1. risk, return & opportunity cost of capital
TRANSCRIPT
Chapter 10Fundamentals of
Corporate FinanceFourth Edition
Introduction to Risk, Return, and the Opportunity Cost of Capital
Slides by
Matthew Will
Irwin/McGraw Hill Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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LEARNING OBJECTIVES
Estimate the opportunity cost of capital for an “average-risk” project.
Calculate returns and standard deviation of returns for individual common stocks or for a stock portfolio.
Understand why diversification reduces riskDistinguish b/w UNIQUE RISK, &
MARKET RISK
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Rates of Return (Review)
15.3%or .153=
=Return Percentage 430.56 + 6
P e rc e n ta g e R e tu rn = C a p i ta l G a in + D iv id e n d In i t ia l S h a re P r ic e
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Rates of Return
D iv id e n d Y ie ld = D iv id e n d In i t ia l S h a re P r ic e
C a p i t a l G a in Y ie ld = C a p i t a l G a inIn i t i a l S h a r e P r i c e
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Rates of Return
%1.3or 013.43
0.56= Yield Dividend
%14.0or 140.43
6= YieldGain Capital
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Rates of Return
1+ real ror = 1 + nominal ror1 + inflation rate
%2.22ror real
222.1=ror real+1 .028 + 1.153 + 1
Nominal return measures how much more money
you will have at the end of the year.
Real rate of return tells you how much more you
will be able to buy with your money at the end of yr
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Self Test
Suppose you buy a bond for $ 1,020.00 with 15 Years of maturity paying an annual coupon of $80. A year later bond price has increased to $1,050.
What are your nominal and real rates of returns? Assume the inflation rate is 4%
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Market Indexes
Market Indexes: Measure of the investment performance of the overall market.
Dow Jones Industrial Average (The Dow)
Index of the investment performance of a portfolio of 30 “Blue-Chip” stocks.
Standard & Poor’s Composite Index (The S&P 500)
Index of the investment performance of a portfolio of 500 large stocks. Also called S&P 500.
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The Value of an Investment of $1 in 1900
Source: Ibbotson Associates
Inde
x
Year End
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Rates of Return
-60
-40
-20
0
20
40
60
Ret
urn
(%)
1901
1908
1915
1922
1929
1936
1943
1950
1957
1964
1971
1978
1985
1992
1999
Year
Common Stocks (1900-2001)
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Market Indexes
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 of risk.
The historical record shows that investors have received a risk premium for holding risky assets. Average returns on high risk assets are higher than those on low risk assets.
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Risk Premium
9.3+1.8=9.5% (2002)
7.7+14=21.7% (1981)
Premium
RiskMarket +
billsTreasury
on rateInterest =
return
market Expected
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Self Test
Here are the average rates of return for common stocks treasury bills for three different periods:
What was the Risk Premium on stocks for each of these periods?
1900-24 1925-49 1950-1974Stocks 9.50% 10.20% 11.10%T-Bills 4.90% 1.10% 3.50%
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Measuring Risk
Variance - Average value of squared deviations
from mean. A measure of volatility.
Standard Deviation – Square Root of Variance.
Another measure of volatility.
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Example
Suppose that you are offered the chance to play the following game:
You start by investing $100. then two coins
are flipped. For each head that comes up your
starting balance will increased by 20%, and
for each tail that comes up your starting
balance will reduced by 10%.
There are four Outcomes……
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Measuring RiskCoin Toss Game-calculating variance and standard deviation
(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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Self Test
Now think of a second game. It is the same as the first except that each head means a 35% gain and each tail means a 25% loss.
Find the Variance and Standard Deviation?
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Risk and Diversification
Deviation from SquaredYear Rate of Return Average Return Deviation
1997 31.29 20.01 400.451998 23.43 12.15 147.651999 23.56 12.28 150.782000 -10.89 -22.17 491.692001 -10.97 -22.25 495.24
Total 56.41 1685.81Average rate of return = 56.41/5 = 11.28Variance = average of squared deviations = 1685.81/5 = 337.16Standard deviation = squared root of variance = 18.36%
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Risk and Diversification
Diversification - Strategy designed to reduce risk by spreading the 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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Example
You can make huge sale while selling umbrellas when its rains, but you are likely to lose all in a heat wave. Selling ice cream is no safer, you will do well in the heat wave, but business is poor in rain.
Suppose however you invest both an umbrella shop and an ice cream shop. By diversifying your investment across the tow businesses, you make an average level of profit.
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Asset versus Portfolio Risk
Rate of Return Assumptions for two stocks:
Scenario Probability
Rate of Return %
Auto Stock Gold Stock
Recession 1/3 -8% 20%
Normal 1/3 5% 3%
Boom 1/3 18% -20%
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Solution
Auto Stock Gold Stock
ScenarioRate of Return
Deviation from
Expected Return
Squared Deviation
Rate of Return
Deviation from
Expected Return
Squared Deviation
Recession -8% -13% 169 20% 19% 361Normal 5% 0% 0 3% 2% 4Boom 18% 13% 169 -20% -21% 441
Expected Return = 5% Expected Return = 1%Variance = 112.7 Variance = 268.7
Standard Deviation = 10.60% Standard Deviation = 16.40%
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Risk and Diversification
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
((
((
))
))
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Asset versus Portfolio Risk
Continuation of earlier example:
Suppose you have $10,000 portfolio and you have decided to invest 75% of this in Auto Stock and 25% in Gold Stock.
Now calculate the Expected Return, Variance & Standard Deviation of above Portfolio.
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Risk and Diversification
0
5 10 15
Number of Securities
Po
rtfo
lio s
tan
da
rd d
ev
iati
on
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05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
Risk and Diversification