Title: CHAPTER 8 Risk and Rates of Return
1CHAPTER 8Risk and Rates of Return
 Outline
 Standalone return and risk
 Return
 Expected return
 Standalone risk
 Portfolio return and risk
 Portfolio return
 Portfolio risk
 Beta
 Link Risk return
 CAPM
 Security Market Line
2I1 Return What is my reward of investing?
3Investment 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
4Rates 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
5Rates of Return Example
 Ending Price 24
 Beginning Price 20
 Dividend 1
 HPR ( 24  20 1 )/ ( 20) 25
6I2 Expected return describe the uncertainty
7Calculating expected return
 Two scenarios and the concept of expected return
 Extending to more than two scenarios
8Investment alternatives
Economy Prob. TBill 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
9Calculating the expected return
10Summary of expected returns
 Expected return
 HT 12.4
 Market 10.5
 USR 9.8
 Tbill 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?
11I3. Standalone risk
12Calculating standard deviation
13Standard deviation for each investment
14Comparing standard deviations
15Comments on standard deviation as a measure of
risk
 Standard deviation (si) measures total, or
standalone, 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.
16Investor 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.
17Comparing risk and return
Security Expected return, r Risk, s
Tbills 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.
18Selected Realized Returns, 1926 2001
 Average Standard
 Return Deviation
 Smallcompany stocks 17.3 33.2
 Largecompany stocks 12.7 20.2
 LT corporate bonds 6.1 8.6
 Source Based on Stocks, Bonds, Bills, and
Inflation (Valuation Edition) 2002 Yearbook
(Chicago Ibbotson Associates, 2002), 28.
19Coefficient of Variation (CV)
 A standardized measure of dispersion about the
expected value, that shows the risk per unit of
return.
20Risk rankings, by coefficient of variation
 CV
 Tbill 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.
21II Risk and return in a portfolio
22Portfolio constructionRisk and return
 Assume a twostock 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.
23II1. Portfolio return
24Calculating 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
25Calculating 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
26An alternative method for determining portfolio
expected return
27II2. Portfolio risk and beta
28Calculating portfolio standard deviation and CV
29Comments 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.
30Returns distribution for two perfectly negatively
correlated stocks (? 1.0)
40
40
15
15
10
31Returns distribution for two perfectly positively
correlated stocks (? 1.0)
32Creating 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.
33Illustrating diversification effects of a stock
portfolio
34Breaking down sources of risk
 Standalone risk Market risk Firmspecific
risk  Market risk portion of a securitys standalone
risk that cannot be eliminated through
diversification. Measured by beta.  Firmspecific risk portion of a securitys
standalone risk that can be eliminated through
proper diversification.
35Beta
 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 welldiversified portfolio.  Portfolio beta is a weighted average of its
individual securities beta
36Calculating 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.
37Comments 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.
38III CAPM
39What risk do we care?
 Stand alone?
 Risk that can not be diversified?
40Capital Asset Pricing Model (CAPM)
 Model based upon concept that a stocks required
rate of return is equal to the riskfree rate of
return plus a risk premium that reflects the
riskiness of the stock after diversification.
41Capital Asset Pricing Model (CAPM)
 Model linking risk and required returns. CAPM
suggests that a stocks required return equals
the riskfree 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)
42Calculating 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
 rTbill 5.5 (5.0)(0.00) 5.50
 rColl 5.5 (5.0)(0.87) 1.15
43Applying 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
44CAPM in a graph the Security Market Line
SML ri 5.5 (5.0) bi
ri ()
SML
.
HT
.
.
rM 10.5 rRF 5.5
.
USR
Tbills
.
Risk, bi
1 0 1 2
Coll.
45Applying 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)
46Problems with CAPM (optional)
 Measurement error of beta
 Empirical relationship between beta and return is
weak  Size and Booktomarket factors
 Momentum
47Optional 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
48diversification 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