Chapter 6

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 Probability Return
• Recession 20 10 .02
• Moderate 30 12 .036
• Strong 50 14 .07
• Expected Return (12.6) .126

5
Standard Deviation (s)

• 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 As return 15 s 9
• Returns range 6 (15 9) to 24
• Stock Bs return 15 s 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

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Risks and Returns
8
Annual Rates of Return1926 to 2000

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

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Risk Over Time
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Company-Unique Risk

• Pfizer new product, unexpected sales and profit
  increase. Stock up 2 one day
• Apples 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 portfolios 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
Gaps and SPs Returns

• Return S D (s)
• Gap 2.88 pa 17.04
• SP -.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 (ß)

• Characteristic line average movement in a stock
  compared to whole market
• Slope of the line called beta relation between
  stocks return and markets returns
• Gaps 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 firms market
  risk after the portfolio has been diversified

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The Gaps 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
• Portfolios 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 Bs returns are the same but A has more
  risk (indicated by SD)
• Cs returns are higher than As 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 stocks systematic risk
• Need to separate out stocks premium from the
  whole markets premium
• Markets risk premium for investing in a market
  portfolio rather than riskless asset
• Stocks risk premium (beta) how much more or
  less risky than whole market.

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Schroederspeak

• Beta Beta ß
• SER Stocks Expected Return
• RF Risk Free Rate
• MRP Markets Risk Premium
• MER Markets Expected Return
• MER RF MRP

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Stocks Expected Rate of Return

• Minimum rate needed to get investor to purchase.
  Called the stocks 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 stocks 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 investments 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