PRESENTED BY: LAUREN RUDD

LVERudd@aol.com

Tel: 941-706-3449 office

March 12, 2015

Portfolio ManagementSlide Set 1

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.

03/12/2915 Copyright Savannah Capital Management 2

Goal

A key 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.

03/12/2915 Copyright Savannah Capital Management 3

Mathematical Concepts

•Mean•Variance•Standard Deviation•Covariance

03/12/2915 Copyright Savannah Capital Management 4

Events that impact the firm

Firms make periodic announcements about events that may significantly impact the profits of the firm.

EarningsConductProduct developmentPersonnel

03/12/2915 Copyright Savannah Capital Management 5

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.

03/12/2915 Copyright Savannah Capital Management 6

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

03/12/2915 Copyright Savannah Capital Management 7

Return

03/12/2915 Copyright Savannah Capital Management 8

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.

Components of return

R – E(R) = U = surprise portion

= Systematic portion + Unsystematic portion = m +

Therefore:

R – E(R) = m + = unsystematic portion of total surprise

m = systematic part of risk

03/12/2915 Copyright Savannah Capital Management 9

RiskSystematic 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.

03/12/2915 Copyright Savannah Capital Management 10

Total risk

Total risk = Systematic risk + Unsystematic risk

03/12/2915 Copyright Savannah Capital Management 11

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.

03/12/2915 Copyright Savannah Capital Management 12

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.

03/12/2915 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.

03/12/2915 Copyright Savannah Capital Management 14

Measuring systematic risk

To be compensated for risk, the risk has to be special.oUnsystematic risk is not special.oSystematic risk is special.

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

systematic risk than average.oAssets with Betas smaller than 1.0 have less

systematic risk than average.

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

03/12/2915 Copyright Savannah Capital Management 15

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

03/12/2915 Copyright Savannah Capital Management 16

Portfolio betasIn 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.

03/12/2915 Copyright Savannah Capital Management 17

Portfolio betaBeta 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?

03/12/2915 Copyright Savannah Capital Management 18

Portfolio beta

03/12/2915 Copyright Savannah Capital Management 19

Beta and risk premiumConsider a portfolio made up of asset A and a risk-free

asset. oFor asset A, E(RA) = 16% and A = 1.6

oThe 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%.

03/12/2915 Copyright Savannah Capital Management 20

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

03/12/2915 Copyright Savannah Capital Management 21

Beta and risk premium

03/12/2915 Copyright Savannah Capital Management 22

Beta and risk premium

03/12/2915 Copyright Savannah Capital Management 23

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.

03/12/2915 Copyright Savannah Capital Management 24

The basic argumentRecall 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?oAsset A has a higher expected returnoAsset B has a lower systematic risk measure

03/12/2915 Copyright Savannah Capital Management 25

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.

03/12/2915 Copyright Savannah Capital Management 26

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

03/12/2915 Copyright Savannah Capital Management 27

The basic argument

03/12/2915 Copyright Savannah Capital Management 28

Portfolio Expected Returns and Betas for both Assets

03/12/2915 Copyright Savannah Capital Management 29

Fundamental resultThe 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.

03/12/2915 Copyright Savannah Capital Management 30

Fundamental result

03/12/2915 Copyright Savannah Capital Management 31

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

Fundamental result

03/12/2915 Copyright Savannah Capital Management 32

Security market line

03/12/2915 Copyright Savannah Capital Management 33

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

03/12/2915 Copyright Savannah Capital Management 34

Therefore:For any asset “ ii” 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

03/12/2915 Copyright Savannah Capital Management 35

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

03/12/2915 Copyright Savannah Capital Management 36

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

Security market line

03/12/2915 Copyright Savannah Capital Management 37

Risk return summary

03/12/2915 Copyright Savannah Capital Management 38

Risk return summary

03/12/2915 Copyright Savannah Capital Management 39

Risk return summary

Assume the following:

Risk free rate Rf is 5%

Expected return E(Rm) of the market is 12%Security beta is 1.2E(R) = Rf + [E(Rm) – Rf] x β

= .05 + (.12 - .05) x 1.2

= .134 or 13.4%

03/12/2915 Copyright Savannah Capital Management 40

Decomposition of total returns

03/12/2915 Copyright Savannah Capital Management 41

Unexpected returns

03/12/2915 Copyright Savannah Capital Management 42

Calculating beta

03/12/2915 Copyright Savannah Capital Management 43

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.

03/12/2915 Copyright Savannah Capital Management 44

CAPM – hotly debatedThe CAPM has a stunning implication:

o What you earn on your portfolio depends only on the level of systematic risk that you bear

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

The above bullet point is a hotly debated question

03/12/2915 Copyright Savannah Capital Management 45

Portfolio statistics03/12/2915 Copyright Savannah Capital Management 46

Kellogg and Exxon03/12/2915 Copyright Savannah Capital Management 47

Portfolio returns03/12/2915 Copyright Savannah Capital Management 48

Portfolio returns cont.03/12/2915 Copyright Savannah Capital Management 49