ợi 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

55 trang |

Chia sẻ: nyanko | Lượt xem: 1421 | Lượt tải: 0
Bạn đang xem trước 20 trang tài liệu **Bài giảng Chương 1: Rủi ro và tỷ suất lợi nhuận**, để xem tài liệu hoàn chỉnh bạn click vào nút DOWNLOAD ở trên

Chương 1
Rủi ro và tỷ suất lợi nhuận
Lợi nhuận :các khái niệm cơ bản
1-1
1.
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
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
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
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
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%) rHT
^
1i
ii
=+
++
+=
=
Summary of expected returns
Expected return
HT 12.4%
Market 10.5%
USR 9.8%
1-10
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
2Variance σ==σ
1-11
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
M
USRHT
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 (σi) measures
total, or stand-alone, risk.
The larger σi is, the lower the
1-14
probability that actual returns will be
closer to expected returns.
Larger σi 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
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
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
σA = σB , 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
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
^
1i
iip
=+=
=∑
=
An 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%
1-22
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%
6.7% (12.0%) 0.10 (9.5%) 0.20
(7.5%) 0.40 (3.0%) 0.20 (0.0%) 0.10 rp
^
=++
++=
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
6.7) - (12.0 0.10
6.7) - (9.5 0.20
p
2
2
==
+
+
Comments on portfolio risk
measures
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 HT and Coll.’s σ (16.6%).
1-24
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
market (i.e., ρ between 0 and 1).
Combining stocks in a portfolio
generally lowers risk.
Returns distribution for two perfectly
negatively correlated stocks (ρ = -1.0)
25 2525
Stock W Stock M Portfolio WM
1-26
-10
15 1515
0
-10
0
-10
0
Returns distribution for two perfectly
positively correlated stocks (ρ = 1.0)
Stock M
25
Stock M’
25
Portfolio MM’
25
1-27
0
15
-10
0
15
-10
0
15
-10
Creating a portfolio:
Beginning with one stock and adding
randomly selected stocks to portfolio
σp decreases as stocks added, because they
would not be perfectly correlated with the
existing portfolio.
Expected return of the portfolio would
1-28
remain relatively constant.
Eventually the diversification benefits of
adding more stocks dissipates (after about
10 stocks), and for large stock portfolios, σp
tends to converge to ≈ 20%.
Illustrating diversification effects of
a stock portfolio
Diversifiable Risk
Stand-Alone Risk, σp
σp (%)
35
1-29
# Stocks in Portfolio
10 20 30 40 2,000+
Market Risk
20
0
Breaking down sources of risk
Stand-alone risk = Market risk + Diversifiable risk
Market risk – portion of a security’s stand-alone
1-30
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.
Failure to diversify
If an investor chooses to hold a one-stock
portfolio (doesn’t diversify), would the investor
be compensated for the extra risk they bear?
NO!
Stand-alone risk is not important to a well-
1-31
diversified investor.
Rational, risk-averse investors are concerned
with σp, 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.
Capital Asset Pricing Model
(CAPM)
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
1-32
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.
Beta
Measures a stock’s market risk, and
shows a stock’s volatility relative to the
market.
1-33
Indicates how risky a stock is if the
stock is held in a well-diversified
portfolio.
Comments on beta
If beta = 1.0, the security is just as risky as
the average stock.
If beta > 1.0, the security is riskier than
average.
1-34
If beta < 1.0, the security is less risky than
average.
Most stocks have betas in the range of 0.5 to
1.5.
Can the beta of a security be
negative?
Yes, if the correlation between Stock
i and the market is negative (i.e.,
ρi,m < 0).
If the correlation is negative, the
1-35
regression line would slope
downward, and the beta would be
negative.
However, a negative beta is highly
unlikely.
Calculating betas
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,
1-36
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.
Tính beta như thế nào ?
Chạy hàm hồi quy regression với các
biến số là suất sinh lời cổ phiếu trên
trục Y và suất sinh lời thị trường trên
trục X.
1-37
Độ nghiêng (hệ số góc) của đường hồi
quy đo lường sự biến động tương quan
của cổ phiếu hay là hệ số beta (b).
VD: dùng số liệu suất sinh lời quá
khứ của cổ phiếu KWE để tính beta
Year Market KWE
1 25.7% 40.0%
2 8.0% -15.0%
3 -11.0% -15.0%
1-38
4 15.0% 35.0%
5 32.5% 10.0%
6 13.7% 30.0%
7 40.0% 42.0%
8 10.0% -10.0%
9 -10.8% -25.0%
10 -13.1% 25.0%
Lưu ý:
suất sinh lời trung bình của cổ phiếu
bao gồm: thu nhập từ cổ tức và chênh
lệch giá cổ phiếu theo thời gian
1-39
Suất sinh lời thị trường là chênh lệch
giá trị thị trường của các cổ phiếu theo
thời gian
Beta for KWE
20%
40%kKWE
1-40
kKWE = 0.83kM + 0.03
R2 = 0.36-40%
-20%
0%
-40% -20% 0% 20% 40%
kM
Tính beta như thế nào ?
Đường hồi quy và beta, tính bằng
EXCELL với hàm “regression” và b =
0.83.
Thường sử dụng suất sinh lời trung
1-41
bình hằng tháng của 4 hay 5 năm để
tạo đường hồi quy. Đôi khi có thể
dùng số liệu trung bình 52 tuần của 1
năm.
Illustrating the calculation of beta
.
.
ri
_
20
15
Year rM ri
1 15% 18%
1-42
.
rM
_
-5 0 5 10 15 20
10
5
-5
-10
Regression line:
ri = -2.59 + 1.44 rM^ ^
2 -5 -10
3 12 16
Beta coefficients for
HT, Coll, and T-Bills
ri
_
40
HT: b = 1.30
1-43
kM
_
-20 0 20 40
20
-20
T-bills: b = 0
Coll: b = -0.87
Comparing expected returns
and beta coefficients
Security Expected Return Beta
HT 12.4% 1.32
Market 10.5 1.00
USR 9.8 0.88
1-44
T-Bills 5.5 0.00
Coll. 1.0 -0.87
Riskier securities have higher returns, so the
rank order is OK.
The Security Market Line (SML):
Calculating required rates of return
SML: ri = rRF + (rM – rRF) bi
r = r + (RP ) b
1-45
i RF M i
Assume the yield curve is flat and that
rRF = 5.5% and RPM = 5.0%.
What is the market risk premium?
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
1-46
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.
Calculating 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%
1-47
rUSR = 5.5% + (5.0%)(0.88) = 9.90%
rT-bill = 5.5% + (5.0%)(0.00) = 5.50%
rColl = 5.5% + (5.0%)(-0.87) = 1.15%
Expected vs. Required returns
r) r( dUndervalue 12.1% 12.4% HT
r r
^
^
^
>
1-48
r) r( Overvalued 1.2 1.0 Coll.
r) r( uedFairly val 5.5 5.5 bills-T
r) r( Overvalued 9.9 9.8 USR
r) r( uedFairly val 10.5 10.5 Market
^
^
^
<
=
<
=
Illustrating the
Security Market Line
.
SML
SML: ri = 5.5% + (5.0%) bi
ri (%)
1-49
.
.
Coll.
HT
T-bills
.
USR
rM = 10.5
rRF = 5.5
-1 0 1 2
.
Risk, bi
An example:
Equally-weighted two-stock portfolio
Create a portfolio with 50% invested in
HT and 50% invested in Collections.
The beta of a portfolio is the weighted
average of each of the stock’s betas.
1-50
bP = wHT bHT + wColl bColl
bP = 0.5 (1.32) + 0.5 (-0.87)
bP = 0.225
Calculating portfolio required returns
The required return of a portfolio is the weighted
average of each of the stock’s required returns.
rP = wHT rHT + wColl rColl
r = 0.5 (12.10%) + 0.5 (1.15%)
1-51
P
rP = 6.63%
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 = 6.63%
Factors that change the SML
What if investors raise inflation expectations
by 3%, what would happen to the SML?
ri (%) SML
1-52
SML1
2
0 0.5 1.0 1.5
13.5
10.5
8.5
5.5
∆ I = 3%
Risk, bi
Factors 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?
r (%) SML
1-53
SML1
i 2
0 0.5 1.0 1.5
13.5
10.5
5.5
∆ RPM = 3%
Risk, bi
Verifying the CAPM empirically
The CAPM has not been verified
completely.
Statistical tests have problems that
1-54
make verification almost impossible.
Some argue that there are additional
risk factors, other than the market risk
premium, that must be considered.
More 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.
r = r + (r – r ) b + ???
1-55
i RF M RF i
CAPM/SML 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.