2. Date 3M Close ($) S&P Close HPR 3M S&P HPR 4-Feb-11 88.29 1,310.87
0.39%
0.29%
3-Feb-11
87.95
1,307.10
0.23%
0.24%
2-Feb-11
87.75
1,304.03
-0.05%
-0.27%
1-Feb-11
87.79
1,307.59

3. Year
1926
2013
Avg. Annual Growth Rate
Asset
Inflation $1 $
3.0%
Treasury Bills $
3.6%
LT Govt. Bonds $
5.5%
Large Cap Stock Index
$ ,673
10.2%
Small Cap Stock Index
$ 17,474
11.9%

4. Probability distributions
A listing of all possible outcomes, and the probability of each occurrence.
Can be shown graphically.
Expected Rate of Return
Rate of
Return (%)
100 15
-70

5. Realized rate of return
Using historical data to measure return and risk
Realized rate of return
Estimated standard deviation: S

6. Expected rate of return
pi is the probability that outcome ri occurs

7. Risk: Variance and standard deviation

8. Calculating portfolio expected return
wi = proportion of portfolio invested in asset i.

9. Portfolio risk: how diversification reduces risk
Percentage returns
State of the world
Probability
Umbrella Mfg. (x)
Beach Resort (y)
Rain
0.5
50%
-25%
Sun

10. Covariance and correlation
NB: Depending on the sample size and whether you are treating the data as a population versus a sample, you may see the covariance with (n-1) in the denominator instead of n.

11. Some useful formulas

12. Portfolio risk (two assets: X and Y): σp

13. General comments about risk
Most stocks are positively correlated with the market (ρi,m  0.65).
σ  35% for an average stock.
Combining stocks in a portfolio generally lowers risk.

14. Illustrating diversification effects of a stock portfolio
# Stocks in Portfolio
,000+
Company-Specific Risk
Market Risk 20
Stand-Alone Risk, sp
sp (%) 35

15. CAPM – Capital Asset Pricing Model The relevant risk to measure for an individual stock is its contribution to the risk of a well-diversified portfolio

16. Two types of risk inherent in a security: Total risk = market risk + diversifiable risk
DIVERSIFIABLE RISK (UNSYSTEMATIC RISK)
Risk unique to company events.
MARKET RISK (SYSTEMATIC RISK)
Risk due to economic system as a whole.
Also known as non-diversifiable risk.
One Measure of a stock’s MARKET risk is beta (βj).

17. How to measure the systematic risk for security i ?
Beta (β) is the measure of a security’s systematic risk – estimated from a simple linear regression model of the stock’s return against the market’s return.

18. Characteristic line

19. βj = (change in stock’s return) = Δrj (change in market’s return) Δrm
βj = 1 stock is as risky as market
βj > 1 stock is more risky than market
βj < 1 stock is less risky than market

20. Portfolio beta

21. return
β >1
β =1
β <1
time

22. CAPM – Capital Asset Pricing Model
ri = required return on stock i rRF = risk free interest rate rM = market return ri = rRF + βi (rM – rRF)

23. Security market line (SML)
Required rate
of return Rj Rm Rf
β=1
β=1.5
Risk (β)

24. If a stock with a beta of 1.5 yielded an expected return below the SML, is the stock under or over valued?
Required rate
of return Rj Rm Rf
β=1
β=1.5
Risk (β)