return = R = change in asset value + income

initial value

Module – 2Risk and ReturnMeasuring Historical Return

• R is ex post– based on past data, and is known

• R is typically annualized

example 1

• Tbill, 1 month holding period

• buy for $9488, sell for $9528

• 1 month R:

9528 - 9488

9488= .0042 = .42%

• annualized R:

(1.0042)12 - 1 = .052 = 5.2%

example 2

• 100 shares IBM, 9 months • buy for $62, sell for $101.50• $.80 dividends• 9 month R:

101.50 - 62 + .80

62= .65 =65%

• annualized R:

(1.65)12/9 - 1 = .95 = 95%

Two types of risk

• Systematic Risk

• unsystematic risk

Systematic Risk• Risk factors that affect a large number of assets• Also known as non-diversifiable risk or market

risk• Includes such things as changes in GDP, inflation,

interest rates, etc.– market risk

– cannot be eliminated through diversification

– due to factors affecting all assets

-- energy prices, interest rates, inflation, business cycles

Systematic RiskThe systematic risk is further divided into

• Market Risk

• Interest Rate Risk

• Purchasing Power Risk

-Demand Pull Inflation

-Cost Push Inflation

Unsystematic Risk• Risk factors that affect a limited number of

assets

• Also known as unique risk and asset-specific risk

• Includes such things as labor strikes, part shortages, availability of raw materials etc.– specific to a firm– can be eliminated through diversification

Unsystematic RiskUnsystematic Risk can be classified into • Business Risk• Financial RiskBusiness risk

Internal Business Risk Fluctuations in sales R&D Personnel Management Fixed Costs Single ProductExternal Risk Social & Regulatory Factors Political Risk Business Cycles

# assets

systematicrisk

unsystematic risk

totalrisk

Measuring Systematic Risk

• How do we measure systematic risk?• We use the beta coefficient to measure systematic

risk• What does beta tell us?

– A beta of 1 implies the asset has the same systematic risk as the overall market

– A beta < 1 implies the asset has less systematic risk than the overall market

– A beta > 1 implies the asset has more systematic risk than the overall market

Total versus Systematic Risk

• Consider the following information: Standard Deviation Beta– Security C 20% 1.25– Security K 30% 0.95

• Which security has more total risk?• Which security has more systematic risk?• Which security should have the higher

expected return?

Beta, • variation in asset/portfolio return

relative to return of market portfolio– mkt. portfolio = mkt. index

-- S&P 500 or NYSE index

= % change in asset return

% change in market return

interpreting • if

– asset is risk free

• if – asset return = market return

• if – asset is riskier than market index

– asset is less risky than market index

Sample betas Amazon 2.23

Anheuser Busch -.107

Microsoft 1.62

Ford 1.31

General Electric 1.10

Wal Mart .80

(monthly returns, 5 years back)

measuring

• estimated by regression– data on returns of assets– data on returns of market index– estimate

mRR

Beta and the Risk Premium

• Remember that the risk premium = expected return – risk-free rate

• The higher the beta, the greater the risk premium should be

• Can we define the relationship between the risk premium and beta so that we can estimate the expected return?– YES!

Example: Portfolio Expected Returns and Betas

0 %

5 %

1 0 %

1 5 %

2 0 %

2 5 %

3 0 %

0 0 . 5 1 1 . 5 2 2 . 5 3

B e t a

Exp

ecte

d R

etu

rn

Rf

E(RA)

A

Reward-to-Risk Ratio: Definition and Example

• The reward-to-risk ratio is the slope of the line illustrated in the previous example– Slope = (E(RA) – Rf) / (A – 0)

– Reward-to-risk ratio for previous example = (20 – 8) / (1.6 – 0) = 7.5

• What if an asset has a reward-to-risk ratio of 8 (implying that the asset plots above the line)?

• What if an asset has a reward-to-risk ratio of 7 (implying that the asset plots below the line)?

Market Equilibrium

• In equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market

M

fM

A

fA RRERRE

)()(

Security Market Line

• The security market line (SML) is the representation of market equilibrium

• The slope of the SML is the reward-to-risk ratio: (E(RM) – Rf) / M

• But since the beta for the market is ALWAYS equal to one, the slope can be rewritten

• Slope = E(RM) – Rf = market risk premium

The Capital Asset Pricing Model (CAPM)

• The capital asset pricing model defines the relationship between risk and return

• E(RA) = Rf + A(E(RM) – Rf)• If we know an asset’s systematic risk, we

can use the CAPM to determine its expected return

• This is true whether we are talking about financial assets or physical assets

Factors Affecting Expected Return

• Pure time value of money – measured by the risk-free rate

• Reward for bearing systematic risk – measured by the market risk premium

• Amount of systematic risk – measured by beta

Example - CAPM

• Consider the betas for each of the assets given earlier. If the risk-free rate is 2.13% and the market risk premium is 8.6%, what is the expected return for each?

Security Beta Expected Return

DCLK 2.685 2.13 + 2.685(8.6) = 25.22%

KO 0.195 2.13 + 0.195(8.6) = 3.81%

INTC 2.161 2.13 + 2.161(8.6) = 20.71%

KEI 2.434 2.13 + 2.434(8.6) = 23.06%

Figure 13.4

Beta, • variation in asset/portfolio return

relative to return of market portfolio– mkt. portfolio = mkt. index

-- S&P 500 or NYSE index

= % change in asset return

% change in market return

interpreting • if

– asset is risk free

• if – asset return = market return

• if – asset is riskier than market index

– asset is less risky than market index

Sample betas Amazon 2.23

Anheuser Busch -.107

Microsoft 1.62

Ford 1.31

General Electric 1.10

Wal Mart .80

(monthly returns, 5 years back)

measuring

• estimated by regression– data on returns of assets– data on returns of market index– estimate

mRR

problems• what length for return interval?

– weekly? monthly? annually?

• choice of market index?– NYSE, S&P 500– survivor bias

• # of observations (how far back?)– 5 years?– 50 years?

• time period?– 1970-1980?– 1990-2000?

III. Asset Pricing Models

• CAPM– Capital Asset Pricing Model– 1964, Sharpe, Linter– quantifies the risk/return tradeoff

assume

• investors choose risky and risk-free asset

• no transactions costs, taxes

• same expectations, time horizon

• risk averse investors

implication

• expected return is a function of– beta– risk free return– market return

]R)R(E[R)R(E fmf or

]R)R(E[R)R(E fmf

fR)R(E is the portfolio risk premium

where

fm R)R(E is the market risk premium

so if

• portfolio exp. return is larger than exp. market return

• riskier portfolio has larger exp. return

fR)R(E fm R)R(E

)R(E )R(E m

>

>

so if

• portfolio exp. return is smaller than exp. market return

• less risky portfolio has smaller exp. return

fR)R(E fm R)R(E

)R(E )R(E m

<

<

so if

• portfolio exp. return is same than exp. market return

• equal risk portfolio means equal exp. return

fR)R(E fm R)R(E

)R(E )R(E m

=

=

so if

• portfolio exp. return is equal to risk free return

fR)R(E

)R(E fR

= 0

=