Chapter 9 - Washington State University

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Characterizing Risk and Return
Chapter 9
Fin 325, Section 04 – Spring 2010
Washington State University
1
Introduction
 Safe investments, risky investments
(Savings account; Stocks)
 Based on what do financial managers and
investors make investment decisions?
(Expectations about future risk and return)
 The relationship between risk and return is
fundamental to finance theory
2
Historical Returns
 Computing Returns
Dollar Return = (Capital gain or loss) + Income
= (Ending Value – Beginning Value) + Income
 Percentage Returns
PercentageReturn 
Ending Value - BeginningValue  Income
BeginningValue
3
 Consider an investment in stock. The income would be
dividends. We can break this equation into two parts to
reflect the capital gains yield and the dividend yield
PercentageReturn 
Ending Price- BeginningPrice
Dividend

BeginningPrice
BeginningPrice
PercentageReturn  CapitalGains Yield  DividendYield
4
 Example: You held 250 shares of Hilton Hotel’s
common stock. The company’s share price was
$24.11 at the beginning of the year. During the
year, the company paid a dividend of $0.16 per
share, and ended the year at a price of $34.90.
What is the dollar return, the percentage return,
the capital gains yield, and the dividend yield for
Hilton?
5
Dollar return = 250 x ($34.90-$24.11+$0.16)
= $2,737.50
Percent return = ($34.90-$24.11+$0.16)/$24.11
= 45.42%
Capital gains yield = ($34.90 - $24.11)/$24.11
= 44.75%
Dividend yield = $0.16/$24.11
= 0.66%
6
Average Return
 The arithmetic average return provides an
estimate for how an investment has
performed over long periods of time
N
AverageRet urn 
 Ret urn
t
t 1
N
7
Performance of Asset Classes
 Over long periods of time, how do stocks, bonds,
and cash securities (e.g. T-bills) perform?
 Historically, stocks have earned higher returns
than either bonds or cash
 [insert Table 9.2]
8
Historical Risks
 When you purchase a U.S. Treasury bill, you know
exactly what your returns are going to be, i.e. there
is no uncertainty, or risk (risk-free rate)
 On the other hand, when you invest in stocks you
do not know what your returns will be, i.e. stock
investing is risky
 It is useful to be able to quantify the uncertainty of
various asset classes
9
Volatility
 High volatility in historical returns are an indication
that future returns will be volatile
 One popular way of quantifying volatility is to compute the
standard deviation of percentage returns
 Standard deviation is the square root of the variance
 Standard deviation is a measure of total risk
 A large standard deviation indicates greater
return variability, or high risk
N
Standard Deviation
2
(Return
Average
Return)

t
t 1
N -1
10
Example: Using the following returns, calculate
the average return, the variance, and the
standard deviation for Acme stock.
Year
1
2
3
4
5
Acme
10 %
4%
-8 %
13 %
5%
11
Average Return=(10% +4% - 8% + 13% + 5% )/5 = 4.80%
σ2Acme = [(10% – 4.8%)2 + (4% – 4.8%)2 (- 8% – 4.8%)2
+ (13% – 4.8%)2 + (5% – 4.8%)2 ] / (5 - 1)
σ2Acme = 0.02588 / 4 = 0.006470
σAcme = (0.00647)1/2 =0.0804= 8.04%
12
 Risk of Asset Classes
 The volatility of stocks is much higher than the
volatility of bonds and T-bills
 While the stock market as averaged a 13.2% return
since 1950, that return comes with high volatility,
with a standard deviation of 17.0%
13
Risk vs. Return
 There is a tradeoff between risk and return
 One way to measure this risk-return
relationship is the coefficient of variation
Standard Deviation
Coefficient of Variation
AverageReturn
 A smaller CoV indicates a better risk-return
relationship
14
Modern Portfolio Theory
 Formalized in the 1950s by Harry Markowitz.
He eventually won the Nobel Prize (1990) in
Economics for his work.
 Diversification reduces risk!
 Risk reduction occurs when securities are
combined. That is, portfolio as a whole could be
less risky than the individual stocks in it.
15
Diversification Reduces Risk
 A stock’s total risk has two components:
 Firm specific risk (diversifiable risk)
 Market risk (systematic risk)
Total Risk = Firm Specific Risk + Market Risk
 Firm specific risk is specific to the company and
common to other companies in the same industry
 Market risk affects all firms
16
How does diversification lower risk?
 Investment in only one stock is very risky (its value rises
and falls based on what happens to the firm).
 When stocks are added to the portfolio, the companies’
firm-specific risk (or unique risk, idiosycratic risk,
diversifiable risk, unsystematic risk) tends to offset each
other.
 As investors add stocks to their portfolio, the firm-
specific portion of the risk declines.
 After a portfolio is fully diversified, the portfolio carries
only market risk (or systematic risk, undiversifiable risk).
17
18
Modern Portfolio Theory
 In addition to showing how risk reduction
occurs when securities are combined,
Markowitz’s modern portfolio theory also
describes how to combine stocks to achieve the
lowest total risk possible for a given expected
return. This is called an optimal portfolio.
19
20
 Portfolios with the highest return possible for each
risk level are called efficient portfolios
 If we added all available securities to the graph in
Figure 9.3, then all of the efficient portfolios of
those securities form the efficient frontier
 Efficient frontier portfolios dominate all other
possible stock portfolios
21
 How Does Diversification Work?
 Diversification comes when stocks are
subject to different kinds of events such that
their returns differ over time, i.e. the stock’s
returns are not perfectly correlated. Their
price movements often counteract each
other
 If two stocks are perfectly positively
correlated, diversification has no effect on
risk.
22
 Correlation measures the tendency of two stock’s
returns to move together, and is represented by A,B
-1.0    +1.0
 Perfect positive correlation means A,B = +1.0
– Returns from two stocks are perfectly in sync
 Perfect negative correlation means A,B = -1.0
– Returns from two stocks move exactly opposite
 Perfect positive correlation gives no risk reduction
 Correlation between -1.0 and +1.0 gives some, but
not all, risk reduction
23
 Portfolio Return
 A portfolio return is a weighted average of the
returns of the individual components of the
portfolio

Weighted by the proportion invested in each security
R p  (w1 R1 )  (w2 R 2 )  ..... (wn R n )
n
R p   w i Ri
i 1
24
 Example: At the beginning of 2007 you
owned $5,000 of Disney stock, $10,000 of
Bank of New York stock, and $15,000 of IBM
stock. In 2007, the three company's returns
were -4.8 percent, 19.4 percent, and 12.8
percent respectively. What is your portfolio
return?
25
Stock
Amount
invested
Weight Calculation
Weight
Disney
$5,000
5,000/30,000
0.1667
Bank of New York
$10,000
10,000/30,000
0.3333
IBM
$15,000
15,000/30,000
0.50
Rp = [0.1667 * (-4.8%)] + (0.3333 * 19.4%) + (0.50 * 12.8%)
Rp = 12.07 %
26
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