risk in return for basic finance

8/13/2019 Risk in Return for Basic Finance

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Chapter 7-8: Risk and Return


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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 AssetPricing Model)


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Inflation, Rates of Return,and the Fisher Effect


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Conceptually:

Nominalrisk-freeInterest

Ratek rf

=

Realrisk-freeInterest

Ratek*

+

Inflation-risk

premium

IRP

Mathematically:

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

This is known as the Fisher Effect

Interest Rates


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Suppose the real rate is 3%, and the nominal rate is8%. What is the inflation rate premium?

(1 + k rf ) = (1 + k*) (1 + IRP)(1.08) = (1.03) (1 + IRP)

(1.08) = (1.03 + 1.03 IRP)(1.03 IRP) = (0.05), so

IRP = 4.85%

Interest Rates


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Term Structure of Interest Rates

The pattern of rates of return for debtsecurities that differ only in the lengthof time to maturity.

yieldtomaturity

time to maturity (years)


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Term Structure of Interest Rates

yieldto

maturity

time to maturity (years)

The yield curve may be downwardsloping or inverted if rates areexpected to fall.


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For a Treasury security, what isthe required rate of return?

Since Treasuries are essentially free ofdefault risk , the rate of return on aTreasury security is considered the

risk-free rate of return.

Required

rate ofreturn =

Risk-free

rate ofreturn


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For a corporate stock or bond ,what is the required rate of return?

How large of a risk premium should werequire to buy a corporate security?

Required

rate ofreturn

= +Risk-free

rate ofreturn

Risk

premium


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Returns

Expected Return - the return that aninvestor expects to earn on an asset,

given its price, growth potential, etc.

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


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State of Probability ReturnEconomy (P) Orl. Utility Orl. Tech

Recession .20 4% -10%

Normal .50 10% 14%Boom .30 14% 30%

For each firm, the expected return on thestock is just a weighted average :

k = P(k 1)*k 1 + P(k 2)*k 2 + ...+ P(k n )*kn

Expected Return


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Expected Return

State of Probability ReturnEconomy (P) Orl. Utility Orl. Tech

Recession .20 4% -10%

Normal .50 10% 14%Boom .30 14% 30%

k = P(k 1)*k 1 + P(k 2)*k 2 + ...+ P(k n )*knk (OU ) = .2 (4%) + .5 (10%) + .3 (14%) = 10%

k (OT ) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%


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Based only on yourexpected return

calculations, whichstock would you

prefer?


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RISK?

Have you considered


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What is Risk?

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

Uncertainty in the distribution ofpossible outcomes.


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What is Risk?

Uncertainty in the distribution ofpossible outcomes.


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How do We Measure Risk?

A more scientific approach is toexamine 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.


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Standard Deviation

= (k i - k) 2 P(k i )n

i =1


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Orlando Util i ty, I nc.

( 4% - 10%) 2 (.2) = 7.2(10% - 10%) 2 (.5) = 0(14% - 10%) 2 (.3) = 4.8Variance = 12Stand. dev. = 12 = 3.46%

= (k i - k) 2 P(k i)n

i =1


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Orlando Technology, I nc.

(-10% - 14%) 2 (.2) = 115.2(14% - 14%) 2 (.5) = 0

(30% - 14%)2

(.3) = 76.8Variance = 192Stand. dev. = 192 = 13.86%

= (k i - k) 2 P(k i)n

i =1


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Which stock would you prefer?

How would you decide?


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Orlando Orlando

Utility Technology

Expected Return 10% 14%

Standard Deviation 3.46% 13.86%

Summary


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It depends on your tolerance for risk!

Remember, theres a tradeoff between

risk and return.

Return

Risk


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Portfolios

Combining several securitiesin a portfolio can actuallyreduce 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 tendto move together over time (they arenot perfectly correlated).

rateof

return

time

k A

k B

Wh h h d h


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rateof

return

time

k pk A

k B

What has happened to thevariability of returns for the

portfolio?


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Diversification

Investing in more than one securityto reduce risk .

If two stocks are perfectly positively correlated , diversification has noeffect 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 ofyour risk?NO! Common stock portfolios stillhave risk.


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Some risk can be diversifiedaway and some cannot.

Market risk (systematic r isk) isnondiversifiable. This type of risk

cannot be diversified away. Company-unique risk (unsystematic

risk) is diversifiable . This type of riskcan be reduced throughdiversification.


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Market Risk

Unexpected changes in interestrates.

Unexpected changes in cash flowsdue to tax rate changes, foreign

competition, and the overallbusiness cycle.


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Company-unique Risk

A companys labor force goes onstrike.

A companys top management diesin a plane crash.

A huge oil tank bursts and floods a

companys 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 moremarket risk than others?

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

which would be more affected:

a) Retail food chainb) Commercial bank


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

which would be more affected:

a) Retail food chainb) Commercial bank

Do some firms have moremarket risk than others?


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Note

As we know, the market compensatesinvestors for accepting risk - butonly for market risk . Company-

unique risk can and should bediversified 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 stocks returns varywith market returns.

Its a measure of the sensitivity ofan individual stocks returns tochanges in the market.


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A firm that has a beta = 1 has averagemarket risk . The stock is no more or lessvolatile than the market.

A firm with a beta > 1 is more volatile thanthe market. (ex: technology firms)

A firm with a beta < 1 is less volatile thanthe market. (ex: utilities)

The markets beta is 1

Ch t i ti li


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Characteristic line

-5-15 5 10 15

-15

-10

-10

-5

5

10

15

XYZ Co. returns

S&P 500returns

. . . .

. . . .. . . .

. . . .. . . .

. . . .

. . . .. . . .

. . .. . . .

. . .

Beta = slope= 1.20

The line of best fit

through a series of

returns for a firmsstock relative to themarket returns.

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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Measuring a Portfolio Beta

Portfolio beta

The relationship between a portfolios returnsand the markets different returns A measure of the portfolios nondiversifiable

risk portfolio =(% invested in stock j) x ( of stock j)


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Summary:

We know how to measure risk, usingstandard deviation for overall riskand beta for market risk.

We know how to reduce overall riskto only market risk throughdiversification .

We need to know how to price risk sowe will know how much extra returnwe should require for accepting extrarisk.


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What is the Required Rate ofReturn?

The return on an investment

required by an investor givenmarket interest rates and theinvestments risk .


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market

riskcompany-

unique risk

can be diversified

away

Requiredrate ofreturn = +

Risk-freerate ofreturn

Riskpremium


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Required

rate ofreturn

Beta

Lets try to graph this relationship!


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Required

rate ofreturn

.

Risk-free

rate ofreturn(6%)

Beta

12%

1

The return line that reflects theattitudes of investors regardingthe minimal acceptable returnfor a given level of systematicrisk.

Security MarketLine (SML)


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This linear relationship between

risk and required return isknown as the Capital Asset

Pricing Model (CAPM).

Required SML


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Required

rate of

return

.

Risk-free

rate ofreturn(6%)

Beta

12%

1

SML

0

Is there a riskless(zero beta) security?

Required SML


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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%)

Required SML


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Required

rate of

return

.

Beta

12%

1

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

Risk-free

rate ofreturn(6%)

0

Required SML


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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

approximation

for the market

Risk-free

rate ofreturn(6%)

0


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Required SMLHi h t h


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Required

rate of

return

.

Beta

12%

1

SMLHigh-techstocks

Risk-free

rate ofreturn(6%)

0


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k j = k rf + j (k m - k rf )

where:

k j = the required return on security j,

k rf = the risk-free rate of interest, j = the beta of security j, and

k m = the return on the market index.

The CAPM equation:

b

b


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Example:

Suppose the Treasury bond rate is6% , the average return on the

S&P 500 index is 12% , and WaltDisney has a beta of 1.2 . According to the CAPM , what

should be the required rate ofreturn on Disney stock?


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k j = k rf + (k m - k rf )

k j = .06 + 1.2 (.12 - .06)k j = .132 = 13.2%

According to the CAPM, Disney

stock should be priced to give a13.2% return.

b

Required SML


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Required

rate of

return

.

Beta

12%

1

SML

0

Risk-free

rate ofreturn(6%)

Required SML


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equ ed

rate of

return

.

Beta

12%

1

SML

0

Theoretically, everysecurity should lie

on the SML

Risk-free

rate ofreturn(6%)

Required SML


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q

rate of

return

.

Beta

12%

1

SML

0

Theoretically, everysecurity should lie

on the SML

If every stockis on the SML,

investors are being fullycompensated for risk.Risk-free

rate ofreturn(6%)

Required SML


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q

rate of

return

.

Beta

12%

1

SML

0

If a security is abovethe SML, it is

underpriced.

Risk-free

rate ofreturn(6%)

Required SML


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q

rate of

return

.

Beta

12%

1

SML

0

If a security is abovethe SML, it is

underpriced.

If a security isbelow the SML, it

is overpriced.Risk-freerate ofreturn(6%)

Si l R C l l i


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P t+1 60

P t 50

Simple Return Calculations

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

P t 50

- 1 = -1 = 20%

t t+1

$50 $60

(a) (b)


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monthly expected month price return return (a - b) 2

Dec $50.00 Jan $58.00 0.160 0.049 0.012321 Feb $63.80 0.100 0.049 0.002601 Mar $59.00 -0.075 0.049 0.015376 Apr $62.00 0.051 0.049 0.000004

May $64.50 0.040 0.049 0.000081 Jun $69.00 0.070 0.049 0.000441 Jul $69.00 0.000 0.049 0.002401 Aug $75.00 0.087 0.049 0.001444

Sep $82.50 0.100 0.049 0.002601 Oct $73.00 -0.115 0.049 0.028960 Nov $80.00 0.096 0.049 0.002090 Dec $86.00 0.075 0.049 0.000676

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