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CHAPTER 8 Risk and Rates of Return

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CHAPTER 8 Risk and Rates of Return Stand-alone risk Portfolio risk Risk & return: CAPM - Capital Asset Pricing Model SML Security Market Line – PowerPoint PPT presentation

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Title: CHAPTER 8 Risk and Rates of Return


1
CHAPTER 8Risk and Rates of Return
  • Stand-alone risk
  • Portfolio risk
  • Risk return
  • CAPM - Capital Asset Pricing Model
  • SML Security Market Line

2
Investment returns
  • Investors
  • Like RETURN
  • Dislike RISK
  • Invest in Risky assets ONLY if paid for risk

3
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.

4
What is investment RISK?
  • Two types of investment risk
  • Stand-alone risk
  • Portfolio risk
  • Investment risk related to the probability of
    earning low or negative actual return.
  • The greater the chance of lower than expected or
    negative returns, the riskier the investment.

5
Probabilities expected return
  • Compare two companies

6
Probabilities expected return
  • First company has 3 possible returns

Return Probability Ret x Prob
100 30 30
15 40 6
-70 30 -21
Expected Return 15
7
Probabilities expected return
  • The Second Company

Return Probability Ret x Prob
20 30 6
15 40 6
10 30 3
Expected Return 15
8
  • But first company has much wider range of
    possible returns
  • Graph the outcomes

9
Probability distributions
  • A listing of all possible outcomes, and the
    probability of each occurrence.
  • Can be shown graphically.

10
Standard Deviation
  • Measures the shape of out comes

11
(No Transcript)
12
Selected Realized Returns, 1926 2009
  • Average Standard
  • Return Deviation
  • Small-company stocks 16.6 32.8
  • Large-company stocks 11.8 20.5
  • L-T corporate bonds 6.2 8.3
  • L-T government bonds 5.8 9.6
  • U.S. Treasury bills 3.7 3.1
  • Source Based on Ibbotson Stocks, Bonds, Bills,
    and Inflation 2010 Valuation Yearbook (Chicago
    Morningstar, Inc.), p23

13
Investment alternatives
Economy Prob. T-Bill HT Coll USR MP
Recession 0.1 5.5 -27.0 27.0 6.0 -17.0
Below avg 0.2 5.5 -7.0 13.0 -14.0 -3.0
Average 0.4 5.5 15.0 0.0 3.0 10.0
Above avg 0.2 5.5 30.0 -11.0 41.0 25.0
Boom 0.1 5.5 45.0 -21.0 26.0 38.0
14
Why is the T-bill return independent of the
economy?
  • T-bills will return the promised 5.5, regardless
    of the economy.

15
T-bills do NOT promise a completely risk-free
return?
  • Inflation risk. -- Small risk, inflation is not
    likely to occur over such a short period of time.
  • Reinvestment rate risk
  • NO default risk
  • U.S. Treasury can print money

16
How do the returns of HT and Coll. behave in
relation to the market?
  • HT Moves with the economy, and has a positive
    correlation. This is typical.
  • Coll. Is countercyclical with the economy, and
    has a negative correlation. This is unusual.

17
Calculating the expected return
18
Summary of expected returns
  • Expected return
  • HT 12.4
  • Market 10.5
  • USR 9.8
  • T-bill 5.5
  • Coll. 1.0
  • HT has the highest expected return, and appears
    to be the best investment alternative, but is it
    really? Have we failed to account for risk?

19
Calculating standard deviation
20
Standard deviation for each investment
21
Comparing standard deviations
22
Comments on standard deviation as a measure of
risk
  • Standard deviation ( si) measures total, or
    stand-alone, risk.
  • Larger si , lower probability that actual returns
    will be close to expected returns.
  • Larger si is associated with a wider probability
    distribution of returns.

23
Comparing risk and return
Security Expected return, r Risk, s
T-bills 5.5 0.0
Market 10.5 15.2



Seem out of place.
24
Coefficient of Variation (CV)
  • A standardized measure of dispersion about the
    expected value, that shows the risk per unit of
    return.

25
Risk rankings, by coefficient of variation
  • CV
  • T-bill 0.0
  • HT 1.6
  • Coll. 13.2
  • USR 1.9
  • Market 1.4
  • Collections has the highest degree of risk per
    unit of return.
  • HT, despite having the highest standard deviation
    of returns, has a relatively average CV.

26
Illustrating the CV as a measure of relative risk
  • sA sB , but A is riskier because of a larger
    probability of losses. In other words, the same
    amount of risk (as measured by s) for smaller
    returns.

27
Investor attitude towards risk
  • Risk aversion assumes investors dislike risk
    and require higher rates of return to encourage
    them to hold riskier securities.
  • Risk premium
  • difference between the return on a risky asset
    and a riskless asset
  • compensation for investors to hold riskier asset

28
Portfolio constructionRisk and return
  • Assume a two-stock portfolio
  • 50,000 invested in each
  • Portfolio expected return is weighted average of
    returns of portfolios component assets.
  • Standard deviation is a little more tricky and
    requires that a new probability distribution for
    the portfolio returns be devised.

29
Calculating portfolio expected return
30
An alternative method for determining portfolio
expected return
Economy Prob. HT Coll Port.
Recession 0.1 -27.0 27.0 0.0
Below avg 0.2 -7.0 13.0 3.0
Average 0.4 15.0 0.0 7.5
Above avg 0.2 30.0 -11.0 9.5
Boom 0.1 45.0 -21.0 12.0
31
Calculating portfolio standard deviation and CV
32
Comments on portfolio risk measures
  • sp 3.4 is much lower than the si of either
    stock (sHT 20.0 sColl. 13.2).
  • sp 3.4 is lower than the weighted average of
    HT and Coll.s s (16.6).
  • Therefore, the portfolio provides the average
    return of component stocks, but lower than the
    average risk.
  • Why? Negative correlation between stocks.

33
General comments about risk
  • s ? 35 for average stock.
  • Most stocks are positively (though not perfectly)
    correlated with the market (i.e., ? between 0 and
    1).
  • Combining stocks in a portfolio generally lowers
    risk.

34
Returns distribution for two perfectly negatively
correlated stocks (? -1.0)
25
25
15
15
-10
35
Returns distribution for two perfectly positively
correlated stocks (? 1.0)
36
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.

37
Illustrating diversification effects of a stock
portfolio
38
Breaking down sources of risk
  • Stand-alone Risk Market Risk Diversifiable
    Risk
  • Market risk portion of a securitys stand-alone
    risk that cannot be eliminated through
    diversification. Measured by beta. ß
  • Diversifiable risk portion of securitys
    stand-alone risk that can be eliminated through
    diversification.

39
Failure to diversify
  • If an investor chooses to hold a one-stock
    portfolio (doesnt diversify), would the investor
    be compensated for the extra risk they bear?
  • NO!
  • Stand-alone risk is not important to a
    well-diversified investor.
  • Rational, risk-averse investors are concerned
    with sp, which is based upon market risk.
  • There can be only one price (the market return)
    for a given security.
  • No compensation should be earned for holding
    unnecessary, diversifiable risk.

40
Capital Asset Pricing Model (CAPM)
  • Model linking risk and required returns. CAPM
    suggests that there is a Security Market Line
    (SML) that states that a stocks required return
    equals the risk-free return plus a risk premium
    that reflects the stocks risk after
    diversification.
  • ri rRF (rM rRF) ßi
  • Primary conclusion The relevant riskiness of a
    stock is its contribution to the riskiness of a
    well-diversified portfolio.

41
Beta ß
  • Measures stocks market risk, and shows stocks
    volatility relative to the market.
  • Indicates how risky a stock is if the stock is
    held in a well-diversified portfolio.

42
Comments on beta ß
  • 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.

43
Can the beta of a security be negative?
  • Yes, if the correlation between Stock i and the
    market is negative ( ?i,m lt 0).
  • If correlation is negative, regression line
    slopes downward, and ß is negative.
  • However, negative ß is highly unlikely.

44
Calculating betas
  • Well-diversified investors are primarily
    concerned with how a stock is expected to move
    relative to the market in the future.
  • Without a crystal ball to predict the future,
    analysts are forced to rely on historical data.
    A typical approach to estimate beta is to run a
    regression of the securitys past returns against
    the past returns of the market.
  • The slope of the regression line is defined as
    the beta coefficient for the security.

45
Illustrating the calculation of beta
46
Beta coefficients for HT, Coll, and T-Bills
47
Comparing expected returns and beta coefficients
  • Security Expected Return Beta
  • HT 12.4 1.32
  • Market 10.5 1.00
  • USR 9.8 0.88
  • T-Bills 5.5 0.00
  • Coll. 1.0 -0.87
  • Riskier securities have higher returns, so the
    rank order is OK.

48
The Security Market Line (SML)Calculating
required rates of return
  • SML ri rRF (rM rRF) ßi
  • ri rRF (RPM) ßi
  • Assume yield curve is flat and that rRF 5.5
    and RPM 5.0.

49
What is the market risk premium?
  • Additional return over risk-free rate compensates
    investors for assuming an average amount of risk.
  • Its size depends on the perceived risk of the
    stock market and investors degree of risk
    aversion.
  • Varies from year to year, but most estimates
    suggest that it ranges between 4 and 8 per year.

50
Calculating required rates of return
  • rHT 5.5 (5.0)(1.32)
  • 5.5 6.6 12.10
  • rM 5.5 (5.0)(1.00) 10.50
  • rUSR 5.5 (5.0)(0.88) 9.90
  • rT-bill 5.5 (5.0)(0.00) 5.50
  • rColl 5.5 (5.0)(-0.87) 1.15

51
Expected vs. Required returns
52
Illustrating the Security Market Line
SML ri 5.5 (5.0) bi
ri ()
SML
.
HT
.
.
rM 10.5 rRF 5.5
.
USR
T-bills
.
Risk, bi
-1 0 1 2
Coll.
53
An exampleEqually-weighted two-stock portfolio
  • Create a portfolio with 50 invested in each of
    two stocks.
  • The ß of a portfolio is the weighted average of
    each of the stocks ß
  • ßP wStk-1 ßStk-1 wStk-2 ßStk-2
  • ßP 0.5 (1.2) 0.5( 0.7)
  • ßP 0.95

54
Calculating portfolio required returns
  • The required return of a portfolio is the
    weighted average of each of the stocks required
    returns.
  • rP wHT rHT wColl rColl
  • rP 0.5 (12.10) 0.5 (1.15)
  • rP 6.63
  • Or, using the portfolios beta, CAPM can be used
    to solve for expected return.
  • rP rRF (RPM) bP
  • rP 5.5 (5.0) (0.225)
  • rP 6.63

55
Factors that change the SML
  • What if investors raise inflation expectations by
    3, what would happen to the SML?

ri ()
SML2
D I 3
SML1
13.5 10.5 8.5 5.5
Risk, bi
0 0.5 1.0 1.5
56
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?

ri ()
SML2
D RPM 3
SML1
13.5 10.5 5.5
Risk, bi
0 0.5 1.0 1.5
57
Verifying the CAPM empirically
  • The CAPM has not been verified completely.
  • Statistical tests have problems that make
    verification almost impossible.
  • Some argue that there are additional risk
    factors, other than the market risk premium, that
    must be considered.

58
More thoughts on the CAPM
  • Investors seem to be concerned with both market
    risk and total risk. Therefore, the SML may not
    produce a correct estimate of ri.
  • ri rRF (rM rRF) bi ???
  • CAPM/SML concepts are based upon expectations,
    but betas are calculated using historical data.
    A companys historical data may not reflect
    investors expectations about future riskiness.
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