1. Presented by: Lauren Rudd
Portfolio Management
Slide Set 1
Presented by: Lauren Rudd
Tel: office
March 12, 2015

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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.

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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.

4. Mathematical Concepts
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Mathematical Concepts
Mean
Variance
Standard Deviation
Covariance

5. Events that impact the firm
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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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Return
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.

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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

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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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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.

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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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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.

15. Measuring systematic risk
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Measuring systematic risk
To be compensated for risk, the risk has to be special.
Unsystematic risk is not special.
Systematic risk is special.
The Beta coefficient () measures the relative systematic risk of an asset.
Assets with Betas larger than 1.0 have more systematic risk than average.
Assets 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.

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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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Beta and risk premium
Consider a portfolio made up of asset A and a risk-free asset.
For asset A, E(RA) = 16% and A = 1.6
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
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
Notice that all the combinations of portfolio expected returns and betas fall on a straight line.
Slope (Rise over Run):

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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?
Asset A has a higher expected return
Asset B has a lower systematic risk measure

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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
Portfolio
Expected 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

29. Portfolio Expected Returns and Betas for both Assets
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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 market
Investors will be attracted to asset A (and buy A shares)
Investors will shy away from asset B (and sell B shares)
This buying and selling will make
The price of A shares increase
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
This price adjustment continues until the two assets plot on exactly the same line.

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Fundamental result

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Security market line
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:

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Security market line
The term E(RM) – Rf is often called the market risk premium because it is the risk premium on a market portfolio.
Therefore:
For any asset “ ii” in the market:

35. Capital asset pricing model
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Capital asset pricing model
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.

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

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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
= ( ) x 1.2
= .134 or 13.4%

41. Decomposition of total returns
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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:
What you earn on your portfolio depends only on the level of systematic risk that you bear
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

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Portfolio statistics

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Kellogg and Exxon

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Portfolio returns

49. Portfolio returns cont.
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Portfolio returns cont.
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