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Chapter 6 - Risk and Rates of Return

Return

Risk

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Tujuan Pembelajaran

Mahasiswa mampu untuk: Menjelaskan hubungan antara tingkat imbal hasil yang diharapkan dengan risiko

Menjelaskan efek inflasi atas tingkat imbal hasil

Menjelaskan term structure dari tingkat bunga

Mendefinisikan dan mengukur tingkat imbal hasil yang diharapkan dan risiko dari suatu suatu investasi

Menjelaskan pengaruh diversifikasi terhadap imbal hasil yang diharapakan dan tingkat risiko dari suatu portofolio atau kombinasi aset

Mengukur risiko pasar dari suatu aset dan portofolio investasi

Menjelaskan hubungan antara tingkat imbal hasil yang diminta

investor dan tingkat risiko dari suatu investasi

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Pokok Bahasan

Tingkat imbal hasil di Pasar Keuangan

Efek inflasi terhadap tingkat imbal hasil dan Efek Fisher

Term Strucuture dari tingkat bunga

Tingkat imbal hasil yang diharapkan

Risiko

Risiko dan diversifikasi

Mengukur risiko pasar

Mengukur beta dari suatu portofolio

Ttingkat imbal hasil yang diminta investor

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Inflation, Rates of Return, and the Fisher Effect

InterestRates

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Conceptually:

Nominalrisk-freeInterest

Rate

krf

=

Realrisk-freeInterest

Rate

k*

+

Inflation-risk

premium

IRP

Mathematically:

(1 + krf) = (1 + k*) (1 + IRP)

This is known as the “Fisher Effect”

Interest Rates

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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%

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Term Structure of Interest Rates

The pattern of rates of return for debt securities that differ only in the length of time to maturity.

yieldto

maturity

time to maturity (years)

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Term Structure of Interest Rates

The yield curve may be downward sloping or “inverted” if rates are expected to fall.

yieldto

maturity

time to maturity (years)

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Term Structure of Interest Rates

The yield curve may be downward sloping or “inverted” if rates are expected to fall.

yieldto

maturity

time to maturity (years)

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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.

Requiredrate of return

=Risk-freerate of return

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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?

Requiredrate of return

= +Risk-freerate of return

Riskpremium

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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.

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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

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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%

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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%

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Based only on your expected return

calculations, which stock would you

prefer?

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RISK?Have you considered

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What is Risk?

The possibility that an actual return will differ from our expected return.

Uncertainty in the distribution of possible outcomes.

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What is Risk?

Uncertainty in the distribution of possible outcomes.

return

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-10 -5 0 5 10 15 20 25 30

Company B

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4 8 12

Company A

return

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How do We Measure Risk?

To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year.

52 weeks Yld Vol NetHi Lo Sym Div % PE 100s Hi Lo Close Chg134 80 IBM .52 .5 21 143402 98 95 9549 -3

115 40 MSFT … 29 558918 55 52 5194 -475

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How do We Measure Risk?

A more 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.

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Standard Deviation

= (ki - k)2 P(ki)s n

i=1S

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Orlando Utility, Inc.

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

(10% - 10%)2 (.5) = 0

(14% - 10%)2 (.3) = 4.8Variance = 12

Stand. dev. = 12 = 3.46%

Orlando Utility, Inc.

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

(10% - 10%)2 (.5) = 0

(14% - 10%)2 (.3) = 4.8Variance = 12

Stand. dev. = 12 = 3.46%

= (ki - k)2 P(ki)s n

i=1S

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Orlando Technology, Inc.

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

(14% - 14%)2 (.5) = 0

(30% - 14%)2 (.3) = 76.8Variance = 192

Stand. dev. = 192 = 13.86%

= (ki - k)2 P(ki)s n

i=1S

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Which stock would you prefer?

How would you decide?

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Summary

Orlando Orlando

UtilityTechnology

Expected Return 10% 14%

Standard Deviation 3.46% 13.86%

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It depends on your tolerance for risk!

Remember, there’s a tradeoff between risk and return.

Return

Risk

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Portfolios

Combining several securities in a portfolio can actually reduce overall risk.

How does this work?

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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).

rateof

return

time

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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).

rateof

return

time

kA

kB

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rateof

return

time

kpkA

kB

What has happened to the variability of returns for the

portfolio?

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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.

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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.

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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.

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Market Risk

Unexpected changes in interest rates.

Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.

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Company-unique Risk

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.

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

portfoliorisk

number of stocks

Market risk

company-unique

risk

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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

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NoteAs 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.

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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.

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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)

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Calculating Beta

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Calculating Beta

-5-15 5 10 15

-15

-10

-10

-5

5

10

15

XYZ Co. returns

S&P 500returns

. . . .

. . . .. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . .

. . . .

. . . .

Beta = slope = 1.20

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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.

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What is the Required Rate of Return?

The return on an investment required by an investor given market interest rates and the investment’s risk.

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marketrisk

company-unique risk

can be diversifiedaway

Requiredrate of return

= +Risk-freerate of return

Riskpremium

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Required

rate of

return

Beta

Let’s try to graph thisrelationship!

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Required

rate of

return

.

Risk-freerate ofreturn(6%)

Beta

12%

1

securitymarket

line (SML)

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This linear relationship between risk and required return is known as the Capital Asset

Pricing Model (CAPM).

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Required

rate of

return

Beta

.12%

1

SML

0

Is there a riskless(zero beta) security?

Treasurysecurities are

as close to risklessas possible. Risk-free

rate ofreturn(6%)

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Required

rate of

return

.

Beta

12%

1

SMLWhere does the S&P 500fall on the SML?

The S&P 500 isa good

approximationfor the market

Risk-freerate ofreturn(6%)

0

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Required

rate of

return

.

Beta

12%

1

SML

UtilityStocks

Risk-freerate ofreturn(6%)

0

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Required

rate of

return

.

Beta

12%

1

SMLHigh-techstocks

Risk-freerate ofreturn(6%)

0

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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.

b

b

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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?

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kj = krf + (km - krf )

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.

b

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Required

rate of

return

.

Beta

12%

1

SML

0

Theoretically, every security should lie on the SML

If every stock is on the SML,

investors are being fully compensated for risk.Risk-free

rate ofreturn(6%)

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Required

rate of

return

.

Beta

12%

1

SML

0

If a security is abovethe SML, it isunderpriced.

If a security is below the SML, it

is overpriced.Risk-freerate ofreturn(6%)

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Pt+1 60

Pt 50

Simple Return Calculations

= = 20%Pt+1 - Pt 60 - 50

Pt 50

- 1 = -1 = 20%

t t+1

$50 $60

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(a) (b)monthly expected

month price return return (a - b)2

Dec $50.00Jan $58.00Feb $63.80Mar $59.00Apr $62.00May $64.50Jun $69.00Jul $69.00Aug $75.00Sep $82.50Oct $73.00Nov $80.00Dec $86.00

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(a) (b)monthly expected

month price return return (a - b)2

Dec $50.00Jan $58.00 0.160 0.049 0.012321Feb $63.80 0.100 0.049 0.002601Mar $59.00 -0.075 0.049 0.015376Apr $62.00 0.051 0.049 0.000004May $64.50 0.040 0.049 0.000081Jun $69.00 0.070 0.049 0.000441Jul $69.00 0.000 0.049 0.002401Aug $75.00 0.087 0.049 0.001444Sep $82.50 0.100 0.049 0.002601Oct $73.00 -0.115 0.049 0.028960Nov $80.00 0.096 0.049 0.002090Dec $86.00 0.075 0.049 0.000676

0.0781St. Dev: sum, divide by (n-1), and take sq root: