4 - 1 CHAPTER 4 Risk and Return: The Basics Basic return concepts Basic risk concepts Stand-alone risk Portfolio (market) risk Risk and return: CAPM/SML

4 - 2 Portfolio Risk and Return An asset held as part of a portfolio is less risky than the same asset held in isolation Most financial assets are actually held as parts of portfolios. Banks, pension funds, insurance companies, mutual funds, and other financial institutions are required by law to hold diversified portfolios.

4 - 3 Portfolio Risk and Return Assume a two-stock portfolio with $50,000 in Alta Inds. and $50,000 in Repo Men. Calculate r p and  p. ^

4 - 4 EconomyProb.AltaRepo Recession % 28.0% Below avg Average Above avg Boom r Alta 17.4%. r Repo 1.7 Assume a two-stock portfolio with in Alta Inds. and in Repo Men. ^^

4 - 5 Portfolio Return, r p r P is a weighted average : expected return on a portfolio, is simply the weighted average of the expected returns on the individual assets in the portfolio, with the weights being the fraction of the total portfolio invested in each asset: r p = 0.5(17.4%) + 0.5(1.7%) = 9.6%. r p is between r Alta and r Repo. ^ ^ ^ ^ ^^ ^^ r p =   w i r i  n i = 1

4 - 6 Alternative Method r p = (3.0%) (6.4%) (10.0%) (12.5%) (15.0%)0.10 = 9.6%. ^ Estimated Return (More...) EconomyProb.AltaRepoPort. Recession % 28.0% 3.0% Below avg Average Above avg Boom

4 - 7 Company Expected Return, rˆ Microsoft 12% General Electric 11.5% Pfizer 10% Coca-Cola 9.5% 1- If we formed a $100,000 portfolio, investing $25,000 in each stock, the expected portfolio return = ???? 2- If we formed a $100,000 portfolio, investing $40,000 in Microsoft and $40,000 in General Electric and $10,000 in each of Pfizer and Coca-Cola, the expected portfolio return = ???? Portfolio Return, r p ^

r p = 0.25 (12%) (11.5%) (10%) (9.5%) = 10.75%. ^ 2- r p = 0.4 (12%) + 0.4(11.5%) (10%) (9.5%) = %. ^

4 - 9 Portfolio Risk As we just saw, the expected return on a portfolio is simply the weighted average of the expected returns on the individual assets in the portfolio. risk of a portfolio, σ p, is generally not the weighted average of the standard deviations of the individual assets in the portfolio

What is the standard deviation of returns for Portfolio?

 p = (( ) ( ) ( ) ( ) ( ) ) 1/2 = 3.3%.  p is much lower than: either stock (20% and 13.4%). average of Alta and Repo (16.7%). The portfolio provides average return but much lower risk.

Two-Stock Portfolios Two stocks can be combined to form a riskless portfolio if  = Risk is not reduced at all if the two stocks have  = In general, stocks have   0.65, so risk is lowered but not eliminated. Investors typically hold many stocks. What happens when  = 0?

Portfolio MW

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Portfolio MW

What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added?  p would decrease because the added stocks would not be perfectly correlated, but r p would remain relatively constant. ^

Large 0 15 Prob. 2 1  1  35% ;  Large  20%. Return

Type of Risk Systematic Risk No diversifiable Risk = Market Risk war, inflation, recessions, and high interest rates. Since most stocks are negatively affected by these factors, market risk cannot be eliminated by diversification.

أنواع المخاطر Unsystematic Risk diversifiable Risk Caused by such random events as lawsuits, strikes, successful and unsuccessful marketing programs, winning or losing a major contract, and other events that are unique to a particular firm.

# Stocks in Portfolio ,000+ Company Specific (Diversifiable) Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35

Stand-alone Market Diversifiable Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification. risk risk risk = +.

Conclusions As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.  p falls very slowly after about 40 stocks are included. The lower limit for  p is about 20% =  M. By forming well-diversified portfolios, investors can eliminate about half the riskiness of owning a single stock.

No. Rational investors will minimize risk by holding portfolios. They bear only market risk, so prices and returns reflect this lower risk. The one-stock investor bears higher (stand-alone) risk, so the return is less than that required by the risk. Can an investor holding one stock earn a return commensurate with its risk?