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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

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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.

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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

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Expected Returns Calculation

Condition Probability Return

Recession 20% 10% .02

Moderate 30 12 .036

Strong 50 14 .07

Expected Return (12.6%) .126

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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%

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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

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Risks and Returns

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Annual Rates of Return1926 to 2000

Avg Ann Stand RiskSecurity Returns Dev PremSmall Co Stocks 17.3% 33.4% 13.4%Common Stocks 13.0 20.2 9.1L-T-Corp Bonds 6.0 8.7 2.1L-T Govt Bonds 5.7 9.4 1.8Med-term Govt 5.5 5.8 1.6US T-Bills 3.9 3.2 0Inflation 3.2 4.4

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Risk Over Time

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Total Risk in Stock_______________

Systematic Risk

Or Market Risk

Cannot be eliminated by buying different

stocks

Unsystematic Risk or

Company Unique Risk

Eliminated by buying different stocks

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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

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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

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Value of Diversification

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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

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Gap’s and S&P’s Returns

Return S D (σ)

Gap 2.88 % pa 17.04 %

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

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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

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The Gap’s 1.29 Beta

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High and Low Beta Portfolios

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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

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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

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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.

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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

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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)

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More Formulas

• MER = SER - RF + (B * RF)

B

• RF = SER - (B * MER)

(1 - B )

• B = SER - RF = SER

MER - RF MER

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FinCoach – What is SER?

• Beta = 1.374, MRP = 9.09, RF = 5.08

• What is MER? MRP + RF = 14.17

SER = RF + (Beta * MRP)5.08 + (1.374 * 9.09) = 17.56

SER = RF + Beta (MER – RF)5.08 + 1.374(14.17 – 5.08) = 17.56

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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 RF Required 0 5 5 + 0 (12-5) = 5

1 5 5 + 1 (12-5) = 12 2 5 5 + 2 (12 –5) = 19

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Security Market Line 6-9

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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