1. Risk, Return & Opportunity Cost of Capital

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

Rates of Return

%1.3or 013.43

0.56= Yield Dividend

%14.0or 140.43

6= YieldGain Capital


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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill

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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Irwin/McGraw Hill


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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Irwin/McGraw Hill

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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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


1. Risk, Return & Opportunity Cost of Capital

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