volatility.
What is risk?
How can it be measured?

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Variance and Standard
Deviation: Example
Coin Toss Game: calculating variance and standard deviation
(assume a mean of 10)
(1) (2) (3)
Percent Rate of Return Deviation from Mean Squared Deviation
+ 40 + 30 900
+ 10 0 0
+ 10 0 0
- 20 - 30 900
Variance = average of squared deviations = 1800 / 4 = 450
Standard deviation = square of root variance = 450 = 21.2%

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Histogram of Returns
What is the relationship
between the volatility of
these securities and their
expected returns?

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Historical Risk
(1900-2010)

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Risk and Diversification
Diversification
Strategy designed to reduce risk by spreading a portfolio
across many investments.
Unique Risk:
Risk factors affecting only that firm. Also called
“diversifiable risk.”
Market Risk:
Economy-wide sources of risk that affect the overall stock
market. Also called “systematic risk.”

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Diversification:
Building a Portfolio
A portfolio’s rate of return is the weighted sum of each asset’s rate of
return.
fraction of portfolio rate of return
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Portfolio Rate of Return = x
in first asset on first asset
fraction of portfolio rate of return
+ x
in second asset on second asset
Two Asset Case:

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Building a Portfolio: Example
Consider the following portfolio:
Stock Weight Rate of Return
IBM
w =
50% r =
8.3% IBM IBM Starbucks
w =
25% r =
12.5% SBUX SBUX Walmart
w =
25% r =
4.7% W W What is the portfolio rate of return?
( wIBM ´rIBM ) + ( wSBUX ´rSBUX ) + ( wW ´rW
)
( ) ( )
Portfolio Rate of Return =
= ´ + ´ + ´
=
(50% 8.3%) 25% 12.5% 25% 4.7%
8.45%

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Do stock prices move together?
What effect does diversification have on a
portfolio’s total risk, unique risk and market risk?

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Risk and Diversification

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Thinking About Risk
 Message 1
• Some Risks Look Big and Dangerous but Really Are
Diversifiable
 Message 2
• Market Risks Are Macro Risks
 Message 3
• Risk Can Be Measured