TOPIC 5 Risk and Rates of Return

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TOPIC 5Risk and Rates of Return
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Investment returns

• The rate of return on an investment can be
  calculated as follows
• (Amount received Amount invested)
• Return ________________________
• 
  Amount invested
• For example, if 1,000 is invested and 1,100 is
  returned after one year, the rate of return for
  this investment is
• (1,100 - 1,000) / 1,000 10.

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What is investment risk?

• Two types of investment risk
• Stand-alone risk
• Portfolio risk
• Investment risk is related to the probability of
  earning a low or negative actual return.
• The greater the chance of lower than expected or
  negative returns, the riskier the investment.

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Probability distributions

• A listing of all possible outcomes, and the
  probability of each occurrence.
• Can be shown graphically.

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Comparing standard deviations
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Selected Realized Returns, 1926 2001

• Average Standard
• Return Deviation
• Small-company stocks 17.3 33.2
• Large-company stocks 12.7 20.2
• L-T corporate bonds 6.1 8.6
• L-T government bonds 5.7 9.4
• U.S. Treasury bills 3.9 3.2
• Source Based on Stocks, Bonds, Bills, and
  Inflation (Valuation Edition) 2002 Yearbook
  (Chicago Ibbotson Associates, 2002), 28.

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HOW DO YOU MEASURE THE RETURN AND RISK OF A
SINGLE ASSET?
RETURN Calculate the expected return
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EXPECTED RETURN
ASSUME Possible Probability Return .20
40 .30 30 .40 20 .10 10 What is
the expected return on the stock?
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The expected return is Prob. X return .20 x
40 8 .30 x 30 9 .40 x 20 8 .10
x 10 1 26
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HOW DO YOU MEASURE THE RISK OF A SINGLE
INVESTMENT?
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CALCULATION OF THE
STANDARD DEVIATION Possible
Expected Prob. Return Return Dev.
Dev.2 Dev.2 X Prob. .20 40
26 14 196 39.2 .30 30
26 4 16 4.8 .40 20
26 6 36 14.4 .10 10
26 16 256
25.6 Variance 84.0 Square root
of 84 is 9.2
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HOW DO YOU MEASURE THE EXPECTED RETURN ON A
PORTFOLIO OF ASSETS?
ASSET A 50 OF PORTFOLIO EXPECTED RETURN
10 ASSET B 50 OF PORTFOLIO EXPECTED RETURN
20 Therefore, the expected return on the
portfolio is (.50) (10) (.50) (20) 15
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HOW DO YOU MEASURE THE RISK ON A PORTFOLIO OF
ASSETS?
Assume Asset A 50 of portfolio Standard
deviation 10 Asset B 50 of
portfolio Standard deviation 20 It is
NOT (.50) (10) (.50) (20)
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In a portfolio, the risk is not a weighted
average of the standard deviations because of
portfolio effects.
EXAMPLE OF ICE CREAM SHOP PLUS A SKI SHOP (Water
skiing shop) And EXAMPLE OF ICE CREAM SHOP PLUS
A SNOW SKIING SHOP
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Returns distribution for two perfectly positively
correlated stocks (? 1.0)
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Returns distribution for two perfectly negatively
correlated stocks (? -1.0)
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25
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15
-10
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EXAMPLE OF PORTFOLIO EFFECTS
Assume 50 in Asset A 50 in Asset B Risk
of Asset A .20 and Risk of Asset B .20
If correlation coefficient is -1 Old
Method Risk is 20 New Method Risk is
0 If correlation coefficient is 1 Old
Method Risk is 20 New Method Risk is
20 If correlation coefficient is 0 Old
Method Risk is 20 New Method Risk is
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Creating a portfolioBeginning with one stock
and adding randomly selected stocks to portfolio

• sp decreases as stocks added, because they would
  not be perfectly correlated with the existing
  portfolio.
• Expected return of the portfolio would remain
  relatively constant.
• Eventually the diversification benefits of adding
  more stocks dissipates (after about 10 stocks),
  and for large stock portfolios, sp tends to
  converge to ? 20.

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Breaking down sources of risk

• Total risk Market risk Firm-specific risk
• Market risk portion of a securitys stand-alone
  risk that cannot be eliminated through
  diversification. Measured by beta.
• Firm-specific risk portion of a securitys
  stand-alone risk that can be eliminated through
  proper diversification.

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Illustrating diversification effects of a stock
portfolio
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Beta

• Measures a stocks market risk, and shows a
  stocks volatility relative to the market.
• Indicates how risky a stock is if the stock is
  held in a well-diversified portfolio.

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Calculating betas

• Run a regression of past returns of a security
  against past returns on the market.
• The slope of the regression line (sometimes
  called the securitys characteristic line) is
  defined as the beta coefficient for the security.

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Illustrating the calculation of beta
THE CHARACTERISTIC LINE
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Comments on beta

• If beta 1.0, the security is just as risky as
  the average stock.
• If beta gt 1.0, the security is riskier than
  average.
• If beta lt 1.0, the security is less risky than
  average.
• Most stocks have betas in the range of 0.5 to 1.5.

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Can the beta of a security be negative?

• Yes, if the correlation between Stock i and the
  market is negative (i.e., ?i,m lt 0).
• If the correlation is negative, the regression
  line would slope downward, and the beta would be
  negative.
• However, a negative beta is highly unlikely.

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Coefficient of Variation (CV)

• A standardized measure of dispersion about the
  expected value, that shows the risk per unit of
  return.

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3 WAYS TO MEASURE RISK

• Standard deviation
• Coefficient of Variation
• Beta

When should each be used?
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Capital Asset Pricing Model (CAPM)

• Model based upon concept that a stocks required
  rate of return is equal to the risk-free rate of
  return plus a risk premium that reflects the
  riskiness of the stock after diversification.
• Primary conclusion The relevant riskiness of a
  stock is its contribution to the riskiness of a
  well-diversified portfolio.

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The Security Market Line (SML)Calculating
required rates of return

• SML ki kRF (kM kRF) ßi
• Assume kRF 8 and kM 15.
• The market (or equity) risk premium is RPM kM
  kRF 15 8 7.

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Illustrating the Security Market Line
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EXPECTED VERSUS REQUIRED RATES OF RETURN
X
RETURN
RISK
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Market equilibrium

• Expected returns are obtained by estimating
  dividends and expected capital gains.
• Required returns are obtained by estimating risk
  and applying the CAPM.

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What is market equilibrium?

• In equilibrium, stock prices are stable and there
  is no general tendency for people to buy versus
  to sell.
• In equilibrium, expected returns must equal
  required returns.

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How is market equilibrium established?

• If expected return exceeds required return
• The current price (P0) is too low and offers a
  bargain.
• Buy orders will be greater than sell orders.
• P0 will be bid up until expected return equals
  required return

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Expected vs. Required returns
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Factors that change the SML

• What if investors raise inflation expectations by
  3, what would happen to the SML?

ki ()
SML2
D I 3
SML1
18 15 11 8
Risk, ßi
0 0.5 1.0 1.5
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Factors that change the SML

• What if investors risk aversion increased,
  causing the market risk premium to increase by
  3, what would happen to the SML?

ki ()
SML2
D RPM 3
SML1
18 15 11 8
Risk, ßi
0 0.5 1.0 1.5