chapter 5 risk and rates of return -...
TRANSCRIPT
-
7-1 2014_4_3
CHAPTER 7 Risk and Rates of Return
-
7-2 2014_4_3
Investment returns
The rate of return on an investment can be calculated as follows:
Holding Period (Amount received – Amount invested)
Rate of 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%.
-
7-3 2014_4_3
What is an investment risk?
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.
Two types of investment risk
Stand-alone risk : unique vs. market risk
Portfolio risk
-
7-4 2014_4_3
Breaking down sources of risk
Stand-alone risk = Market risk + Firm-specific risk
Market risk (non-diversifiable, systematic)– portion of a security’s stand-alone risk that cannot be eliminated through diversification. (war, inflation, recessions, etc.)
Firm-specific risk (company-specific, unsystematic) – portion of a security’s stand-alone risk that can be eliminated through proper diversification. (strikes, M&A, lawsuits)
-
7-5 2014_4_3
Illustrating diversification effects of a stock portfolio
# Stocks in Portfolio 10 20 30 40 2,000+
Company-Specific Risk
Portfolio’s Market Risk
20
0
Portfolio’s Stand-Alone Risk
sp (%)
35
-
7-6 2014_4_3
Probability distributions
A listing of all possible outcomes, and the probability of each occurrence.
Expected Rate of Return
Rate of
Return (%) 100 15 0 -70
Firm X
Firm Y
-
7-7 2014_4_3
Expected Rate of Return
15.0% (0.3) (-70%)
(0.4) (15%) (0.3) (100%) k
P k k
return of rate expected k
M
^
n
1i
ii
^
^
-
7-8 2014_4_3
Stand-Alone Risk: the standard deviation
2variancedeviation Standard ss
2222 )ˆ( kEkEkkE s
21
2
22
n
1i
i
2^
i
(0.3)15.0) - (-70.0
(0.4)15.0) - (15.0 (0.3)15.0) - (100.0
P )k (k
Ms
s
=65.84%
-
7-9 2014_4_3
Normal Distribution with Mean of 12%
and St Dev of 20%
-
7-10 2014_4_3
Comments on standard deviation as a measure of risk
Standard deviation (σi) measures total, or
stand-alone, risk.
Larger σi is associated with a wider probability
distribution of returns.
The larger σi is, the lower the probability that
actual returns will be close to expected returns.
Difficult to compare standard deviations,
because return has not been accounted for.
-
7-11 2014_4_3
Comparing standard deviations
F1
Prob. T - bill
F2
0 8 13.8 17.4 Rate of Return (%)
-
7-12 2014_4_3
Investor attitude towards risk
Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities.
Risk lover, Risk neutral
Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.
-
7-13 2014_4_3
Portfolio construction: Risk and return
Expected return of a portfolio is a weighted average of the expected return of each of the component assets in the portfolio.
Standard deviation is not a weighted average of the individual asset’s S.D. It is generally smaller than the average of the assets’ S.D.
-
7-14 2014_4_3
Calculating portfolio expected return
10.75% 0.25(9.5%)0.25(10%)
(11.5%) 0.25 (12%) 0.25 k
kw k
:average weighteda is k
p
^
n
1i
i
^
ip
^
p
^
-
7-15 2014_4_3
Calculating portfolio Risk
1 2 n
1 w12s1
2 w2w1 s21 wnw1 sn1
2 w1w2 s12 w22 s22 wnw2 sn2
N w1wns1n w2wn s2n wn2sn2
< Variance-Covariance Matrix >
구분 E(ki) σi wi
S1 15% 15% 30%
S2 30% 40% 50%
S3 25% 30% 20%
E(Rp)= 0.245; σp= 0.2625
Ρ12
S1 S2 S3
S1 1 0.45 -0.3
S2 1 0.7
S3 1
예)
N
i
N
j
jiijji
N
i
N
j
ijjiP
ww
ww
1 1
1 1
2
ss
ss
-
7-16 2014_4_3
투자비율 P sP
xA xB AB=+1 AB=0 AB=-1
1 0 0.30 0.4 0.4 0.4
0.75 0.25 0.25 0.35 0.3 0.25
0.5 0.5 0.2 0.3 0.22 0.1
0.25 0.75 0.15 0.25 0.18 0.05
0 1 0.1 0.2 0.2 0.2
※ 포트폴리오 효과(분산투자효과; gains from diversification)
투자안 A: A=30% sA=40%; 투자안 B: B=10% sB=20%
Portfolio Risks with different ρ
-
7-17 2014_4_3
Portfolio Risks with different ρ
A
B
Z
AB=1
AB=0
AB=-1
AB=-1
P
sP
0.3
0.4
0.1
0.2
-
7-18 2014_4_3
※ 공분산(covariance)
- 두 확률변수(수익률)의 공조성(co-movement)
- 수익률이 체계적인 관계없이 움직이면 sAB0
기대수익률의주식
수익률의주식상황에서
확률발생할상황이
jRE
BAjjiR
niip
RERRERp
RERRERpRERRERp
RERRERE
j
ij
i
BnBAnAn
BBAABBAA
BBAAAB
:)(
),( :
),,2,1( :
))())(((
))())((())())(((
)()(((
,
,,
2,2,21,1,1
s
-
7-19 2014_4_3
※ 상관계수(correlation coefficient)
- 두 수익률의 표준화된 공조성
AB>0 : 양의 상관관계 (rho)
AB=+1 : 완전 양의 상관관계
AB
-
7-20 2014_4_3
※ 공분산, 상관계수 산출
상태(s) 1 2 3 4 5
확률(ps) 0.1 0.15 0.25 0.35 0.15
수익률(RA,s) -0.4 -0.1 0.2 0.5 0.8
수익률(RB,s) -0.15 -0.05 0.2 0.25 0.15
78726.0
137727.0;35623.0;1375.0)(;29.0)(
038625.0))())(((
))())((())())(((
)()(((
,,
2,2,21,1,1
BA
ABAB
BABA
BnBAnAn
BBAABBAA
BBAAAB
RERE
RERRERp
RERRERpRERRERp
RERRERE
ss
s
ss
s
-
7-21 2014_4_3
Capital Asset Pricing Model (CAPM)
A model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification.
concerns about only stock’s market risk, beta, not its stand-alone risk
The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.
-
7-22 2014_4_3
The Security Market Line (SML): Calculating required rates of return
The line shows the relationship between risk as measured by beta and the required rate of return for individual securities and portfolios.
SML: ki = kRF + (kM – kRF) βi
Assume kRF = 8% and kM = 15%.
The market risk premium is RPM = kM – kRF = 15% – 8% = 7%. (premium investors require for bearing the risk of an average stock)
-
7-23 2014_4_3
Illustrating the Security Market Line
SML: ki = 8% + (15% – 8%) βi
.
. HT
T-bills
.
SML
kM = 15
kRF = 8
-1 0 1 2
.
ki (%)
Risk, βi
. Expected
Required
-
7-24 2014_4_3
Beta
Measures a stock’s market risk, and shows a stock’s tendency to move up and down with the market
Indicates how risky a stock is if the stock is held in a well-diversified portfolio.
Measures a stock’s contribution to the riskiness of a portfolio => measure of the stock’s riskiness
N
i
iiNNp
m
im
i wwww1
22112,
s
s
-
7-25 2014_4_3
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.
If beta < 1.0, the security is less risky than average.
Most betas in the range of 0.5 to 1.5