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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
• 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
• 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
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
• 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
• 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
• 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
• 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

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
• 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