1. Class Business Debate #1 Upcoming Groupwork

2. Hedge Funds A private investment pool, open to wealthy or institutional investors. – Minimum investment at least $1million (by law) Not registered as mutual funds and not subject to SEC regulation. Pursues more speculative policies. Name comes from the fact that hedge funds want to create market-neutral strategies by going long in some assets and going short in related assets.

3. Hedge Funds vs. Mutual Funds Mutual FundsHedge Funds Investment methodsBuy publicly traded securities. Little use of leverage or short-sales. Buy also non-public securities, currencies and commodities. Wide use of leverage and short-sales. DiversificationHold broad mix of assets.Holdings are often concentrated. FeesRelatively low fees that do not depend on performance Relatively high fees that depend on performance. Share buybacksUsually daily after close.Often limited to a few times a year. RegulationHeavy RegulationLight Regulation Initial investmentsRelatively lowVery high investments necessary.

4. Other Investment Companies Real estate investment trusts (REITS) – closed-end fund that holds real estate assets – some hold properties directly - usually have 70% debt some hold mortgages on properties – exempt from taxes as long as 95% of taxable income is distributed

5. Chapter 17: Investors and the Investment Process Specify objectives Identify constraints Formulate an investment policy Monitor performance Reevaluate and modify portfolio as determined from monitoring

6. Portfolios Suppose we have (1-w) of our wealth in a risk-free asset and w of our wealth in some portfolio of stocks. Suppose we know the rate of return on the risk-free asset, r f (e.g., 3%) We expect the return on S&P 500 to be E[r S ] (e.g., 8%)

7. Portfolios Intuitively: – The more we invest in the risk-free asset, and the less in the stock portfolio, the lower will be our expected return, and the lower the variance (or the risk) of the portfolio –... and vice versa – If portfolio standard deviation = risk expected return = reward what is the reward-risk tradeoff?

8. Portfolio of Risk-Free Asset and One Risky Asset Return: Expected Return: Variance: Standard Deviation:

9. Capital Allocation Line: Note: since it follows that We also know Substituting for w, gives the Capital Allocation Line (CAL):

10. Capital Allocation Line This is just the equation for a line! y=b+mx where y= E(r p ) b= r f m=[E(r S )-r f ]/  s x=  p

11. Capital Allocation Line

12. The Capital Allocation Line shows the risk-return combinations available by changing the proportion invested in a risk-free asset and a risky asset. The slope of the CAL is the reward-to-variability ratio The choice is determined by the risk aversion of investors. – Risk-averse investors will invest more in the risk-free asset. – Risk-tolerant investors will invest more in the risky asset.

13. Example Expected return on risky portfolio: 12% Stdev of risky portfolio is.32 Risk free rate is 7% What is formula for CAL line?

14. Passive Investing Select a broad diversified portfolio Invest a fraction of your wealth in the portfolio according to your level of risk aversion, and the rest in a risk free asset. Benefits: – No need to spend time researching stocks – No need to pay someone else to research Performance vs. Active strategy?

15. Another CAL Example E[r s ]=8%  s =.12 r f =4% E[r p ]=wE[r S ]+(1-w)r f  p =w  s RiskyRisk-Free A: 0% 100% B: 100% 0% C: 50% 50% D: 150% -50% 4% E[r p ] pp A 8%.12 B.06 6% C.18 10% D

16. CAL Example Continued Suppose you want expected return of 9%, what are the weights? w=1.25 E[r p ]=w(.08)+(1-w)(.04) =.09  p =1.25(.12)=.15

17. Risk We don’t like uncertainty (variance) We don’t like assets that “lose” when bad things happen We like assets that “win” when bad things happen: insurance To incorporate these ideas into a concrete theory, we need to understand covariance.

18. Covariance Covariance is a measure of “how much two variables move with each other”. When one variable is abnormally high, is the other variable abnormally high or low? It is measured as the “expected product of the deviations from the mean.” Cov[r 1,r 2 ] =E [ (r 1 -E[r 1 ]) (r 2 -E[r 2 ]) ]

19. Covariance Cov[r 1,r 2 ] =E[(r 1 -E[r 1 ]) (r 2 -E[r 2 ])] Positive covariance:

20. Covariance Cov[r 1,r 2 ] =E[(r 1 -E[r 1 ]) (r 2 -E[r 2 ])] Negative covariance:

21. Covariance: From Probability model Cov[r 1,r 2 ] =E[(r 1 -E[r 1 ]) (r 2 -E[r 2 ])] Steps: 1) Find expected return for each asset 2) Find deviations from mean for each asset in each state. 3) Take product of deviations 4) Find expected product of deviations Probabilityr1r1 r2r2 State 10.8010%5% State 20.20-5%0%

22. Covariance: Probability Model Step 1: Find expected return for each asset E[r 1 ]=.80(.10) +.20(-.05) = 0.07 E[r 2 ]=.80(.05) +.20(0.0) =0.04 Step 2: Find Deviations Probabilityr1r1 r2r2 State 10.8010%5% State 20.20-5%0% Dev1Dev2 State 1.10-.07=.03.05-.04=.01 State 2-0.05-0.07= -.120-.04= -.04

23. Covariance: Probability Model Step 3: Find product of deviations in each state – Product 1 =.03(.01)=.0003 – Product 2 = (-.12)(-.04)=.0048 Step 4: Find expected product of deviations – Covariance =.8(.0003) +.2(.0048)=.0012

24. Covariance: Probability Model Even if we don’t know correct probability model, we can still estimate the covariance from past data. Covariance is average product of deviations. Average