Ch 9: Risk and Rates of Return

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Ch 9 Risk and Rates of Return
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In Chapter 9we examine RISK

• How to measure risk
• (variance, standard deviation, beta)
• How to reduce risk
• (diversification)
• How to price risk
• (security market line, CAPM)

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For a Treasury security, what is the required
rate of return?

• Since Treasuries are essentially free of default
  risk, the rate of return on a Treasury security
  is considered the risk-free rate of return.

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For a corporate stock or bond, what is the
required rate of return?

• How large of a risk premium should we require to
  buy a corporate security?

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Expected Return

• State of Probability Return
• Economy (P) Orl. Utility
  Orl. Tech
• Recession .20 4
  -10
• Normal .50 10
  14
• Boom .30 14
  30
• k P(k1)k1 P(k2)k2 ... P(kn)kn
• k (OI) .2 (-10) .5 (14) .3 (30) 14

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What is Risk?

• Uncertainty in the distribution of possible
  outcomes.

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How do we Measure Risk?

• To get a general idea of a stocks price
  variability, we could look at the stocks price
  range over the past year.

52 weeks Yld Vol
Net Hi Lo Sym Div PE 100s Hi
Lo Close Chg 139 81 IBM .48 .5 26
56598 108 106 1065/8 -2 119 75 MSFT
60 254888 96 93 953/8 1/4
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How do we Measure Risk?

• A more scientific approach is to examine the
  stocks standard deviation of returns.
• Standard deviation is a measure of the dispersion
  of possible outcomes.
• The greater the standard deviation, the greater
  the uncertainty, and therefore , the greater the
  risk.

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Standard Deviation

• (ki - k)2 P(ki)

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• Orlando Utility, Inc.
• ( 4 - 10)2 (.2) 7.2
• (10 - 10)2 (.5) 0
• (14 - 10)2 (.3) 4.8
• Variance 12
• Stand. dev. 12 3.46

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• Orlando Technology, Inc.
• (-10 - 14)2 (.2) 115.2
• (14 - 14)2 (.5) 0
• (30 - 14)2 (.3) 76.8
• Variance 192
• Stand. dev. 192 13.86

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Summary

• Orlando
  Orlando
• Utility Technology
• Expected Return 10 14
• Standard Deviation 3.46 13.86

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• It depends on your tolerance for risk!
• Remember, theres a tradeoff between risk and
  return.

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Portfolios

• Combining several securities in a portfolio can
  actually reduce overall risk.
• How does this work?

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Diversification

• Investing in more than one security to reduce
  risk.
• If two stocks are perfectly positively
  correlated, diversification has no effect on
  risk.
• If two stocks are perfectly negatively
  correlated, the portfolio is perfectly
  diversified.

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• If you owned a share of every stock traded on the
  NYSE and NASDAQ, would you be diversified?
• YES!
• Would you have eliminated all of your risk?
• NO! Common stock portfolios still have risk.

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Some risk can be diversified away and some can
not.

• Market risk (systematic risk) is
  nondiversifiable. This type of risk can not be
  diversified away.
• Company-unique risk (unsystematic risk) is
  diversifiable. This type of risk can be reduced
  through diversification.

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Market Risk

• Unexpected changes in interest rates.
• Unexpected changes in cash flows due to tax rate
  changes, foreign competition, and the overall
  business cycle.

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Company-unique Risk

• A companys labor force goes on strike.
• A companys top management dies in a plane crash.
• A huge oil tank bursts and floods a companys
  production area.

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• As you add stocks to your portfolio,
  company-unique risk is reduced.

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Do some firms have more market risk than others?

• Yes. For example
• Interest rate changes affect all firms, but which
  would be more affected
• a) Retail food chain
• b) Commercial bank

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• Note
• As we know, the market compensates investors for
  accepting risk - but only for market risk.
  Company-unique risk can and should be diversified
  away.
• So - we need to be able to measure market risk.

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This is why we have Beta.

• Beta a measure of market risk.
• Specifically, beta is a measure of how an
  individual stocks returns vary with market
  returns.
• Its a measure of the sensitivity of an
  individual stocks returns to changes in the
  market.

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The markets beta is 1

• A firm that has a beta 1 has average market
  risk. The stock is no more or less volatile than
  the market.
• A firm with a beta gt 1 is more volatile than the
  market.
• (ex technology firms)
• A firm with a beta lt 1 is less volatile than the
  market.
• (ex utilities)

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Calculating Beta
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Summary

• We know how to measure risk, using standard
  deviation for overall risk and beta for market
  risk.
• We know how to reduce overall risk to only market
  risk through diversification.
• We need to know how to price risk so we will know
  how much extra return we should require for
  accepting extra risk.

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What is the Required Rate of Return?

• The return on an investment required by an
  investor given market interest rates and the
  investments risk.

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• Required
• rate of
• return

security market line (SML)
.
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Risk-free rate of return (6)
Beta
1
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• This linear relationship between risk and
  required return is known as the Capital Asset
  Pricing Model (CAPM).

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• Required
• rate of
• return

SML
.
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Risk-free rate of return (6)
0
Beta
1
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• Required
• rate of
• return

SML
Is there a riskless (zero beta) security?
.
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Treasury securities are as close to riskless as
possible.
Risk-free rate of return (6)
0
Beta
1
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• Required
• rate of
• return

SML
Where does the SP 500 fall on the SML?
.
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The SP 500 is a good approximation for the
market
Risk-free rate of return (6)
0
Beta
1
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• Required
• rate of
• return

SML
Utility Stocks
.
12
Risk-free rate of return (6)
0
Beta
1
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• Required
• rate of
• return

SML
High-tech stocks
.
12
Risk-free rate of return (6)
0
Beta
1
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The CAPM equation
b

• kj krf j (km - krf )
• where
• kj the required return on security j,
• krf the risk-free rate of interest,
• j the beta of security j, and
• km the return on the market index.

b
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Example

• Suppose the Treasury bill rate is 6, the average
  return on the SP 500 index is 12, and Walt
  Disney has a beta of 1.2.
• According to the CAPM, what should be the
  required rate of return on Disney stock?

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kj krf (km - krf )
b

• kj .06 1.2 (.12 - .06)
• kj .132 13.2
• According to the CAPM, Disney stock should be
  priced to give a 13.2 return.

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• Required
• rate of
• return

SML
Theoretically, every security should lie on the
SML
.
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If every stock is on the SML, investors are
being fully compensated for risk.
Risk-free rate of return (6)
0
Beta
1
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• Required
• rate of
• return

SML
If a security is above the SML, it is underpriced.
.
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If a security is below the SML, it is
overpriced.
Risk-free rate of return (6)
0
Beta
1
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Practice Problem

• Find the intrinsic value of a common stock with
  the following information
• ROE 20
• 50 retention of earnings
• Beta 1.4
• recent dividend 4.30
• Treasury bond yield 7.5
• Return on the SP 500 12
• Market price for common stock 100
• Should you buy the stock?

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Practice Problem

• g ROE x r .20 x .50 10
• D0 4.30, so D1 4.30 (1.10) 4.73
• k .075 1.4 (.12 - .075) .138