2. • Two types of investment risk
– Stand-alone risk: Unsystematic
– Portfolio risk: Systematic
• Investment risk is related to the
probability of earning a low or negative
actual return.
• The greater the chance of lower than
expected, or negative returns, the riskier
the investment.
8-2
3. • A listing of all possible outcomes, and the
probability of each occurrence.
• Can be shown graphically.
8-3
Expected Rate of Return
Rate of
Return (%)
100
15
0
-70
Firm X
Firm Y
5. • T-bills will return the promised 5.5%,
regardless of the economy.
• No, T-bills do not provide a completely
risk-free return, as they are still exposed
to inflation. Although, very little
unexpected inflation is likely to occur
over such a short period of time.
• T-bills are also risky in terms of
reinvestment risk.
• T-bills are risk-free in the default sense
of the word.
8-5
6. • High Tech: Moves with the economy, and has a
positive correlation. This is typical.
• Collections: Is countercyclical with the economy,
and has a negative correlation. This is unusual.
8-6
8. Expected Return
High Tech 12.4%
Market 10.5%
US Rubber 9.8%
T-bills 5.5%
Collections 1.0%
High Tech has the highest expected return, and
appears to be the best investment alternative,
but is it really? Have we failed to account for
risk?
8-8
11. • Standard deviation (σi) measures total, or stand-
alone, risk.
• The larger σi is, the lower the probability that
actual returns will be close to expected returns.
• Larger σi is associated with a wider probability
distribution of returns.
8-
11
12. 8-
12
Security Expected Return, Risk,
T-bills 5.5% 0.0%
High Tech 12.4 20.0
Collections* 1.0 13.2
US Rubber* 9.8 18.8
Market 10.5 15.2
*Seems out of place.
r̂
13. Source: Based on Ibbotson Stocks, Bonds, Bills, and Inflation:
2013 Valuation Yearbook (Chicago: Morningstar, Inc., 2013), p.
23.
8-
13
14. • A standardized measure of dispersion
about the expected value, that shows the
risk per unit of return.
8-
14
r̂
return
Expected
deviation
Standard
CV
15. CV
T-bills 0.0
High Tech 1.6
Collections 13.2
US Rubber 1.9
Market 1.4
• Collections has the highest degree of risk per
unit of return.
• High Tech, despite having the highest
standard deviation of returns, has a relatively
average CV.
8-
15
16. • 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 riskless
asset, which serves as compensation for
investors to hold riskier securities.
8-
16
17. • Assume a two-stock portfolio is created with
$50,000 invested in each High Tech and Collections.
• A portfolio’s expected return is a weighted average
of the returns of the portfolio’s component assets.
• Standard deviation is a little more tricky and requires
that a new probability distribution for the portfolio
returns be constructed.
8-
17
21. • σp = 3.4% is much lower than the σi of
either stock (σHT = 20.0%; σColl = 13.2%).
• σp = 3.4% is lower than the weighted
average of High Tech and Collections’ σ
(16.6%).
• Therefore, the portfolio provides the
average return of component stocks, but
lower than the average risk.
• Why? Negative correlation between stocks.
8-
21
22. • σ 35% for an average stock.
• Most stocks are positively (though not
perfectly) correlated with the market (i.e.,
ρ between 0 and 1).
• Combining stocks in a portfolio generally
lowers risk.
8-
22
23. • σp decreases as stocks are 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 40 stocks), and for large
stock portfolios, σp tends to converge to 20%.
8-
23
24. Covariance and Correlation
◦ Portfolio risk depends on covariance between returns of
assets
◦ Expected return on two-security portfolio
2
2
1
1
)
( r
W
r
W
r
E p
2
security
on
return
Expected
1
security
on
return
Expected
2
security
in
funds
of
Proportion
1
security
in
funds
of
Proportion
2
1
2
1
r
r
W
W
25. Covariance Calculations
Correlation Coefficient
]
)
(
)
(
)][
(
)
(
)[
(
)
,
Cov(
1
B
S
S
i
B
B
S
S r
E
i
r
r
E
i
r
i
p
r
r
B
S
B
S
SB
r
r
σ
σ
)
,
Cov(
ρ
B
S
SB
B
S r
r σ
σ
ρ
)
,
Cov(
26.
27.
28. CV for the portfolio is CV = 6.65% / 7.0%= .95
For each one unit of risk there is .95 units of return. This is
less than one which implies that the portfolio has lower risk
than average. GOOD
31. Stand-alone risk = Market risk +
Diversifiable risk
• Market risk: portion of a security’s stand-
alone risk that cannot be eliminated
through diversification. Measured by
beta.
• Diversifiable risk: portion of a security’s
stand-alone risk that can be eliminated
through proper diversification.
8-
31
32. • Model linking risk and required returns.
CAPM suggests that there is a Security
Market Line (SML) that states that a stock’s
required return equals the risk-free return
plus a risk premium that reflects the
stock’s risk after diversification.
ri = rRF + (rM – rRF)bi
• Primary conclusion: The relevant riskiness
of a stock is its contribution to the
riskiness of a well-diversified portfolio.
8-
32
33. • Measures a stock’s market risk, and
shows a stock’s volatility relative to the
market.
• Indicates how risky a stock is if the stock
is held in a well-diversified portfolio.
8-
33
34. • If beta = 1.0, the security is just as risky
as the average stock.
• If beta > 1.0, the security is riskier than
average.
• If beta < 1.0, the security is less risky
than average.
• Most stocks have betas in the range of
0.5 to 1.5.
8-
34
35. • Yes, if the correlation between Stock i and
the market is negative (i.e., ρi,m < 0).
• If the correlation is negative, the
regression line would slope downward,
and the beta would be negative.
• However, a negative beta is highly
unlikely.
8-
35
36. • 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
security’s past returns against the past
returns of the market.
• The slope of the regression line is defined
as the beta coefficient for the security. 8-
36
39. Security Expected Return Beta
High Tech 12.4% 1.32
Market 10.5 1.00
US Rubber 9.8 0.88
T-Bills 5.5 0.00
Collections 1.0 -0.87
Riskier securities have higher returns, so the
rank order is OK.
8-
39
40. ri = rRF + (rM – rRF)bi
ri = rRF + (RPM)bi
• Assume that rRF = 5.5% and
RPM = rM rRF = 10.5% 5.5% = 5.0%.
8-
40
41. • Additional return over the risk-free rate
needed to compensate 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.
8-
41
43. r
High Tech 12.4
%
12.1% Undervalu
ed
Market 10.5 10.5 Fairly
valued
US Rubber 9.8 9.9 Overvalued
T-bills 5.5 5.5 Fairly
valued
Collection
s
1.0 1.15 Overvalued
8-
43
r̂
)
r
r̂
(
)
r
r̂
(
)
r
r̂
(
)
r
r̂
(
)
r
r̂
(
44. • Create a portfolio with 50% invested in
High Tech and 50% invested in
Collections.
• The beta of a portfolio is the weighted
average of each of the stock’s betas.
bP = wHTbHT + wCollbColl
bP = 0.5(1.32) + 0.5(-0.87)
bP = 0.225
8-
44
45. The required return of a portfolio is the
weighted average of each of the stock’s
required returns.
rP = wHTrHT + wCollrColl
rP = 0.5(12.10%) + 0.5(1.15%)
rP = 6.625%
Or, using the portfolio’s beta, CAPM can be
used to solve for expected return.
rP = rRF + (RPM)bP
rP = 5.5% + (5.0%)(0.225)
rP = 6.625%
8-
45
46. • 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 concepts are based upon
expectations, but betas are calculated
using historical data. A company’s
historical data may not reflect investors’
expectations about future riskiness.
8-
46
