Slides_Fundamentals of Investments - Chapter 18 docx

Systematic and Unsystematic RiskSystematic risk Risk that influences a large number of assets.. The Systematic Risk PrincipleŠ The systematic risk principle states that the reward for be

Valuation & Management

Charles J Corrado Bradford D.Jordan

Return, Risk, & the Security Market Line

Our goal in this chapter is to define risk more precisely, and discuss how

to measure it Then, we will quantify the relation between risk and return

in financial markets

Goal

Expected and Unexpected Returns

Š The return on any stock traded in a financial

market is composed of two parts

c The normal, or expected, part of the return is the return that investors predict or expect.

d The uncertain, or risky, part of the return comes from unexpected information revealed during the year.

Total return – Expected return = Unexpected return

R – E(R) = U

or

Announcements and News

Š The impact of an announcement depends on

how much of it represents new information

Î When the situation is not as bad as previously thought, what seems to be bad news is actually good news.

Š News about the future is what matters

Î Market participants factor predictions into the expected part of the stock return.

Announcement = Expected part + Surprise

Systematic and Unsystematic Risk

Systematic risk

Risk that influences a large number of

assets Also called market risk.

Unsystematic risk

Risk that influences a single company or a small group of companies Also called

unique or asset-specific risk.

Total risk = Systematic risk + Unsystematic risk

Systematic & Unsystematic Components of Return

Š R – E(R) = U

= Systematic portion+ Unsystematic portion

= m + ε

R – E(R) = m + ε

Diversification and Risk

Š In a large portfolio, some stocks will go up in value because of positive company-specific events, while others will go down in value because of negative company-specific events

Š Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets has almost no unsystematic risk

Š Unsystematic risk is also called diversifiable

risk, while systematic risk is also called

nondiversifiable risk.

The Systematic Risk Principle

Š The systematic risk principle states that the

reward for bearing risk depends only on the systematic risk of an investment

Š So, no matter how much total risk an asset has, only the systematic portion is relevant in

determining the expected return (and the risk premium) on that asset

What determines the size of the risk premium on a risky asset?

Measuring Systematic Risk

Š Because assets with larger betas have greater

systematic risks, they will have greater expected returns

Š Note that not all betas are created equal

Beta coefficient ( β)

Measure of the relative systematic risk of an asset Assets with betas larger than 1.0 have more systematic risk than average, and vice versa

Measuring Systematic Risk

Work the Web

 Beta coefficients are widely available

online For example, check out:

http://finance.yahoo.com

Portfolio Betas

Š The riskiness of a portfolio has no simple

relation to the risks of the assets in the portfolio

Š In contrast, a portfolio beta can be calculated

just like the expected return of a portfolio

Î In general, you can multiply each asset’s beta by its portfolio weight and then add the results to get the portfolio’s beta.

Beta and the Risk Premium

Š Consider a portfolio made up of asset A and a

risk-free asset For asset A, E(R A ) = 20% and

βA = 1.6 The risk-free rate R f = 8% Note that for a risk-free asset, β = 0 by definition

— We can calculate some different possible portfolio

expected returns and betas by varying the percentages invested in these two assets.

— Note that when the investor borrows at the risk-free

rate and invests the proceeds in asset A, the investment in asset A will exceed 100%.

Beta and the Risk Premium

Beta and the Risk Premium

The Reward-to-Risk Ratio

Š Notice that all the combinations of portfolio

expected returns and betas fall on a straight line

Š Slope

Š What this tells us is that asset A offers a

reward-to-risk ratio of 7.50% In other words,

asset A has a risk premium of 7.50% per “unit”

of systematic risk

( )

%50

76

.1

%8

E

The Basic Argument

Š Consider a second asset, asset B, with E(R B ) =

16% and βA = 1.2 Which investment is better, asset A or asset B?

The Basic Argument

The Basic Argument

The Basic Argument

The Fundamental Result

Š The situation we have described for assets A

and B cannot persist in a well-organized, active market because investors will be attracted to asset A and away from asset B

Š This buying and selling will continue, and A’s price will rise and B’s price will fall, until the two assets plot on exactly the same line

Š So, E( )R A R f E( )R B R f

ββ

−

=

−

The Fundamental Result

In general …

Š The reward-to-risk ratio must be the same for

all assets in a competitive financial market

Š If one asset has twice as much systematic risk

as another asset, its risk premium will simply

be twice as large

Š Because the reward-to-risk ratio must be the

same, all assets in the market must plot on the same line

The Fundamental Result

The Security Market Line

Š For a market portfolio,

Security market line (SML)

Graphical representation of the linear relationship between systematic risk and expected return in financial markets

( )M f

f M

M

f M

R R

E

R R

E R

R E

SML slope

The Security Market Line

Š The term E(R M ) – R f is often called the market risk premium because it is the risk premium on

a market portfolio

Š For any asset i in the market,

f M

i

f i

R R

E

R R

E

−

=

−β

Capital asset pricing model (CAPM)

A theory of risk and return for securities on a competitive capital market

The Security Market Line

Š The CAPM shows that E(R i ) depends on

cR f, the pure time value of money.

e βi, the amount of systematic risk.

( )R i R f [E( )R M R f ] i

The Security Market Line

The Security Market Line

The Security Market Line

A Closer Look at Beta

Š R – E(R) = m + ε, where m is the systematic

portion of the unexpected return

Š m = β × [R M – E(R M )]

Š So, R – E(R) = β × [R M – E(R M )] + ε

Š In other words, a high-beta security is simply

one that is relatively sensitive to overall market movements, whereas a low-beta security is one that is relatively insensitive

A Closer Look at Beta

A Closer Look at Beta

Where Do Betas Come From?

Š A security’s beta depends on

c how closely correlated the security’s return is with the overall market’s return, and

d how volatile the security is relative to the market.

Š A security’s beta is equal to the correlation

multiplied by the ratio of the standard deviations

M i

σ

σ,

Corr

Where Do Betas Come From?

Why Do Betas Differ?

Š Betas are estimated from actual data Different sources estimate differently, possibly using

different data

Î For data, the most common choices are three to five years of monthly data, or a single year of weekly data.

Î To measure the overall market, the S&P 500 stock market index is commonly used.

Î The calculated betas may be adjusted for various statistical reasons.

Chapter Review

Š Announcements, Surprises, and Expected

Returns

Î Expected and Unexpected Returns

Î Announcements and News

Š Risk: Systematic and Unsystematic

Î Systematic and Unsystematic Risk

Î Systematic and Unsystematic Components of Return

Chapter Review

Š Diversification, Systematic Risk, and

Unsystematic Risk

Î Diversification and Unsystematic Risk

Î Diversification and Systematic Risk

Š Systematic Risk and Beta

Î The Systematic Risk Principle

Î Measuring Systematic Risk

Î Portfolio Betas

Chapter Review

Š The Security Market Line

Î Beta and the Risk Premium

Î The Reward-to-Risk Ratio

Î The Basic Argument

Î The Fundamental Result

Î The Security Market Line

Chapter Review

Š More on Beta

Î A Closer Look at Beta

Î Where Do Betas Come From?

Î Why Do Betas Differ?