1 Chapter 6 – Risk and Return Key Sections: Expected return Measure riskiness of individual assets Risk of a portfolio, benefit of diversification Interaction of risk and return over time Mutual Funds supplement

2 What is Risk? Uncertain outcome – good or bad. In Finance, the potential variation in future cash flows. Usually measured by standard deviation, a statistics concept.

3 Expected Returns Come from cash flows- income + cap gains Weighted average of all possible returns; weight based on probability of occurrence. Risk – potential variation around expected return measured by standard deviation; wider the range, more risk. Selection determined by attitude to risk –Right for you, maybe not right for me

4 Expected Returns Calculation Condition ProbabilityReturn Recession20%10%.02 Moderate Strong Expected Return (12.6%).126

5 Standard Deviation (σ) Dispersion of observations around the average –The lower the SD, the lower the risk Compare 90 day T-bill with publishing co. : –T-bill – no risk – 6% “guaranteed” –Stock A’s return = 15%; σ = 9% –Returns range 6% (15 – 9) to 24% –Stock B’s return = 15%; σ = 7%; Range 8 to 22%

6 Risk and Diversification Diversification – holding many securities Company-unique risk – Unsystematic Risk –From factors unique to firm – UAW strikes GM –Can be diversified away with other stocks Market risk – called systematic risk –Result from factors affecting all companies (the economy, taxes) –Cannot be diversified away

7 Risks and Returns

8 Annual Rates of Return 1926 to 2000 Avg Ann StandRisk SecurityReturns Dev Prem Small Co Stocks 17.3% 33.4% 13.4% Common Stocks L-T-Corp Bonds L-T Govt Bonds Med-term Govt US T-Bills Inflation

9 Risk Over Time

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11 Company-Unique Risk Pfizer – new product, unexpected sales and profit increase. Stock up 2% one day Apple’s profits fell 61%. Stock down 5% Events unique, investors acted accordingly Other random factors: technological breakthroughs, patents, antitrust, product failure, getting a contract, expropriation, significant earthquake damage

12 Diversifying Risk Declines until there are about 20 stocks –By diversifying, risk can be reduced without sacrificing return Market risk- about 40% of portfolio’s total risk “Market portfolio” has only systematic risk which cannot be diversified away

13 Value of Diversification

14 Holding Period Returns Earned between two points in time Usually expressed as an annual percent HPR = Ending Value minus 1 Beginning Value Above formula is oversimplified – ignores dividends and interest received

15 Gap’s and S&P’s Returns ReturnS D (σ) Gap2.88 % pa17.04 % S&P-.36 % pa 5.10 % Gap did better than the whole market (which had a loss) but its risk was more than three times greater. Also moved in same direction 19 of 24 months

16 Beta (β) Characteristic line – average movement in a stock compared to whole market Slope of the line called beta – relation between stock’s return and market’s returns Gap’s beta is 1.29; on average for every 1.0% change in the market, Gap moves 1.29% Beta, not SD, is a measure of the firm’s market risk after the portfolio has been diversified

17 The Gap’s 1.29 Beta

18 High and Low Beta Portfolios

19 More on Beta Most stocks have betas between.6 and 1.6 Beta of 1.0 has systematic (market) risk of a typical stock in the index –If over 1.0, more risky than market, under 1.0, less risky Portfolio’s beta – average of the individual stocks’ betas weighted by share of portfolio

20 Risk, Return, Diversification Three portfolios: A, B and C. Major points: –A and B’s returns are the same but A has more risk (indicated by SD) –C’s returns are higher than A’s but risk is the same Conclusion: Market rewards diversification; risk lowered without sacrificing returns Asset allocation

22 Capital Asset Pricing Model Equation relating required/expected return on a stock to the risk-free rate plus a premium for the stock’s systematic risk Need to separate out stock’s premium from the whole market’s premium Market’s risk premium for investing in a market portfolio rather than riskless asset Stock’s risk premium (beta) –how much more or less risky than whole market.

23 Schroederspeak Beta = Beta = ß SER=Stock’s Expected Return RF=Risk Free Rate MRP=Market’s Risk Premium MER= Market’s Expected Return MER – RF=MRP

24 Stock’s Expected Rate of Return Minimum rate needed to get investor to purchase. Called the stock’s expected return Two factors affect: Risk-free rate plus risk premium for riskiness of asset In Schroederspeak: SER = RF + Beta * (MER – RF) or SER = RF +(Beta * MRP)

25 More Formulas MER =SER - RF + (B * RF) B RF=SER - (B * MER) (1 - B ) B=SER - RF=SER MER - RF MER

26 FinCoach – What is SER? Beta = 1.374, MRP = 9.09, RF = 5.08 What is MER? MRP + RF = SER = RF + (Beta * MRP) (1.374 * 9.09)=17.56 SER = RF + Beta (MER – RF) (14.17 – 5.08) =17.56

27 Security Market Line Graphic representation of CAPM showing required rate given the stock’s systematic risk (beta). Risk-free = 5.0, Market Expected Rate =12 Beta RFRequired (12-5)= (12-5)= (12 –5)=19

28 Security Market Line 6-9

29 Risk Summary Beta (slope of the characteristic line) relationship between an investment’s return and the return of the whole market. Security Market Line (SML) return line reflects the attitude of investors regarding the minimum acceptable level of return for a given level of systematic risk