Risk, Return, and the CAPM

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• Chapter 6
• Risk, Return, and the CAPM

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Measuring Return

• Total return is the sum of _____ plus
  _____.
• A 100 stock grows in value to 110 and pays a 3
  dividend. What is the holding period return?

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• Investors are risk-averse, which means that faced
  with higher risk, investors require a _____
  return.
• When the finance community first attempted to
  measure risk, it turned to the familiar area of
  _____.

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Measuring Stand-Alone Risk

• Consider the investment HT below
• Economy Probability Return
• Recession 0.10 -22
• Below Avg. 0.20 - 2
• Average 0.40 20
• Above Avg. 0.20 35
• Boom 0.10 50

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• What is the expected return on HT?
• What is HTs standard deviation of return?

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• Econ Prob T-bill HT Coll MP
• Rec 0.10 8 -22 28 -13
• BAvg 0.20 8 - 2 15 1
• Avg 0.40 8 20 0 15
• AAvg 0.20 8 35 -10 29
• Boom 0.10 8 50 -20 43

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• The return and stand-alone risk measures for each
  investment are
• Asset ? s
• HT 17.4 20.0
• MP 15.0 15.3
• T-Bills 8.0 0.0
• Coll 1.8 13.4

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Prob.
T-bill
Normal Risk-Return Trade-Off
MP
HT
0
8
15.0
17.4
Rate of Return ()
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• Note that Coll is _____ than T-bills, yet it
  provides a _____ expected return. This violates
  the normal trade-off between _____ and _____.
• The results suggest that s _____ a valid measure
  of investment risk.

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• A major weakness of stand-alone risk measures is
  that they ignore the role of _____ (i.e., _____).

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Risk and Correlation

• The returns of HT and the market portfolio (MP)
  move _____ over time, which indicates _____
  correlation.
• The returns of Coll and the market portfolio (MP)
  move _____ over time, which indicates _____
  correlation.

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• Which type of correlation provides the greater
  diversification benefit (i.e., greater risk
  reduction)?
• Consider combining HT and MP in a 50/50 portfolio.

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• Econ Prob HT MP 50/50
• Rec 0.10 -22 -13 -17.5
• BAvg 0.20 - 2 1 - 0.5
• Avg 0.40 20 15 17.5
• AAvg 0.20 35 29 32
• Boom 0.10 50 43 46.5

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• The expected return and standard deviation of
  returns on the 50/50 portfolio of HT and MP are
• E(R) 0.10(-17.5) 0.20(-0.5) 0.40(17.5)
  0.20(32) 0.10(46.5) 16.2
• ? (-17.5 16.2)20.10 (-0.5 16.2)20.20
• (17.5 16.2)20.40 (32 16.2)20.20
• (46.5 16.2)20.101/2 17.7

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• Econ Prob HT Coll 50/50
• Rec 0.10 -22 28 3.0
• BAvg 0.20 - 2 15 6.5
• Avg 0.40 20 0 10.0
• AAvg 0.20 35 -10 12.5
• Boom 0.10 50 -20 15.0

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• The expected return and standard deviation of
  returns on the 50/50 portfolio of HT and Coll
  are
• E(R) 0.10(3.0) 0.20(6.4) 0.40(10.0)
  0.20(12.5) 0.10(15.0) 9.6
• ? (3.0 9.6)20.10 (6.4 9.6)20.20
• (10.0 9.6)20.40 (12.5 9.6)20.20
• (15.0 9.6)20.101/2 3.3

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• _____ correlation provides the greater
  diversification benefits.
• The most common type of correlation, however, is
  _____ correlation since almost all investments
  are linked to performance of the domestic and or
  global economy.
• Note The average correlation between random
  stock pairs is _____.

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• If most assets are positively correlated, does it
  pay to diversify? _____
• As long as the correlation coefficient is less
  than _____, some benefits of diversification are
  achieved.
• The closer the correlation is to _____, the
  greater the diversification benefits.

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?p ()
Company Specific (Diversifiable) Risk
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Stand-Alone Risk, ?p
20 0
Market Risk
10 20 30 40 2,000
Stocks in Portfolio
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• Can all risk be diversified away? No, only
  roughly ___ of an assets risk can be removed
  through diversification.
• The portion of risk removed through
  diversification is called _____ risk, and the
  risk that remains regardless of the level of
  diversification is called _____ risk.

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• A portfolio needs roughly _____ assets to achieve
  efficient diversification (i.e., the point where
  unsystematic risk is negligible).
• The stock market is dominated by _____ investors,
  who are _____ diversified.

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Measuring Systematic Risk

• Systematic risk is found by regressing a stocks
  returns on the returns of the _____ (usually
  approximated by the returns on the
  _____).
• The slope of the line is the measure of
  systematic risk, called _____.

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• KWEs beta is _____.
• Since the beta of an average stock is _____, KWE
  has a level of systematic risk that is _____
  average.
• Most stocks have a beta between _____ and _____.

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The Capital Asset Pricing Model

• The relationship between systematic risk and
  required return is shown by the _____.
• The CAPM assumes investors are risk-_____ and
  well _____.
• What is the CAPM formula?

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• If the beta for HT is 1.29, what is the required
  return on HT?
• HT would be considered _____-valued since its
  expected return (17.4) is _____ than the
  required return (17.0).

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• If the beta for KWE is 0.83 and its expected
  return is 12.0, is KWE under-valued or
  over-valued?
• KWE would be considered _____-valued since its
  expected return (12.0) is _____ than the
  required return (13.8).

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Security Market Line

• The graph on the next slide is called the
  Security Market Line, and it shows the
  relationship between a stocks _____ (i.e.,
  systematic risk) and its _____.
• The upward slope of the line shows that stocks
  with higher betas (risk) have _____ required
  returns.

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SML

rHT17 rm15 rRF8
Stocks Risk Premium

Market Risk Premium
Beta
0 1.0 1.29
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• The additional return required above the
  risk-free rate is the _____.
• In our example, the risk premium for an
  average-risk stock is 7, which is called the
  _____.
• HTs risk premium is _____ at _____ because it
  has _____ risk (i.e., its beta is greater than
  1.0).

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ri ()
SML ri rRF (MRP) bi
.
HT
.
kM 15 kRF 8
.
.
T-bills
.
KWE
Coll.
Risk, bi
-1 0 1 2
Security Market Line
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• The CAPMs required returns plot _____ the SML,
  because the SML is simply a graphical
  presentation of the _____.
• Note that HT is _____-priced and plots _____ the
  SML, while KWE is _____-priced and plots _____
  the SML.

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Market adjustments to mis-priced stocks

• What happens to over-priced stocks?
• As investors try to _____ over-priced stocks, the
  selling pressure drives their prices _____, which
  also drives _____ their expected returns.
• As their expected returns rise, they move back up
  to the SML line.

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• What happens to under-priced stocks?
• As investors try to _____ under-priced stocks,
  the buying pressure drives _____ their prices,
  which also drives _____ their expected
  returns.
• As their expected returns fall, they move back
  down to the SML line.

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Portfolio Betas

• Portfolio betas are found by a simple
  weighted-average. A portfolio with 30,000
  invested in KWE and 20,000 invested in HT would
  be
• Note that this portfolio would also be loaded
  with unsystematic risk since it is comprised of
  _____ stocks, and roughly 20 stocks are needed to
  ignore unsystematic risk.

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Independent Reading

• What happens to the SML when the expected rate of
  inflation changes? (p. 228-229)
• What happens to the SML when investors aversion
  to risk changes? (p.229-230)
• Does a stocks beta coefficient stay the same, or
  change over time? (p. 230)