Slide 1

Risk and Rates of Return Remembering axioms Inflation and rates of return How to measure risk

(variance, standard deviation, beta) How to reduce risk

(diversification) How to price risk

(security market line, CAPM)

Slide 2

Ten Axioms of Financial Management Risk-Return Tradeoff

Save and invest for future consumption Investments should provide appropriate compensation

for forgone consumption

Slide 3

Ten Axioms of Financial Management

90%

Large-companystocks 13.3% 20.1

Small-companystocks 17.6 33.6

Long-termcorporate bonds 5.9 8.7

Long-termgovernment 5.5 9.3

Intermediate-termgovernment 5.4 5.8

U.S. Treasurybills 3.8 3.2

Inflation 3.2 4.5

-90% 0%

SeriesAverageReturn

StandardDeviation Distribution

Slide 4

Interest Rates The real, risk-free rate is the rate which would

exist on default-free (and free of other risks) obligations in an inflation-free environment (k*)

Most economists believe that the real rate of interest is approximately one to three percent

The Fisher equation indicates that the nominal rate of interest (krf) includes a component for inflation

risk premium (IRP))1*)(1()1( IRPkkrf

Slide 5

Interest Rates (Continued) Suppose the real rate is 3%, and the nominal rate

is 8%. What is the inflation rate premium?

(1.08) = (1.03) (1 + IRP)

(1 + IRP) = (1.0485), so

IRP = 4.85%

)1*)(1()1( IRPkkrf

Slide 6

Term Structure of Interest Rates The pattern of rates of return for debt securities

that differ only in the length of time to maturity1. Normal

Maturity

Yie

ld

2. Inverted

Maturity

Yie

ld

Slide 7

Term Structure of Interest Rates (Continued)

3. Flat

Maturity

Yie

ld

4. Humped

Maturity

Yie

ld

Slide 8

Term Structure of Interest Rates (Continued)Treasury Yield Curve

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0 5 10 15 20 25 30

Maturity (in years)

Yie

ld (%

)

Nov. 2, 2001 Jun. 27, 2003 Jun. 18, 2004

http://www.smartmoney.com/onebond/index.cfm?story=yieldcurve

http://www.stockcharts.com/charts/YieldCurve.html

Slide 9

Term Structure of Interest Rates (Continued) Expected Return - the return that an investor

expects to earn on an asset, given its price, growth potential, etc

Required Return - the return that an investor requires on an asset given its risk and market interest rates

Slide 10

Treasury Securities Required Return The required return on Treasury securities is equal

to risk-free rate of return Since Treasuries are essentially free of default

risk, the rate of return on a Treasury security is considered the “risk-free” rate of return

Slide 11

Required Return on Risky Investments Required return on risky investments should take

into account what investors can earn on riskless investments and the risk premium for the risky investment

The problem is to determine how large of a risk premium we should require to buy a corporate security

Slide 12

Expected Return

For each firm, the expected return on the stock is

n

iiiA

nnA

kPkk

kPkkPkkPkk

1

2211

)(

or )(......)()(

Return

State of Economy Probability (P) Utility Tech

Recession 0.20 4.00% -10.00%

Normal 0.50 10.00% 14.00%

Boom 0.30 14.00% 30.00%

Slide 13

Expected Return (Continued)

For each firm, the expected return on the stock is

%14%)30)(30.0(%)14)(50.0(%)10)(20.0(

%10%)14)(30.0(%)10)(50.0(%)4)(20.0(

)(......)()( 2211

T

U

nnA

k

k

kPkkPkkPkk

Return

State of Economy Probability (P) Utility Tech

Recession 0.20 4.00% -10.00%

Normal 0.50 10.00% 14.00%

Boom 0.30 14.00% 30.00%

Slide 14

What is RISK? Based only on your expected return calculations,

which stock would you prefer? Have you considered the RISK? The possibility that an actual return will differ

from our expected return Uncertainty in the distribution of possible

outcomes

Slide 15

How do we Measure Risk? A scientific approach is to examine the stock’s

standard deviation of returns Standard deviation is a measure of the dispersion of

possible outcomes The greater the standard deviation, the greater the

uncertainty, and therefore, the greater the risk

n

iii kPkk

1

2 )()(

Slide 16

Standard Deviation (Utility)

( 4% - 10%)2 (0.20) = 7.2%

(10% - 10%)2 (0.50) = 0%

(14% - 10%)2 (0.30) = 4.8%

Variance (Sum) = 12.0%

Standard Deviation = Square Root of Variance (12.0%) = 3.46%

Slide 17

Standard Deviation (Tech)

(-10% - 14%)2 (0.20) = 115.2%

( 14% - 14%)2 (0.50) = 0%

( 30% - 14%)2 (0.30) = 76.8%

Variance (Sum) = 192.0%

Standard Deviation = Square Root of Variance (192.0%) = 13.86%

Slide 18

Which Stock Would You Prefer

Utility Tech

Expected Return 10.00% 14.00%

Standard Deviation 3.46% 13.86% It depends on your tolerance for risk! Remember, there’s a tradeoff between risk and

return

Slide 19

Portfolios Combining several securities in a portfolio can actually reduce overall

risk How does this work?

rateof

return

time

kp

kA

kB

Slide 20

Diversification Investing in more than one security to reduce risk If two stocks are perfectly positively correlated,

diversification has no effect on risk If two stocks are perfectly negatively correlated,

the portfolio is perfectly diversified If you owned a share of every stock traded on the

NYSE and NASDAQ, would you be diversified? – YES!

Would you have eliminated all of your risk? – NO! Common stock portfolios still have risk

Slide 21

Types of Risk Market risk (systematic risk) is non-diversifiable.

This type of risk cannot be diversified away Unexpected changes in interest rates Unexpected changes in cash flows due to tax rate

changes, foreign competition, and the overall business cycle

Slide 22

Types of Risk Company-unique risk (unsystematic risk) is diversifiable.

This type of risk can be reduced through diversification A company’s labor force goes on strike A company’s top management dies in a plane crash A huge oil tank bursts and floods a company’s production area

Slide 23

As you add stocks to your portfolio, company-unique risk is reduced

Slide 24

Do some firms have more market risk than others? Yes. For example: Interest rate changes affect all firms, but which

would be more affected: Retail food chain Commercial bank

As we know, the market compensates investors for accepting risk - but only for market risk. Company-unique risk can and should be diversified away

So - we need to be able to measure market risk

Slide 25

This is why we have Beta Beta: a measure of market risk Specifically, beta is a measure of how an

individual stock’s returns vary with market returns It’s a measure of the “sensitivity” of an individual

stock’s returns to changes in the market

Slide 26

-5-15 5 10 15

-15

-10

-10

-5

5

10

15

XYZ Co. returns

S&P 500returns

. . . .

. . . .. . . .

. . . .. . . .

. . . .

. . . .

. . . .

. . . .

. . .

. . . .

. . . .

Calculating BetaBeta = slope = 1.20

Slide 27

The Market’s Beta is 1 A firm that has a beta = 1 has average market risk.

The stock is no more or less volatile than the market

A firm with a beta > 1 is more volatile than the market

(ex: technology firms) A firm with a beta < 1 is less volatile than the

market (ex: utilities)

Slide 28

Summary We know how to measure risk, using standard

deviation for overall risk and beta for market risk We know how to reduce overall risk to only

market risk through diversification We need to know how to price risk so we will

know how much extra return we should require for accepting extra risk

Slide 29

What is the Required Return? The return on an investment required by an investor given

market interest rates and the investment’s risk. Required Return = Risk-free rate of return

+ Risk premium Risk premium is the compensation for holding the market

risk Compensation per amount of market risk is the market

risk premium or (km – krf) Depending on the amount of market risk (Beta) some

firms will have greater required return

Slide 30

What is the Required Return? (Continued) This linear relationship between risk and required

return is known as the Capital Asset Pricing Model (CAPM)

indexmarket on thereturn the:

jsecurity of beta the:

interest of rate free-risk the:

jsecurity on return required the:

where,

)(

m

j

rf

j

rfmjrfj

k

k

k

kkkk

Slide 31

0%

5%

10%

15%

20%

25%

30%

0 0.5 1 1.5 2 2.5 3

Beta

Req

uire

d R

etur

n

krf

km

m

Security Market Line

Note that the slope of SML is the market risk premium or (km – krf)

Security Market Line (SML)

Slide 32

Example Suppose the Treasury bond rate is 6%, the average

return on the S&P 500 index is 12%, and Walt Disney has a beta of 1.2

According to the CAPM, what should be the required rate of return on Disney stock?

kDIS = 0.06 + 1.2 (0.12 - 0.06)

kDIS = 0.132 = 13.2% According to the CAPM, Disney stock should be

priced to give a 13.2% return

Slide 33

SLM and Fair Pricing Theoretically, every security should lie on the

SML If every stock is on the SML, investors are being

fully compensated for risk If a security is above the SML, it is underpriced If a security is below the SML, it is overpriced

Slide 34

Return Calculations

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