title: introduction to risk, return and the opportunity ...c12… · module 8 introduction to risk...
TRANSCRIPT
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Title: Introduction to Risk, Return and
the Opportunity Cost of Capital
Speaker: Rebecca Stull
Created by: Gene Lai
online.wsu.edu
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MODULE 8
INTRODUCTION TO RISK AND
RETURN, AND THE
OPPORTUNITY COST OF
CAPITAL
Revised by Gene Lai
2
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11-3
Risk and Return
Risk and Return are related.
How?
This module will focus on risk and return and their
relationship to the opportunity cost of capital.
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Outline
Rates of Return
A Century of Capital Market History
Measuring Risk
Risk & Diversification
Thinking About Risk
11-4
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11-5
Equity Rates of Return:
A Review
Capital Gain + Dividend
Initial Share PricePercentage Return =
Capital Gain
Initial Share PriceCapital Gain Yield =
Dividend Initial Share Price
Dividend 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?
$18.29 $15.13 $.46
$15.13
23.93%Percentage Return
$18.29 $15.13
$15.1320.89%Capital Gain Yield
$.46Dividend Yield = 3.04%
$15.13
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11-7
Real Rates of Return
1 + nominal rate of return1 + inflation rate
1 real rate of return =
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%?
Recall the relationship between real rates and nominal rates:
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11-8
Capital Market History:
Market Indexes
• Market Index - Measure of the investment performance
of the overall market.
• Dow Jones Industrial Average (The Dow)
• Value of a portfolio holding one share in each of
30 large industrial firms.
• Standard & Poor’s Composite Index (S&P 500)
• Value of a portfolio holding shares in 500 firms.
Holdings are proportional to the number of
shares in the issues.
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11-9
Total Returns for Different
Asset Classes
The Value of an Investment of $1 in 1900
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11-10
Annual Total Returns,1926-1998
Average Standard Return Deviation Distribution
Small-company stocks 17.4% 33.8%
Large-company stocks 13.2 20.3
Long-term corporate bonds 6.1 8.6
Long-term government 5.7 9.2
Intermediate-term government 5.5 5.7
U.S. Treasury bills 3.8 3.2
Inflation 3.2 4.5
0 17.4%
0 13.2%
0 6.1%
0 5.7%
0 5.5%
0 3.8%
0 3.2%
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11-11
The Difference in Total Returns?
Risk Premium: Expected return in excess of
risk-free return as compensation for risk.
Maturity Premium: Extra average return from
investing in long- versus short-term Treasury
securities.
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11-12
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%
2012: 7.47% = 0.07% + 7.4%
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Returns and Risk
We next show how to measure
expected return and risk.
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Measuring Expected Rate of Return (for a Single Stock)
.Pr = E(r)n
1=iii
r = or E (r) = expected rate of return.
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Measuring Risk (for a Single
Stock)
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? Uncertainty
How can it be measured?
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Standard Deviation of a Single Stock
= Standard deviation.
= =
=
Variance 2
.P))r(Er(n
1ii
2
i
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11-17
Investment Alternatives
Economy Prob. T-Bill HT Coll USR MP
Recession 0.1 8.0% -22.0% 28.0% 10.0% -13.0%
Below avg. 0.2 8.0 -2.0 14.7 -10.0 1.0
Average 0.4 8.0 20.0 0.0 7.0 15.0
Above avg. 0.2 8.0 35.0 -10.0 45.0 29.0
Boom 0.1 8.0 50.0 -20.0 30.0 43.0
1.0
There are five possible states of economy next year. The probability
associated each state is presented below. In addition, the returns
associated with each state is also presented below.
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Do the returns of HT and Coll.
move with or counter to the
economy?
HT: Moves with the economy, and has a
positive correlation. This is typical.
HT is for high tech
Coll: Is countercyclical of the economy, and has a negative correlation. This is unusual.
Coll is for collection agency
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Calculate the Expected Rate of Return for HT
.Pr = E(r)n
1=iii
r = Expected rate of return.
= (-22%)0.1 + (-2%)0.20
+ (20%)0.40 + (35%)0.20
+ (50%)0.1 = 17.4%.
E(r)
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11-20
r
HT 17.4%
Market 15.0
USR 13.8
T-bill 8.0
Coll. 1.7
HT appears to be the best, but is it really?
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What’s the standard deviation of returns for each alternative?
= Standard deviation.
= =
=
Variance 2
.P))r(Er(n
1ii
2
i
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22
T-bills = 0.0%.
1/2
T - bills =
.P))r(Er(n
1ii
2
i
(8.0 – 8.0)20.1 + (8.0 – 8.0)20.2
+ (8.0 – 8.0)20.4 + (8.0 – 8.0)20.2
+ (8.0 – 8.0)20.1
Standard deviation for T-Bill
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23
HT = 20.0%.
1/2
HT =
.P))r(Er(n
1ii
2
i
(-.22 – .174)20.1 + (-.02 –.174)20.2
+ (.2 – .174)20.4 + (.35 –.174)20.2
+ (.50 – .174)20.1
Standard deviation for HT
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11-24
Expected Returns vs. Risk
Security Expected
return Risk,
HT 17.4% 20.0%
Market 15.0 15.3
USR 13.8* 18.8*
T-bills 8.0 0.0
Coll. 1.7* 13.4*
*Seems misplaced.
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Portfolio Risk and Return
Assume a two-stock portfolio with
$50,000 in HT and $50,000 in
Collections. Calculate E(rp) and
Calculate E(rp) and p.
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Portfolio Expected Return, rp
is a weighted average:
E(rp) = 0.5(17.4%) + 0.5(1.7%) = 9.6%.
E(rP)
E(rp) = S wi r i. n
i = 1
Note: This is one method to calculate portfolio return.
11-26
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Portfolio Return for 2 Assets
Portfolio rate
of return=
fraction of portfolio
in first assetx
rate of return
on first asset
+fraction of portfolio
in second assetx
rate of return
on second asset
((
(())
))
Note that we can calculate portfolio rate of return
for each scenario first, please see next slide.
11-27
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11-28
Alternative Method to
Calculate Mean
What is Port. Return if the economy is
booming? 15% = (50 + (-20))/2
Estimated Return
Economy Prob. HT Coll. Port.
Recession 0.10 -22.0% 28.0% 3.0%
Below avg. 0.20 -2.0 14.7 6.4
Average 0.40 20.0 0.0 10.0
Above avg. 0.20 35.0 -10.0 12.5
Boom 0.10 50.0 -20.0 ?
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11-29
Alternative Method to
Calculate Mean
rp = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40
+ (12.5%)0.20 + (15.0%)0.10 = 9.6%.
Estimated Return
Economy Prob. HT Coll. Port.
Recession 0.10 -22.0% 28.0% 3.0%
Below avg. 0.20 -2.0 14.7 6.4
Average 0.40 20.0 0.0 10.0
Above avg. 0.20 35.0 -10.0 12.5
Boom 0.10 50.0 -20.0 15.0
Note: we can treat port. as a single security when calculating
and variance.
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p = = 3.3%.
1 2 /
(3.0 – 9.6)20.10
+ (6.4 – 9.6)20.20
+ (10.0 – 9.6)20.40
+ (12.5 – 9.6)20.20
+ (15.0 – 9.6)20.10
Alternative Method to Calculate
Standard Deviation
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Some Comments
p = 3.3% is much lower than that of either stock
(20% and 13.4%).
p = 3.3% is lower than the average of HT and
Coll’s standard deviation = (.5)(20%) +
(.5)(13.4%) = 16.7%.
The Portfolio provides average r but lower risk.
Reason: negative correlation for this specific case.
11-31
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Returns Distribution for Two Perfectly Negatively Correlated Stocks (-1.0) and for
Portfolio WM
25
15
0
-10 -10 -10
0 0
15 15
25 25
Stock W Stock M Portfolio WM
.
. .
. .
.
.
.
.
. . . .
. .
σWM = correlation coefficient between W and M
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Returns Distributions for Two Perfectly
Positively Correlated Stocks (+1.0) and for Portfolio MM’
Stock M
0
15
25
-10
Stock M’
0
15
25
-10
Portfolio MM’
0
15
25
-10
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11-34
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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Correlation Coefficient and
Diversification
Maximum diversification: correlation of
coefficient = -1
No diversification: correlation of coefficient =
+1
Correlation of coefficient <1, there is still
diversification.
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11-36
Risk and Diversification
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11-37
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