Date 3M Close ($) S&P Close HPR 3M S&P HPR 4-Feb ,310.87

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Presentation transcript:

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

Year 1926 2013 Avg. Annual Growth Rate Asset Inflation $1 $ 13 3.0% Treasury Bills $ 21 3.6% LT Govt. Bonds $ 109 5.5% Large Cap Stock Index $ 4,673 10.2% Small Cap Stock Index $ 17,474 11.9%

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

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

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

Risk: Variance and standard deviation

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

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

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.

Some useful formulas

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

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.

Illustrating diversification effects of a stock portfolio # Stocks in Portfolio 10 20 30 40 2,000+ Company-Specific Risk Market Risk 20 Stand-Alone Risk, sp sp (%) 35

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

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).

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.

Characteristic line

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

Portfolio beta

return β >1 β =1 β <1 time

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

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

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)