Week 8: Portfolio Theory

1. Week 8: Portfolio Theory April 7th, 2011

2. What is Return? Risk? • Return = • Also seen as • Risk: Future uncertainty or volatility Ending Value – Beginning Value Beginning Value Ending Value Beginning Value -1

3. Expected Return • E[Ra] = (.2)(.30)+(.7)(.18)+(.10)(-.2) • E[Ra] = 16.6%

4. Variance • Variance: Spread of possible outcomes for an asset • Va2= .2(.3-.166)2+.7(.18-.166) 2+.1(-.2-.166)2 • Va2= .017124 • Standard deviation is square root of variance (Va)=.1309

5. Expected Return of Portfolio • Weight of stocks is equal in portfolio • Weight must always be 1 • E[Rp] = (.5)(16.6%)+(.5)(8.3%) = 12.45%

6. Portfolio Variance • Weight of A is 80%, weight of B is 20% • First find covariance of two stocks (correlation coefficient assumed to be .5) • VA,B = (.5)(.05)(.11) = .00275 • Vp2= (.8)2(.0025)+(.2)2(.0121)+2(.8)(.2)(.00275) • Vp2= .002964 • Vp= .0544

7. Portfolio with Various Correlations • For line A, stocks have correlation of 1 • Line D has correlation of -1 • Point Z has zero risk

8. Diversification • As one increases the number of stocks, standard deviation usually decreases • This decreases the risk of the portfolio

9. Portfolio Construction • Efficient Frontier: minimizes risk for given return or maximizes return for given risk

10. Sharpe Ratio • The Sharpe ratio measures the risk premium per unit of risk for an investment or portfolio • When constructing a portfolio, investors look to maximize the Sharpe ratio • Get most bang for their buck • Calculated as

11. Capital Market Line • Every investor should be on CML • Combination of risk-free rate and market portfolio

12. Risk • Unsystematic risk: variability in stock price due to factors only relating to an individual company • Systematic risk: basic variability • Some stocks more sensitive to systematic risk • Measured by beta • Systematic risk can’t be diversified away, while unsystematic risk can

13. Capital Asset Pricing Model • Investors should be compensated for taking on more risk with higher expected returns • Unsystematic risk can essentially be eliminated • Higher returns should only come from systematic risk • CAPM says returns will be related to beta

14. CAPM • Calculating return • E[Ra] = Rf+ βa(E[Rm] – Rf) • Market premium times beta is return above risk free rate

15. Security Market Line • Expected returns against beta • Uses CAPM model to create line • Above line is considered good buy • Generates alpha

16. Arbitrage Pricing Theory • Similar to CAPM, but uses more factors • Each RP term is the risk premium associated with that factor • Factors could be commodity prices, interest rates, foreign exchange, etc.

17. Fama-French Results • Two characteristics best describe variations in returns • Firm size and Book-To-Market ratio • The smaller the firm, the greater the return • Book-To-Market is book value over market value • The higher the ratio, the larger the returns

18. Problems with MPT • Asset returns are not normally distributed variables • Correlations between assets aren’t constant • Investors aren’t always rational and may not have access to information at the same time • Investors can influence stock price with big purchases

19. What to be aware of • Utilize your strengths • Be aware of herding toward a group of assets • Don’t just accept popular ideas taken for granted • Take advantage of constraints of other investors