Finance management cengage 2013 chapter 08

Risk and Rates of ReturnStand-Alone Risk Portfolio Risk Risk and Return: CAPM/SML Chapter 8... What is investment risk?– Stand-alone risk – Portfolio risk earning a low or negative actu

Risk and Rates of Return

Stand-Alone Risk Portfolio Risk Risk and Return: CAPM/SML

Chapter 8

What is investment risk?

– Stand-alone risk

– Portfolio risk

earning a low or negative actual return.

negative returns, the riskier the investment.

Probability Distributions

probability of each occurrence.

Expected Rate of Return

Rate of Return (%) 100

15 0

-70

Firm X

Firm Y

Selected Realized Returns, 1926-2010

Source: Based on Ibbotson Stocks, Bonds, Bills, and Inflation: 2011 Classic

Yearbook (Chicago: Morningstar, Inc., 2011), p 32.

Hypothetical Investment Alternatives

Why is the T-bill return independent of the economy?

Do T-bills promise a completely risk-free return?

the economy.

return, as they are still exposed to inflation

Although, very little unexpected inflation is likely to occur over such a short period of time.

How do the returns of High Tech and Collections

behave in relation to the market?

positive correlation This is typical.

and has a negative correlation This is unusual.

Calculating the Expected Return

12.4%

(0.1)(45%) (0.2)(30%)

(0.4)(15%) (0.2)(-7%)

-27%) )(

1 0 ( rˆ

r P rˆ

return

of rate Expected

rˆ

N 1

i i i

=

+ +

+ +

Summary of Expected Returns

High Tech has the highest expected return, and

appears to be the best investment alternative, but is it

really? Have we failed to account for risk?

Calculating Standard Deviation

∑

=

−

= σ

σ

=

= σ

= σ

N 1

2

2

P ) rˆ r(

Variance

deviation Standard

Standard Deviation for Each Investment

% 0 0

) 1 0 ( ) 5 5 5 5 (

) 2 0 ( ) 5 5 5 5 ( ) 4 0 ( ) 5 5 5 5 (

) 2 0 ( ) 5 5 5 5 ( ) 1 0 ( ) 5 5 5 5 (

P ) rˆ r(

bills - T

2 / 1

2

2 2

2 2

bills - T

N 1

2

= σ

− +

−

− +

−

= σ

Comparing Standard Deviations

Comments on Standard Deviation as a Measure of

Risk

stand-alone, risk.

• The larger σ i is, the lower the probability that actual

returns will be close to expected returns.

distribution of returns.

Comparing Risk and Return

Security Expected Return, Risk, σ

Coefficient of Variation (CV)

expected value, that shows the risk per unit of return.

rˆ return

Expected

deviation Standard

Illustrating the CV as a Measure of Relative Risk

σ A = σ B , but A is riskier because of a larger probability of

losses In other words, the same amount of risk (as

measured by σ) for smaller returns.

0

Rate of Return (%) Prob.

Risk Rankings by Coefficient of Variation

• High Tech, despite having the highest standard

deviation of returns, has a relatively average CV.

Investor Attitude Towards Risk

require higher rates of return to encourage them to hold riskier securities.

on a risky asset and a riskless asset, which serves as compensation for investors to hold riskier

securities.

Portfolio Construction: Risk and Return

invested in both High Tech and Collections

the returns of the portfolio’s component assets.

that a new probability distribution for the portfolio returns be constructed.

Calculating Portfolio Expected Return

% 7 6

%) 0 1 ( 5 0

%) 4 12 ( 5 0 rˆ

rˆ w rˆ

: average weighted

a is rˆ

p

N 1

i i i p

p

= +

=

=

An Alternative Method for Determining

Portfolio Expected Return

(9.5%) 0.20

(7.5%) 0.40

(3.0%) 0.20

(0.0%) 0.10

rˆ p

= +

+

+ +

=

Calculating Portfolio Standard Deviation and CV

51

0

% 7 6

% 4

3 CV

% 4 3

6.7) -

(12.0 0.10

6.7) -

(9.5 0.20

6.7) -

(7.5 0.40

6.7) -

(3.0 0.20

6.7) -

(0.0 0.10

p

2 1

2 2 2 2 2

+

= σ

Comments on Portfolio Risk Measures

• σ p = 3.4% is much lower than the σ i of either stock

(σ HT = 20.0%; σ Coll = 13.2%).

High Tech and Collections’ σ (16.6%).

return of component stocks, but lower than the average risk.

General Comments about Risk

correlated with the market (i.e., ρ between 0 and 1).

risk

Returns Distribution for Two Perfectly Negatively Correlated Stocks (ρ = -1.0)

Returns Distribution for Two Perfectly Positively

-10

Portfolio MM’

0 15 25

-10

Partial Correlation, ρ = +0.35

Creating a Portfolio: Beginning with One Stock and

Adding Randomly Selected Stocks to Portfolio

would not be perfectly correlated with the existing portfolio.

relatively constant.

more stocks dissipates (after about 40 stocks), and for large stock portfolios, σ p tends to converge

to ≈ 20%

Illustrating Diversification Effects of a Stock

Portfolio

Breaking Down Sources of Risk

Stand-alone risk = Market risk + Diversifiable risk

that cannot be eliminated through diversification

Measured by beta.

stand-alone risk that can be eliminated through proper diversification.

Failure to Diversify

(doesn’t diversify), would the investor be compensated for the extra risk they bear?

Capital Asset Pricing Model (CAPM)

suggests that there is a Security Market Line (SML) that states that a stock’s required return equals the risk-free return plus a risk premium that reflects the stock’s risk after diversification.

r i = r RF + (r M – r RF )b i

is its contribution to the riskiness of a diversified portfolio.

volatility relative to the market.

well-diversified portfolio.

Comments on Beta

• If beta = 1.0, the security is just as risky as the

average stock.

• If beta > 1.0, the security is riskier than average.

• If beta < 1.0, the security is less risky than average.

Can the beta of a security be negative?

market is negative (i.e., ρ i,m < 0).

would slope downward, and the beta would be negative.

Calculating Betas

with how a stock is expected to move relative to the market in the future.

are forced to rely on historical data A typical approach to estimate beta is to run a regression of the security’s past returns against the past returns

of the market.

beta coefficient for the security

Illustrating the Calculation of Beta

-5 -10

Beta Coefficients for High Tech, Collections, and

Comparing Expected Returns and Beta Coefficients

The Security Market Line (SML): Calculating

Required Rates of Return

SML: r i = r RF + (r M – r RF )b i

r i = r RF + (RP M )b i

RP M = r M − r RF = 10.5% − 5.5% = 5.0%.

What is the market risk premium?

compensate investors for assuming an average amount of risk.

market and investors’ degree of risk aversion.

suggest that it ranges between 4% and 8% per year.

Calculating Required Rates of Return

r High Tech

( >

) r rˆ

( =

) r rˆ

( <

) r rˆ

( =

) r rˆ ( <

Illustrating the Security Market Line

An Example:

Equally-Weighted Two-Stock Portfolio

and 50% invested in Collections.

each of the stock’s betas.

b P = w HT b HT + w Coll b Coll

b P = 0.5(1.32) + 0.5(-0.87)

b P = 0.225

Calculating Portfolio Required Returns

average of each of the stock’s required returns.

r P = w HT r HT + w Coll r Coll

r P = 0.5(12.10%) + 0.5(1.15%)

r P = 6.625%

solve for expected return.

r P = r RF + (RP M )b P

r P = 5.5% + (5.0%)(0.225)

r P = 6.625%

Factors That Change the SML

what would happen to the SML?

SML 1

r i (%)

SML 2

13.5 10.5 8.5 5.5

ΔI = 3%

Risk, b i

Factors That Change the SML

the market risk premium to increase by 3%, what would happen to the SML?

Verifying the CAPM Empirically

verification almost impossible.

other than the market risk premium, that must be considered.

More Thoughts on the CAPM

risk and total risk Therefore, the SML may not produce a correct estimate of r i

r i = r RF + (r M – r RF )b i + ???

but betas are calculated using historical data A company’s historical data may not reflect investors’

expectations about future riskiness.