1. Portfolio Analysis and Theory

2. Portfolio Analysis

3. Definitions
A portfolio is the collection of securities an investor holds
A portfolio weight is the proportion of total wealth allocated to a given security

4. Risk and Return for a Portfolio
The expected portfolio return is the weighted average of the expected returns on component securities
The risk of a portfolio is measured by the standard deviation of return

5. Diversification
Portfolio standard deviation depends upon the correlation of the returns of component stocks
If stocks are not perfectly correlated, the portfolio standard deviation is less than the sum of the component standard deviations
Therefore, diversification reduces risk

6. Systematic and Unsystematic Risk
The risk of a portfolio can be divided into systematic and unsystematic risk
Systematic risk can be explained by factors that are common to all securities
Unsystematic risk can be explained by factors that are unique to a given security
Systematic means part of the system

7. Diversification and Risk
Unsystematic risk can be reduced through diversification
Systematic risk cannot be reduced through diversification
Systematic risk is measured by Beta

8. Beta and the Market Model
Beta is the slope of the regression of the historical stock return on the return of a market index, like the S&P 500, containing a large number of stocks
Unsystematic risk is the variation in the stock’s return that cannot be explained by the variation in the market index

9. Market Model (continued)
The systematic risk of a portfolio is the weighted sum of the systematic risk of each component
You cannot reduce systematic risk through diversification
You can only obtain low systematic risk by choosing securities with low systematic risk for your portfolio

10. Systematic Risk
For very large portfolios unsystematic risk can be almost eliminated
In this situation the risk each security contributes to the portfolio is approximately equal to its systematic risk or Beta
Therefore, the relevant risk for an individual security held within a well-diversified portfolio is its Beta
Remember, that for a portfolio the relevant risk is the standard deviation

11. Example
Suppose you put all your wealth in a General Motors stock. Then the relevant risk is the standard deviation because your portfolio consists of a single security
On the other hand, suppose your holdings of General Motors is a small fraction of a large diversified portfolio. Then the relevant risk is the Beta

12. Portfolio Theory

13. Risk Aversion
Risk averse investors require compensation, in the form of extra return, for assuming financial risk
The risk-free asset has zero risk and is usually assumed to be the one-year U. S. treasury bill
A risk averse investor will hold a risky portfolio only if its expected return is greater than the risk-free rate

14. Risk Aversion (continued)
Investors are only compensated for bearing systematic risk
Investors are not compensated for bearing unsystematic risk because it can be eliminated by diversification

15. Example
Suppose investors A and B choose portfolios by throwing darts at the Wall Street Journal. Assume that the average return and average standard deviation of stock in the paper is 10% and 14%, respectively. If investor A throws one dart, then his expected return and risk will be 10% and 14%. If investor B throws ten darts, her expected return will still be 10% but her portfolio standard deviation will be (probably) less because of the effect of diversification.
Should A be compensated for assuming more risk?

16. Risk-Return Relationship
There should be a positive relationship between expected return and the Beta measure of systematic risk.
There should be no relationship between the expected return and unsystematic risk.
Formal economic model is the Capital Asset Pricing Model (CAPM)

17. The Capital Asset Pricing Model Assumptions
risk aversion
rational behavior
investors choose a portfolio on the basis of expected returns and standard deviation
investors have same expectations about the future expected returns, standard deviations and correlations among stocks
existence of risk-free security
perfect markets: no taxes, transaction costs, or restrictions on short sales

18. The security market line (SML)
SML is the relationship between the expected return on an asset and its Beta measure of systematic risk
Under the CAPM, the relationship is linear

19. Beta
The Beta of the risk-free asset is zero and of course its return is the risk-free rate
The Beta of the market portfolio is one
Any stock or portfolio with a Beta = 1 has the same expected return as the market
Any stock with a Beta = 0 returns the risk-free rate

20. Beta (continued)
A stock with a Beta > 1 has more systematic risk than the market and has an expected return that is greater than the market
A stock with a Beta < 1 has less systematic risk than the market and an expected return less than the market.

21. Beta (continued)
A stock with high systematic risk (Beta > 1) will on average (not always) go up by a greater percentage than the market index when the market goes up.
And of course will on average go down by greater percentage when the market goes down.
This is what systematic risk means.
So if you thought the market were going down, you would buy stocks with low Betas

22. The Price of Risk
If systematic risk is priced, than high beta stocks should have an average return, over the ups and downs in the market, higher than the market index.
The high Beta stock has greater systematic risk because when the market goes down the high Beta stock will go down even more.
However, in theory, when you average over the ups and downs the risk averse investor will earn a higher average return

23. Required Return
An investor demands a positive expected return for two reasons: time value of money and a risk aversion.
The return to compensate for the time value of money is the risk-free rate.
The extra return to compensate a risk averse for bearing risk is called the risk premium.
The required return equals the risk free rate plus the risk premium.

24. Security Market Line
The market risk premium (the premium on the market index) by definition equals the expected market return minus the risk-free rate
Under the CAPM, the risk premium on any security equals the Beta multiplied by market risk premium

25. Security Market Line (continued)
The security market line relates the required return on a security to its Beta systematic risk. The required return equals the risk-free rate plus the Beta times the market risk premium

26. The benefits of diversification and portfolio analysis are well established. The conclusions drawn from portfolio theory are tentative and debatable

27. Alternative Explanation
A relatively small number of stocks have high performance
Most of the return on a diverisified portfolio can be explained by a small number of high performing stocks in the portfolio
If you fail to diversify, then you run the risk of not holding any high performing stocks
Your portfolio will have below average return

28. Alternative Explanation
A relatively small number of stocks will perform badly
Some will go under
If you fail to diversify, then you might end up with a large fraction of wealth in a failed stock
Your return distribution will have fat tails