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CHAPTER 8 Risk and Rates of Return

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CHAPTER 8 Risk and Rates of Return Outline Stand-alone return and risk Return Expected return Stand-alone risk Portfolio return and risk Portfolio return – PowerPoint PPT presentation

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Title: CHAPTER 8 Risk and Rates of Return


1
CHAPTER 8Risk and Rates of Return
  • Outline
  • Stand-alone return and risk
  • Return
  • Expected return
  • Stand-alone risk
  • Portfolio return and risk
  • Portfolio return
  • Portfolio risk
  • Beta
  • Link Risk return
  • CAPM
  • Security Market Line

2
I-1 Return What is my reward of investing?
3
Investment returns
  • 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.
  • The rate of return on an investment can be
    calculated as follows
  • (Amount received Amount invested)
  • Return ________________________

  • Amount invested

4
Rates of Return stocks

HPR Holding Period Return P1 Ending price P0
Beginning price D1 Dividend during period
one Define return? Your gain per dollar
investment
5
Rates of Return Example
  • Ending Price 24
  • Beginning Price 20
  • Dividend 1
  • HPR ( 24 - 20 1 )/ ( 20) 25

6
I-2 Expected return describe the uncertainty
7
Calculating expected return
  • Two scenarios and the concept of expected return
  • Extending to more than two scenarios

8
Investment alternatives
Economy Prob. T-Bill HT Coll USR MP
Recession 0.1 5.5 -27.0 27.0 6.0 -17.0
weak 0.2 5.5 -7.0 13.0 -14.0 -3.0
normal 0.4 5.5 15.0 0.0 3.0 10.0
strong 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
9
Calculating the expected return
10
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?

11
I-3. Stand-alone risk
12
Calculating standard deviation
13
Standard deviation for each investment
14
Comparing standard deviations
15
Comments on standard deviation as a measure of
risk
  • Standard deviation (si) measures total, or
    stand-alone, risk.
  • The larger si is, the lower the probability that
    actual returns will be closer to expected
    returns.
  • Larger si is associated with a wider probability
    distribution of returns.

16
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 the difference between the return
    on a risky asset and a risk free asset, which
    serves as compensation for investors to hold
    riskier securities.

17
Comparing risk and return
Security Expected return, r Risk, s
T-bills 5.5 0.0
HT 12.4 20.0
Coll 1.0 13.2
USR 9.8 18.8
Market 10.5 15.2

Seem out of place.
18
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
  • Source Based on Stocks, Bonds, Bills, and
    Inflation (Valuation Edition) 2002 Yearbook
    (Chicago Ibbotson Associates, 2002), 28.

19
Coefficient of Variation (CV)
  • A standardized measure of dispersion about the
    expected value, that shows the risk per unit of
    return.

20
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.

21
II Risk and return in a portfolio
22
Portfolio constructionRisk and return
  • Assume a two-stock portfolio is created with
    50,000 invested in both HT and Collections.
  • Expected return of a portfolio is a weighted
    average of each of the component assets of the
    portfolio.
  • Standard deviation is a little more tricky and
    requires that a new probability distribution for
    the portfolio returns be devised.

23
II-1. Portfolio return
24
Calculating portfolio expected return
Economy Prob. HT Coll Port.
Recession 0.1 -27.0 27.0
weak 0.2 -7.0 13.0
normal 0.4 15.0 0.0 7.5
strong 0.2 30.0 -11.0
Boom 0.1 45.0 -21.0
25
Calculating portfolio expected return
Economy Prob. HT Coll Port.
Recession 0.1 -27.0 27.0 0.0
weak 0.2 -7.0 13.0 3.0
normal 0.4 15.0 0.0 7.5
strong 0.2 30.0 -11.0 9.5
Boom 0.1 45.0 -21.0 12.0
26
An alternative method for determining portfolio
expected return
27
II-2. Portfolio risk and beta
28
Calculating portfolio standard deviation and CV
29
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.

30
Returns distribution for two perfectly negatively
correlated stocks (? -1.0)
40
40
15
15
-10
31
Returns distribution for two perfectly positively
correlated stocks (? 1.0)
32
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.

33
Illustrating diversification effects of a stock
portfolio
34
Breaking down sources of risk
  • Stand-alone 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.

35
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.
  • Portfolio beta is a weighted average of its
    individual securities beta

36
Calculating betas
  • Run a regression of past returns of a security
    against past returns on the market.
  • The slope of the regression line is defined as
    the beta coefficient for the security.

37
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.

38
III CAPM
39
What risk do we care?
  • Stand alone?
  • Risk that can not be diversified?

40
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.

41
Capital Asset Pricing Model (CAPM)
  • Model linking risk and required returns. CAPM
    suggests 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) bi
  • Risk premium RP additional return to take
    additional risk
  • The market (or equity) risk premium is (rM rRF)

42
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

43
Applying CAPM
  • Portfolio beta Beta of a portfolio is a weighted
    average of its individual securities betas.
  • Computing other variables risk free rate, market
    return, market risk premium
  • Computing the difference of return between two
    stocks.
  • Computing price in the future when current price
    is given

44
CAPM in a graph 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.
45
Applying CAPM in real world(optional)
  • Total Risk vs. Beta. An experiment
  • The difference between commonly referred risk and
    beta (Are these high beta stocks really high
    beta)
  • High risk( total risk), low beta stock can hedge
    your portfolio (reduce portfolio risk)

46
Problems with CAPM (optional)
  • Measurement error of beta
  • Empirical relationship between beta and return is
    weak
  • Size and Book-to-market factors
  • Momentum

47
Optional diversification in real world
  • Stock Index ETF
  • Style Value vs. Growth
  • Style Small vs. Big
  • Performance, Risk, Expense(0.1 is low, 0.5 is
    about average)
  • Examples
  • Vanguard Small Cap Value ETF  VBR
  • Small growth VBK
  • Large value VTV
  • Large growth VUG

48
diversification in real world
  • Foreign ETFRBL
  • Pros
  • More diversification
  • Low PE ratio
  • cons
  • Higher risk
  • Higher expense 0.6 vs. 0.1
  • Higher spread
  • Poor prior performance
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