Chương 1
Rủi ro và tỷ suất lợi nhuận
Lợi
nhuận
:
các
khái
niệm
cơ
bản
1-1
1.
Lợi
nhuận
:
các
khái
niệm
cơ
bản
2. Rủi ro: các khái niệm cơ bản
3. Rủi ro riêng lẻ
4. Rủi ro thị trường (rủi ro danh mục)
5. Rủi ro và lợi nhuận: CAPM/SML
Investment returns
The rate of return on an investment can be
calculated as follows:
(Amount received – Amount invested)
Return =
________________________
1-2

Average Standard
Return Deviation
Small-company stocks 17.5% 33.1%
Large
-
company stocks
12.4
20.3
1-5
Large
-
company stocks
12.4
20.3
L-T corporate bonds 6.2 8.6
L-T government bonds 5.8 9.3
U.S. Treasury bills 3.8 3.1
Source: Based on
Stocks, Bonds, Bills, and Inflation: (Valuation
Edition) 2005 Yearbook
(Chicago: Ibbotson Associates, 2005), p28.
Investment alternatives
Economy Prob. T-Bill HT Coll USR MP
Recession
0.1 5.5% -27.0% 27.0% 6.0% -17.0%
1-6
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%

–
Is countercyclical with the
economy, and has a negative
correlation. This is unusual.
Calculating the expected return
P

r
r

return of rate expected r
N
^
^
=
=
∑
1-9
12.4% (0.1) (45%)
(0.2) (30%) (0.4) (15%)
(0.2) (-7%) (0.1) (-27%) r
P

r

Standard
=
σ
2
Variance
σ
=
=
σ
1-11
2
Variance
σ
=
=
σ
i
2
N
1i
i
P)r(rσ
∑
=
−=
ˆ
Standard deviation for each investment

(0.2)
5.5)

1-12
15.2%
18.8% 20.0%
13.2% 0.0%
(0.1)5.5) - (5.5
(0.2)5.5) - (5.5 (0.4)5.5) - (5.5

(0.2)
5.5)

-

(5.5

(0.1)
5.5)

-

(5.5

M
USR
HT
CollbillsT
2
22
billsT
=
==

 Standard deviation (σ
i
) measures
total, or stand-alone, risk.

The larger
σ
i
is, the lower the
1-14

The larger
σ
i
is, the lower the
probability that actual returns will be
closer to expected returns.
 Larger σ
i
is associated with a wider
probability distribution of returns.
Comparing risk and return
Security Expected
return, r
Risk, σ
T
-
bills
5.5%
0.0%

T-bill 0.0
HT 1.6
Coll. 13.2
USR
1.9
1-17
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.
Illustrating the CV as a
measure of relative risk
A B
Prob.
1-18
σ
A
= σ
B
, but A is riskier because of a larger probability of
losses. In other words, the same amount of risk (as
measured by σ) for smaller returns.
0
Rate of Return (%)
Investor attitude towards risk
 Risk aversion – assumes investors dislike
risk and require higher rates of return to

N
1i
i
^
i
p
^
=+=
=
∑
=
An alternative method for determining
portfolio expected return
Economy Prob. HT Coll Port.Port.
Recession 0.1 -27.0% 27.0% 0.0%0.0%
Below avg
0.2
-
7.0%
13.0%
3.0%3.0%
1-22
Below avg
0.2
-
7.0%
13.0%
3.0%3.0%
Average 0.4 15.0% 0.0% 7.5%7.5%
Above avg 0.2 30.0% -11.0% 9.5%9.5%

p
=










+
+
=
σ
1-23
0.51
6.7%
3.4%
CV
3.4%6.7) - (12.0 0.10
6.7) - (9.5 0.20

6.7)

-

 σ
p
= 3.4% is much lower than the σ
i
of
either stock (σ
HT
= 20.0%; σ
Coll.
= 13.2%).
 σ
p
= 3.4% is lower than the weighted
average of HT and Coll.’s
σ
(16.6%).
1-24
p
average of HT and Coll.’s
σ
(16.6%).
 Therefore, the portfolio provides the
average return of component stocks, but
lower than the average risk.
 Why? Negative correlation between stocks.
General comments about risk
 σ ≈ 35% for an average stock.
 Most stocks are positively (though
not perfectly) correlated with the
1-25