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Chapter 4 - Risk and Rates of Return

Ó 2005, Pearson Prentice Hall

Chapter 6 Objectives

- 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, Capital Asset Pricing

Model)

Inflation, Rates of Return, and the Fisher Effect

Interest Rates

Conceptually

Interest Rates

Interest Rates

Interest Rates

Interest Rates

Interest Rates

Interest Rates

Interest Rates

Interest Rates

Interest Rates

- Suppose the real rate is 3, and the nominal rate

is 8. What is the inflation rate premium? - (1 krf) (1 k) (1 IRP)
- (1.08) (1.03) (1 IRP)
- (1 IRP) (1.0485), so
- IRP 4.85

Term Structure of Interest Rates

- The pattern of rates of return for debt

securities that differ only in the length of time

to maturity.

Term Structure of Interest Rates

- The pattern of rates of return for debt

securities that differ only in the length of time

to maturity.

Term Structure of Interest Rates

- The pattern of rates of return for debt

securities that differ only in the length of time

to maturity.

Term Structure of Interest Rates

- The yield curve may be downward sloping or

inverted if rates are expected to fall.

Term Structure of Interest Rates

- The yield curve may be downward sloping or

inverted if rates are expected to fall.

For a Treasury security, what is the required

rate of return?

For a Treasury security, what is the required

rate of return?

For a Treasury security, what is the required

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.

For a corporate stock or bond, what is the

required rate of return?

For a corporate stock or bond, what is the

required rate of return?

For a corporate stock or bond, what is the

required rate of return?

For a corporate stock or bond, what is the

required rate of return?

- How large of a risk premium should we require to

buy a corporate security?

Returns

- 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.

Expected Return

- State of Probability Return
- Economy (P) Orl. Utility

Orl. Tech - Recession .20 4

-10 - Normal .50 10

14 - Boom .30 14

30 - For each firm, the expected return on the stock

is just a weighted average

Expected Return

- State of Probability Return
- Economy (P) Orl. Utility

Orl. Tech - Recession .20 4

-10 - Normal .50 10

14 - Boom .30 14

30 - For each firm, the expected return on the stock

is just a weighted average - k P(k1)k1 P(k2)k2 ... P(kn)kn

Expected Return

- State of Probability Return
- Economy (P) Orl. Utility

Orl. Tech - Recession .20 4

-10 - Normal .50 10

14 - Boom .30 14

30 - k P(k1)k1 P(k2)k2 ... P(kn)kn
- k (OU) .2 (4) .5 (10) .3 (14) 10

Expected Return

- State of Probability Return
- Economy (P) Orl. Utility

Orl. Tech - Recession .20 4

-10 - Normal .50 10

14 - Boom .30 14

30 - k P(k1)k1 P(k2)k2 ... P(kn)kn
- k (OI) .2 (-10) .5 (14) .3 (30) 14

- Based only on your expected return calculations,

which stock would you prefer?

Have you considered

RISK?

What is Risk?

- The possibility that an actual return will differ

from our expected return. - Uncertainty in the distribution of possible

outcomes.

What is Risk?

- Uncertainty in the distribution of possible

outcomes.

What is Risk?

- Uncertainty in the distribution of possible

outcomes.

What is Risk?

- Uncertainty in the distribution of possible

outcomes.

How do We Measure Risk?

- To get a general idea of a stocks price

variability, we could look at the stocks price

range over the past year.

52 weeks Yld Vol

Net Hi Lo Sym Div PE 100s Hi

Lo Close Chg 134 80 IBM .52 .5 21

143402 98 95 9549 -3 115 40 MSFT

29 558918 55 52 5194

-475

How do We Measure Risk?

- A more scientific approach is to examine the

stocks 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.

Standard Deviation

- (ki - k)2 P(ki)

- Orlando Utility, Inc.

- Orlando Utility, Inc.
- ( 4 - 10)2 (.2) 7.2

- Orlando Utility, Inc.
- ( 4 - 10)2 (.2) 7.2
- (10 - 10)2 (.5) 0

- Orlando Utility, Inc.
- ( 4 - 10)2 (.2) 7.2
- (10 - 10)2 (.5) 0
- (14 - 10)2 (.3) 4.8

- Orlando Utility, Inc.
- ( 4 - 10)2 (.2) 7.2
- (10 - 10)2 (.5) 0
- (14 - 10)2 (.3) 4.8
- Variance 12

- Orlando Utility, Inc.
- ( 4 - 10)2 (.2) 7.2
- (10 - 10)2 (.5) 0
- (14 - 10)2 (.3) 4.8
- Variance 12
- Stand. dev. 12

- Orlando Utility, Inc.
- ( 4 - 10)2 (.2) 7.2
- (10 - 10)2 (.5) 0
- (14 - 10)2 (.3) 4.8
- Variance 12
- Stand. dev. 12 3.46

- Orlando Technology, Inc.

- Orlando Technology, Inc.
- (-10 - 14)2 (.2) 115.2

- Orlando Technology, Inc.
- (-10 - 14)2 (.2) 115.2
- (14 - 14)2 (.5) 0

- Orlando Technology, Inc.
- (-10 - 14)2 (.2) 115.2
- (14 - 14)2 (.5) 0
- (30 - 14)2 (.3) 76.8

- Orlando Technology, Inc.
- (-10 - 14)2 (.2) 115.2
- (14 - 14)2 (.5) 0
- (30 - 14)2 (.3) 76.8
- Variance 192

- Orlando Technology, Inc.
- (-10 - 14)2 (.2) 115.2
- (14 - 14)2 (.5) 0
- (30 - 14)2 (.3) 76.8
- Variance 192
- Stand. dev. 192

- Orlando Technology, Inc.
- (-10 - 14)2 (.2) 115.2
- (14 - 14)2 (.5) 0
- (30 - 14)2 (.3) 76.8
- Variance 192
- Stand. dev. 192 13.86

- Which stock would you prefer?
- How would you decide?

- Which stock would you prefer?
- How would you decide?

Summary

- Orlando

Orlando - Utility Technology
- Expected Return 10 14
- Standard Deviation 3.46 13.86

- It depends on your tolerance for risk!
- Remember, theres a tradeoff between risk and

return.

- It depends on your tolerance for risk!
- Remember, theres a tradeoff between risk and

return.

- It depends on your tolerance for risk!
- Remember, theres a tradeoff between risk and

return.

Portfolios

- Combining several securities in a portfolio can

actually reduce overall risk. - How does this work?

Suppose we have stock A and stock B. The returns

on these stocks do not tend to move together over

time (they are not perfectly correlated).

Suppose we have stock A and stock B. The returns

on these stocks do not tend to move together over

time (they are not perfectly correlated).

Suppose we have stock A and stock B. The returns

on these stocks do not tend to move together over

time (they are not perfectly correlated).

What has happened to the variability of returns

for the portfolio?

What has happened to the variability of returns

for the portfolio?

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.

Some risk can be diversified away and some cannot.

- Market risk (systematic risk) is

nondiversifiable. This type of risk cannot be

diversified away. - Company-unique risk (unsystematic risk) is

diversifiable. This type of risk can be reduced

through diversification.

Market Risk

- Unexpected changes in interest rates.
- Unexpected changes in cash flows due to tax rate

changes, foreign competition, and the overall

business cycle.

Company-unique Risk

- A companys labor force goes on strike.
- A companys top management dies in a plane crash.
- A huge oil tank bursts and floods a companys

production area.

- As you add stocks to your portfolio,

company-unique risk is reduced.

- As you add stocks to your portfolio,

company-unique risk is reduced.

- As you add stocks to your portfolio,

company-unique risk is reduced.

- As you add stocks to your portfolio,

company-unique risk is reduced.

Do some firms have more market risk than others?

- Yes. For example
- Interest rate changes affect all firms, but which

would be more affected - a) Retail food chain
- b) Commercial bank

Do some firms have more market risk than others?

- Yes. For example
- Interest rate changes affect all firms, but which

would be more affected - a) Retail food chain
- b) Commercial bank

- Note
- 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.

This is why we have Beta.

- Beta a measure of market risk.
- Specifically, beta is a measure of how an

individual stocks returns vary with market

returns. - Its a measure of the sensitivity of an

individual stocks returns to changes in the

market.

The markets 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 gt 1 is more volatile than the

market.

The markets 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 gt 1 is more volatile than the

market. - (ex technology firms)

The markets 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 gt 1 is more volatile than the

market. - (ex technology firms)
- A firm with a beta lt 1 is less volatile than the

market.

The markets 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 gt 1 is more volatile than the

market. - (ex technology firms)
- A firm with a beta lt 1 is less volatile than the

market. - (ex utilities)

Calculating Beta

Calculating Beta

Calculating Beta

Calculating Beta

Calculating Beta

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.

What is the Required Rate of Return?

- The return on an investment required by an

investor given market interest rates and the

investments risk.

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- Required
- rate of
- return

Lets try to graph this relationship!

Beta

- Required
- rate of
- return

.

- Required
- rate of
- return

.

- This linear relationship between risk and

required return is known as the Capital Asset

Pricing Model (CAPM).

- Required
- rate of
- return

.

- Required
- rate of
- return

.

- Required
- rate of
- return

.

Beta

- Required
- rate of
- return

.

- Required
- rate of
- return

.

- Required
- rate of
- return

.

- Required
- rate of
- return

.

The CAPM equation

The CAPM equation

b

- kj krf j (km - krf )

The CAPM equation

- kj krf j (km - krf )
- where
- kj the required return on security j,
- krf the risk-free rate of interest,
- j the beta of security j, and
- km the return on the market index.

Example

- Suppose the Treasury bond rate is 6, the average

return on the SP 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?

kj krf (km - krf )

b

- kj .06 1.2 (.12 - .06)
- kj .132 13.2
- According to the CAPM, Disney stock should be

priced to give a 13.2 return.

- Required
- rate of
- return

.

- Required
- rate of
- return

.

- Required
- rate of
- return

.

- Required
- rate of
- return

.

- Required
- rate of
- return

.

Simple Return Calculations

Simple Return Calculations

Simple Return Calculations

Simple Return Calculations

Pt1 60 Pt 50

- 1 -1 20

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Calculator solution using HP 10B

- Enter monthly return on 10B calculator, followed

by sigma key (top right corner). - Shift 7 gives you the expected return.
- Shift 8 gives you the standard deviation.