Introductory Investment Analysis Part II Course Leader: Lauren Rudd January 12, 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. 01/12/2011Copyright Savannah Capital Management2

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. 01/12/2011Copyright Savannah Capital Management3

Return 01/12/2011Copyright Savannah Capital Management4 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 01/12/2011Copyright Savannah Capital Management5

Components of return R – E(R) = U = surprise portion = Systematic portion + Unsystematic portion = m +  = Systematic portion + Unsystematic portion = m + Therefore: R – E(R) = m +   = unsystematic portion of total surprise m = systematic part of risk 01/12/2011Copyright Savannah Capital Management6

Events that the firm 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 01/12/2011Copyright Savannah Capital Management7

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. 01/12/2011Copyright Savannah Capital Management8

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 01/12/2011Copyright Savannah Capital Management9

Risk  is risk that influences a large number of assets. Also called.  Systematic risk is risk that influences a large number of assets. Also called market risk.  is risk that influences a single company or a small group of companies. Also called  Unsystematic risk is risk that influences a single company or a small group of companies. Also called unique risk or firm-specific risk. 01/12/2011Copyright Savannah Capital Management10

Total risk Total risk = Systematic risk + Unsystematic risk 01/12/2011Copyright Savannah Capital Management11

Two types of risk  risk.  Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets has almost no unsystematic risk.  risk is also called risk.  Unsystematic risk is also called diversifiable risk.  risk risk.  Systematic risk is also called non-diversifiable risk. 01/12/2011Copyright Savannah Capital Management12

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. 01/12/2011Copyright Savannah Capital Management13

Systematic risk So, no matter how much total risk an asset has: portion is relevant in determining the expected return (and the risk premium) on that asset. Only the systematic portion is relevant in determining the expected return (and the risk premium) on that asset. 01/12/2011Copyright Savannah Capital Management14

Measuring systematic risk  To be compensated for risk, the risk has to be special. o Unsystematic risk is not special. o o Systematic risk is special.  The Beta coefficient (  ) measures the relative systematic risk of an asset. o o Assets with Betas larger than 1.0 have more systematic risk than average. o 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. 01/12/2011Copyright Savannah Capital Management15

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 01/12/2011Copyright Savannah Capital Management16

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. 01/12/2011Copyright Savannah Capital Management17

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? 01/12/2011Copyright Savannah Capital Management18

Portfolio beta 01/12/2011Copyright Savannah Capital Management19

Beta and risk premium  Consider a portfolio made up of asset A and a risk-free asset. o For asset A, E(R A ) = 16% and  A = 1.6 o The risk-free rate R f = 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%. 01/12/2011Copyright Savannah Capital Management20

Beta and risk premium % of Portfolio in Asset A Portfolio Expected Return Portfolio Beta 0% /12/2011Copyright Savannah Capital Management21

Beta and risk premium 01/12/2011Copyright Savannah Capital Management22

Beta and risk premium 01/12/2011Copyright Savannah Capital Management23 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. 01/12/2011Copyright Savannah Capital Management24

The basic argument  Recall that for asset A: E(R A ) = 16% and  A = 1.6  Suppose there is a second asset, asset B.  For asset B: E(R B ) = 12% and  A = 1.2  Which investment is better, asset A or asset B? o Asset A has a higher expected return o Asset B has a lower systematic risk measure 01/12/2011Copyright Savannah Capital Management25

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. 01/12/2011Copyright Savannah Capital Management26

The basic argument % of Portfolio in Asset B Portfolio Expected ReturnPortfolio Beta 0% /12/2011Copyright Savannah Capital Management27

The basic argument 01/12/2011Copyright Savannah Capital Management28

Portfolio Expected Returns and Betas for both Assets 01/12/2011Copyright Savannah Capital Management29

Fundamental result  The situation for assets A and B cannot persist in a well- organized, active market o 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 increase o The price of B shares decrease  This price adjustment continues until the two assets plot on exactly the same line. 01/12/2011Copyright Savannah Capital Management30

Fundamental result 01/12/2011Copyright Savannah Capital Management31 This price adjustment continues until the two assets plot on exactly the same line.

Fundamental result 01/12/2011Copyright Savannah Capital Management32

Security market line 01/12/2011Copyright Savannah Capital Management33 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 01/12/2011Copyright Savannah Capital Management34 Therefore: For any asset “i” in the market: The term E(R M ) – R f is often called the market risk premium because it is the risk premium on a market portfolio.

Capital asset pricing model 01/12/2011Copyright Savannah Capital Management35 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 01/12/2011Copyright Savannah Capital Management36 The Capital Asset Pricing Model (CAPM) is a theory of risk and return for securities in a competitive capital market.

Security market line 01/12/2011Copyright Savannah Capital Management37

Risk return summary 01/12/2011Copyright Savannah Capital Management38

Risk return summary 01/12/2011Copyright Savannah Capital Management39

Risk return summary Assume the following:   Risk free rate R f is 5%   Expected return E(R m ) of the market is 12%   Security beta is 1.2   E(R) = R f + [E(R m ) – R f ] x β   =.05 + ( ) x 1.2   =.134 or 13.4% 01/12/2011Copyright Savannah Capital Management40

Decomposition of total returns 01/12/2011Copyright Savannah Capital Management41

Unexpected returns 01/12/2011Copyright Savannah Capital Management42

Calculating beta 01/12/2011Copyright Savannah Capital Management43

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. 01/12/2011Copyright Savannah Capital Management44

CAPM – hotly debated  The 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 01/12/2011Copyright Savannah Capital Management45