Title: CHAPTER 8 Risk and Rates of Return
1CHAPTER 8Risk and Rates of Return
 Standalone risk
 Portfolio risk
 Risk return
 CAPM  Capital Asset Pricing Model
 SML Security Market Line
2Investment returns
 Investors
 Like RETURN
 Dislike RISK
 Invest in Risky assets ONLY if paid for risk
3Investment 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.
4What is investment RISK?
 Two types of investment risk
 Standalone 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.
5Probabilities expected return
6Probabilities 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
7Probabilities expected return
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
9Probability distributions
 A listing of all possible outcomes, and the
probability of each occurrence.  Can be shown graphically.
10Standard Deviation
 Measures the shape of out comes
11(No Transcript)
12Selected Realized Returns, 1926 2009
 Average Standard
 Return Deviation
 Smallcompany stocks 16.6 32.8
 Largecompany stocks 11.8 20.5
 LT corporate bonds 6.2 8.3
 LT 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
13Investment alternatives
Economy Prob. TBill 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
14Why is the Tbill return independent of the
economy?
 Tbills will return the promised 5.5, regardless
of the economy.
15Tbills do NOT promise a completely riskfree
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
16How 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.
17Calculating the expected return
18Summary 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?
19Calculating standard deviation
20Standard deviation for each investment
21Comparing standard deviations
22Comments on standard deviation as a measure of
risk
 Standard deviation ( si) measures total, or
standalone, 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.
23Comparing risk and return
Security Expected return, r Risk, s
Tbills 5.5 0.0
Market 10.5 15.2
Seem out of place.
24Coefficient of Variation (CV)
 A standardized measure of dispersion about the
expected value, that shows the risk per unit of
return.
25Risk 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.
26Illustrating 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.
27Investor 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
28Portfolio constructionRisk and return
 Assume a twostock 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.
29Calculating portfolio expected return
30An 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
31Calculating portfolio standard deviation and CV
32Comments 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.
33General 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.
34Returns distribution for two perfectly negatively
correlated stocks (? 1.0)
25
25
15
15
10
35Returns distribution for two perfectly positively
correlated stocks (? 1.0)
36Creating 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.
37Illustrating diversification effects of a stock
portfolio
38Breaking down sources of risk
 Standalone Risk Market Risk Diversifiable
Risk  Market risk portion of a securitys standalone
risk that cannot be eliminated through
diversification. Measured by beta. ß  Diversifiable risk portion of securitys
standalone risk that can be eliminated through
diversification.
39Failure to diversify
 If an investor chooses to hold a onestock
portfolio (doesnt diversify), would the investor
be compensated for the extra risk they bear?  NO!
 Standalone risk is not important to a
welldiversified investor.  Rational, riskaverse 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.
40Capital 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 riskfree 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
welldiversified portfolio.
41Beta 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 welldiversified portfolio.
42Comments 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.
43Can 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.
44Calculating betas
 Welldiversified 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.
45Illustrating the calculation of beta
46Beta coefficients for HT, Coll, and TBills
47Comparing expected returns and beta coefficients
 Security Expected Return Beta
 HT 12.4 1.32
 Market 10.5 1.00
 USR 9.8 0.88
 TBills 5.5 0.00
 Coll. 1.0 0.87
 Riskier securities have higher returns, so the
rank order is OK.
48The 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.
49What is the market risk premium?
 Additional return over riskfree 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.
50Calculating 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
51Expected vs. Required returns
52Illustrating 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.
53An exampleEquallyweighted twostock 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 wStk1 ßStk1 wStk2 ßStk2
 ßP 0.5 (1.2) 0.5( 0.7)
 ßP 0.95
54Calculating 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
55Factors 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
56Factors 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
57Verifying 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.
58More 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.