Introductory Investment Analysis

Part II

Course Leader: Lauren RuddJanuary 12, 2011

8 weeks

What you will learn

The difference between expected and unexpected returns.

The difference between systematic risk and unsystematic risk.

The security market line and the capital asset pricing model.

The importance of beta.01/12/2011 Copyright Savannah Capital Management 2

Goal

Our goal is to define risk more precisely, and discuss how to measure it.

In addition, we will quantify the relation between risk and return in financial markets.

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Return

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The return on any stock traded in a financial market is composed of two parts.

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

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

Total return

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E(R) -R U

Return Expected - Return Total Return Unexpected

Return Unexpected Return Expected Return Total

Components of return

R – E(R) = U = surprise portion

= Systematic portion + Unsystematic

portion = m +

Therefore: R – E(R) = m + = unsystematic portion of total surprisem = systematic part of risk

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Events that impact the firm

Firms make periodic announcements about events that may significantly impact the profits of the firm. Earnings Conduct Product development Personnel

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Impact of news

The impact of an announcement depends on how much of the announcement represents new information.

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

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

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News about the future

News about the future is what really matters

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

Announcement = Expected News + Surprise News

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Risk

Systematic risk is risk that influences a large number of assets. Also called market risk.

Unsystematic risk is risk that influences a single company or a small group of companies. Also called unique risk or firm-specific risk.

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Total risk

Total risk = Systematic risk + Unsystematic risk

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Two types of risk

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

Unsystematic risk is also called diversifiable risk.

Systematic risk is also called non-diversifiable risk.

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Expected return

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

The systematic risk principle states:

The expected return on an asset depends

only on its systematic risk.01/12/2011 Copyright Savannah Capital Management 13

Systematic risk

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.

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Measuring systematic risk

To be compensated for risk, the risk has to be special.o Unsystematic risk is not special.o Systematic risk is special.

The Beta coefficient () measures the relative systematic risk of an asset. o Assets with Betas larger than 1.0 have more systematic

risk than average.o Assets with Betas smaller than 1.0 have less systematic

risk than average.

Because assets with larger betas have greater systematic risks, they will have greater expected returns.

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Portfolio betas

The total risk of a portfolio has no simple relation to the total risk of the individual assets in the portfolio.

For two assets, you need two variances and the covariance.

For four assets, you need four variances, and six covariances

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Portfolio betas

In contrast, a portfolio’s Beta can be calculated just like the expected return of a portfolio.

That is, you can multiply each asset’s Beta by its portfolio weight and then add the results to get the portfolio’s Beta.

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Portfolio beta

Beta for Southwest Airlines (LUV) is 1.05

Beta for General Motors (GM) 1.45

You put half your money into LUV and half into GM.

What is your portfolio Beta?

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Portfolio beta

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1.25

1.45.501.05.50

β.50β.50β GMLUVp

Beta and risk premium

Consider a portfolio made up of asset A and a risk-free asset. o For asset A, E(RA) = 16% and A = 1.6

o The risk-free rate Rf = 4%. Note that for a risk-free asset, = 0 by definition.

We can calculate some different possible portfolio expected returns and betas by changing the percentages invested in these two assets.

Note that if the investor borrows at the risk-free rate and invests the proceeds in asset A, the investment in asset A will exceed 100%.

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Beta and risk premium

% of Portfolio

in Asset A

Portfolio

Expected

Return

Portfolio

Beta

0% 4 0.0

25 7 0.4

50 10 0.8

75 13 1.2

100 16 1.6

125 19 2.0

150 22 2.4

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Beta and risk premium

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Beta and risk premium

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7.50%

1.6

4%16%

β

RRE

A

fA

Notice that all the combinations of portfolio expected returns and betas fall on a straight line.

Slope (Rise over Run):

Beta and risk premium

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.

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The basic argument

Recall that for asset A: E(RA) = 16% and A = 1.6

Suppose there is a second asset, asset B. For asset B: E(RB) = 12% and A = 1.2

Which investment is better, asset A or asset B?o Asset A has a higher expected returno Asset B has a lower systematic risk

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The basic argument

As before with Asset A, we can calculate some different possible portfolio expected returns and betas by changing the percentages invested in asset B and the risk-free rate.

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The basic argument

% of Portfolio in Asset B

PortfolioExpected Return Portfolio Beta

0% 4 0.0

25 6 0.3

50 8 0.6

75 10 0.9

100 12 1.2

125 14 1.5

150 16 1.8

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The basic argument

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Portfolio Expected Returns and Betas for both Assets

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Fundamental result

The situation for assets A and B cannot persist in a well-organized, active marketo Investors will be attracted to asset A (and buy A

shares)o Investors will shy away from asset B (and sell B

shares)

This buying and selling will make o The price of A shares increaseo The price of B shares decrease

This price adjustment continues until the two assets plot on exactly the same line.

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Fundamental result

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B

fB

A

fA

β

RRE

β

RRE

This price adjustment continues until the two assets plot on exactly the same line.

Fundamental result

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Security market line

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fM

fM

M

fM

RRE

1

RRE

β

RRE

The Security market line (SML) is a graphical representation of the linear relationship between systematic risk and expected return in financial markets.

For a market portfolio,

Security market line

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fMi

fi RREβ

RRE

Therefore:For any asset “i” in the market:

The term E(RM) – Rf is often called the market risk premium because it is the risk premium on a market portfolio.

Capital asset pricing model

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ifMfi βRRERRE

Setting the reward-to-risk ratio for all assets equal to the market risk premium results in an equation known as:

The capital asset pricing model.

Capital asset pricing model

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ifMfi βRRERRE

The Capital Asset Pricing Model (CAPM) is a theory of risk and return for securities in a competitive capital market.

Security market line

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Risk return summary

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Risk return summary

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Risk return summary

Assume the following:

Risk free rate Rf is 5% Expected return E(Rm) of the market is

12% Security beta is 1.2 E(R) = Rf + [E(Rm) – Rf] x β

= .05 + (.12 - .05) x 1.2 = .134 or 13.4%

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Decomposition of total returns

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Unexpected returns

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Calculating beta

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Betas vary

Betas are estimated from actual data. Different sources estimate differently, possibly using different data.For data, the most common choices are

three to five years of monthly data, or a single year of weekly data.

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

The calculated betas may be adjusted for various statistical reasons.

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CAPM – hotly debated

The CAPM has a stunning implication: oWhat you earn on your portfolio

depends only on the level of systematic risk that you bear

oAs a diversified investor, you do not need to worry about total risk, only systematic risk.

The above bullet point is a hotly debated question01/12/2011 Copyright Savannah Capital Management 45