Risk & Return

Total return: the total gain or loss experienced on an investment over a given period of time Components of the total return Income stream from the investment Capital gain or loss due to changes in asset prices Total return can be expressed either in dollar terms or in percentage terms. 2

Variance The greater the variance The greater the dispersion of expected returns from the mean The greater the uncertainty (risk) 3

Coefficient of Variation A standardized measure of dispersion about the expected value, that shows the risk per unit of return. 4

Standard Deviation (σ) Measures total, or stand-alone, risk. It is a measure of the variability of returns The larger σ i is, the lower the probability that actual returns will be closer to expected returns. Larger σ i is associated with a wider probability distribution of returns. 5

Standard Deviation (σ) 6

Which is Riskier? Investment AInvestment B Expected Return7%12% Standard Deviation (σ) 5%7% 7

Average Standard Return Deviation Small-company stocks17.5%33.1% Large-company stocks L-T corporate bonds L-T government bonds U.S. Treasury bills Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2014 Yearbook (Chicago: Ibbotson Associates, 2014) 8

Average Return and St. Dev. for Individual Securities,

Investors Attitude Towards Risk Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium – the difference between the return on a risky asset and a riskless asset, which serves as compensation for investors to hold riskier securities. 10

Diversification Most individual stock prices show higher volatility than the price volatility of portfolio of all common stocks. How can the standard deviation for individual stocks be higher than the standard deviation of the portfolio? Diversification: investing in many different assets reduces the volatility of the portfolio. The ups and downs of individual stocks partially cancel each other out. 11

The Impact of Additional Assets on Portfolio Risk 12

Most stocks are positively correlated. –Average correlation between two stocks is As long as the stocks in the portfolio are not perfectly correlated (i.e.,  <1), the standard deviation of the portfolio will be less than the weighted average of the standard deviation of the stocks in the portfolio. When we add more securities in the portfolio, we can lower the risk of the portfolio even further. –This is because the added securities would not be perfectly correlated with existing securities in the portfolio. Q: Can we eliminate the portfolio risk completely by adding more assets/securities into our portfolio? 13

Stand-alone risk consists of: –Diversifiable risk Company or industry specific Also called unsystematic, unique, or idiosyncratic risk –Non-diversifiable risk Related to market as a whole Also called systematic, portfolio, or market risk It shows the degree to which a stock moves systematically with other stocks. Total risk of security = unsystematic risk + portfolio risk We can eliminate unsystematic risk by adding more securities into the portfolio. 14

e.g. Insurance Consider the variance of the portfolio: It seems that selling more policies causes risk to fall Flaw is similar to the idea that long-term stock investment is less risky 15

Returns distribution for two perfectly negatively correlated stocks (ρ = -1.0) Stock W 0 Stock M Portfolio WM 16

Returns distribution for two perfectly positively correlated stocks (ρ = 1.0) Stock X Stock Y Portfolio XY

Creating a portfolio: Beginning with one stock and adding randomly selected stocks to portfolio σ p decreases as stocks added, because they would not be perfectly correlated with the existing portfolio. Expected return of the portfolio would remain relatively constant. Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, σ p tends to converge to  20%. 18

Effect of diversification on a stock portfolio # Stocks in Portfolio ,000+ Diversifiable Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35 19

Beta (β)  Measures a stock’s market risk, and shows a stock’s volatility relative to the market.  Indicates how risky a stock is if the stock is held in a well-diversified portfolio.  If β = 1.0, the security is just as risky as the average stock.  If β > 1.0, the security is riskier than average.  If β < 1.0, the security is less risky than average.  Most stocks have betas in the range of 0.5 to

3 Factor Model (Fama & French) Portfolio return is a result of asset allocation: Small Cap Value (Low Price to Book Ratio) Beta (70% of most portfolio return is β 21

Failure to Diversify If an investor chooses to hold a one-stock portfolio (doesn’t diversify), would the investor be compensated for the additional risk? o NO! o Stand-alone risk is not important to a well- diversified investor. o Rational, risk-averse investors are concerned with σ p, which is based upon market risk. o There can be only one price (the market return) for a given security. o No compensation should be earned for holding unnecessary, diversifiable risk. 22