Bài giảng tài chính doanh nghiệp chương 1 rủi ro và tỷ suất lợi nhuận

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

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%.
What is investment risk?
 Two types of investment risk
 Stand-alone risk
 Portfolio risk
1-3
 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.
Probability distributions
 A listing of all possible outcomes, and the
probability of each occurrence.
 Can be shown graphically.
1-4
Expected Rate of Return
Rate of
Return (%)
100150-70
Firm X
Firm Y
Selected Realized Returns,
1926 – 2004

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%

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%
Why is the T-bill return independent
of the economy? Do T-bills promise a
completely risk-free return?
 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.
1-7
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 rate
risk.
 T-bills are risk-free in the default sense of the
word.
How 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
1-8

Coll.

–
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

r

HT
^
1i
ii
^
=+
++
+=
=
∑
=
Summary of expected returns
Expected return
HT 12.4%
Market 10.5%
USR
9.8%
1-10
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?
Calculating standard deviation
deviation

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)

-

(5.5

(0.1)
5.5)

-

(5.5
P )r (r
22
N
1i
i
2
^
i




+
−=
=
∑
σ
2
1

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
=
==

==










+
++
+
=
−
−
σ
σσ
σσ
σ
Comparing standard deviations
Prob.
T - bill
1-13
USR
HT
0 5.5 9.8 12.4 Rate of Return (%)
Comments on standard
deviation as a measure of risk

 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%

^
1-15
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.
Coefficient of Variation (CV)
A standardized measure of dispersion about
the expected value, that shows the risk per
unit of return.
1-16
r

return Expected
deviation

Standard
CV
ˆ
σ
==
Risk rankings,
by coefficient of variation
CV

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

encourage them to hold riskier securities.
1-19
 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.
Portfolio construction:
Risk and return
 Assume a two-stock portfolio is created with
$50,000 invested in both HT and Collections.
 A portfolio’s expected return is a weighted
average of the returns of the portfolio’s
1-20
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 devised.
Calculating portfolio expected return
:average weighted a is r
N
^
^
p
^
1-21
6.7% (1.0%) 0.5 (12.4%) 0.5 r
rw r
p
^

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%

Boom 0.1 45.0% -21.0% 12.0%12.0%
6.7% (12.0%) 0.10 (9.5%) 0.20
(7.5%) 0.40 (3.0%) 0.20 (0.0%) 0.10 r
p
^
=++
++=
Calculating portfolio standard
deviation and CV
3.4%



6.7)

-

(7.5

0.40

6.7) - (3.0 0.20
6.7) - (0.0 0.10


2
1
2
2
2

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)

-

(7.5

0.40



p
2
2
p
==
=










+
+
+
=
σ
Comments on portfolio risk
measures

 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

not perfectly) correlated with the
market (i.e., ρ between 0 and 1).
 Combining stocks in a portfolio
generally lowers risk.