part 2-3 評價
DESCRIPTION
Part 2-3 評價. 報酬與風險. Outlines. Statistical calculations of risk and return measures Risk Aversion Systematic and firm-specific risk Efficient diversification The Capital Asset Pricing Model Market Efficiency. Rates of Return: Single Period. HPR = Holding Period Return - PowerPoint PPT PresentationTRANSCRIPT
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Part 2-3 評價報酬與風險
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Outlines Statistical calculations of risk and
return measures Risk Aversion Systematic and firm-specific risk Efficient diversification The Capital Asset Pricing Model Market Efficiency
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Rates of Return: Single Period HPR = Holding Period Return
P0 = Beginning price P1 = Ending price D1 = Dividend during period one
PDPPHPR
0
101
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Rates of Return: Single Period ExampleEnding Price = 48Beginning Price = 40Dividend = 2
HPR = (48 - 40 + 2 )/ (40) = 25%
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Return for Holding Period – Zero Coupon Bonds Zero-coupon bonds are bonds that
are sold at a discount from par value.
Given the price, P (T ), of a Treasury bond with $100 par value and maturity of T years
1)(
100)( TP
Trf
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Example - Zero Coupon Bonds Rates of ReturnHorizon,
T Price, P(T) [100/P(T)]-1Risk-free
Return for Given Horizon
Half-year $97.36 100/97.36-1 = .0271 rf(.5) = 2.71%
1 year $95.52 100/95.52-1 = .0580 rf(1) = 5.80%
25 years $23.30 100/23.30-1 = 3.2918
rf(25) = 329.18%
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Effective annual rates, EARs
Annual percentage rates, APRs
Formula for EARs and APRs 1)(1
1 Tf TrEAR
TEARAPR
T
f TrT
1)1()(1
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Table - Annual Percentage Rates (APR) and Effective Annual Rates (EAR)
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Continuous Compounding Continuous compounding, CC
rCC is the annual percentage rate for the continuously compounded case e is approximately 2.71828
CCrT
TTeAPRTEAR
1
00]1[)1( limlim
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Characteristics of Probability Distributions Mean
most likely value Variance or standard deviation Skewness
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Subjective returns
ps = probability of a state rs = return if a state occurs
Mean Scenario or Subjective Returns
n
sss rprE
1
)(
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Subjective or Scenario Standard deviation = [variance]1/2
ps = probability of a state rs = return if a state occurs
Variance or Dispersion of Returns
n
sss rErp
1
22
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Deviations from Normality Skewness
Kurtosis3
3)]()([
rEsrESkew
3)]()([4
4
rEsrEKurtosis
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Figure - The Normal Distribution
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Figure - Normal and Skewed (mean = 6% SD = 17%)
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Figure - Normal and Fat Tails Distributions (mean = .1 SD =.2)
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Spreadsheet - Distribution of HPR on the Stock Index Fund
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Mean and Variance of Historical Returns Arithmetic average or rates of return
Variance
Average return is arithmetic average
n
ss
n
sssA rn
rpr11
1
n
sAs rr
n 1
2)(112
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Geometric Average Returns Geometric Average Returns
TV = Terminal Value of the Investment rG = geometric average rate of return
nrrrrTV
G
nn
)1()1()1)(1( 21
1/1 TV nGr
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Spreadsheet - Time Series of HPR for the S&P 500
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Example - Arithmetic Average and Geometric Average
%58.9095844.1)15.1()20.1()95(.)10.1(
)1()1()1()1()1(4
43214
g
g
r
RRRRr
%104
%15%20%5%104
4321
RRRRrA
Year 1 2 3 4Return 10% -5% 20% 15%
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Measurement of Risk with Non-Normal Distributions Value at Risk, VaR Conditional Tail Expectation, CTE Lower Partial Standard Deviation, LPSD
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Figure - Histograms of Rates of Return for 1926-2005
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Table - Risk Measures for Non-Normal Distributions
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Risk Averse Reject investment portfolios that are
fair games or worse Risk Neutral
Judge risky prospects solely by their expected rates of return
Risk Seeking Engage in fair games and gamble
Investor’s View of Risk
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Fair Games and Expected Utility Assume a log utility function
A simple prospect
)ln()( WWU
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Fair Games and Expected Utility (cont.)
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Diversification and Portfolio Risk Sources of uncertainty
Come from conditions in the general economy Market risk, systematic risk, nondiversifiable risk
Firm-specific influences Unique risk, firm-specific risk, nonsystematic risk, diversifiable risk
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Diversification and Portfolio Risk Example
Normal Year for Sugar Abnormal Year
Bullish Stock Market
Bearish Stock Market
Sugar Crisis
.5 .3 .2Best
Candy25% 10% -25%
SugarKane 1% -5% 35%
T-bill 5% 5% 5%
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Diversification and Portfolio Risk Example (cont.)
%73.14,%6)(%9.18,%5.10)(
SugarSugar
BestBest
rErE
Portfolio Expected Return
Standard Deviation
All in Best 10.50% 18.90%Half in T-bill 7.75% 9.45%Half in Sugar 8.25% 4.83%
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Components of Risk Market or systematic risk
Risk related to the macro economic factor or market index.
Unsystematic or firm specific risk Risk not related to the macro factor or
market index. Total risk = Systematic +
Unsystematic
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Figure - Portfolio Risk as a Function of the Number of Stocks in the Portfolio
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Figure - Portfolio Diversification
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Two-Security Portfolio: Return Consider two mutual fund, a bond
portfolio, denoted D, and a stock fund, E
)()()(1
EEDDP
ED
EEDDP
rEwrEwrEww
rwrwr
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Two-Security Portfolio: Risk The variance of the portfolio, is not a weighted average of the individual asset variances
The variance of the portfolio is a weighted sum of covariances),(2
),(),(),(222222
EDED
EEEEDDDD
EDEDEEDDP
rrCovwwrrCovwwrrCovwwrrCovwwww
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Table - Computation of Portfolio Variance from the Covariance Matrix
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Covariance and Correlation Coefficient The covariance can be computed
from the correlation coefficient
ThereforeEDDEED rrCov ),(
DEEDEDEEDDP wwww 222222
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Example - Descriptive Statistics for Two Mutual Funds
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Portfolio Risk and Return Example Apply this analysis to the data as
presented in the previous slide
2
22
22222
144400144
3.201222012
138)(
PP
EDED
EDEDP
EDP
wwww
wwww
wwrE
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Table - Expected Return and Standard Deviation with Various Correlation Coefficients
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Figure - Portfolio Opportunity Set
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Figure - The Minimum-Variance Frontier of Risky Assets
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Figure - Capital Allocation Lines with Various Portfolios from the Efficient Set
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Capital Allocation and the Separation Property A portfolio manager will offer the
same risky portfolio, P, to all clients regardless of their degree of risk aversion
Separation property Determination of the optimal risky
portfolio Allocation of the complete portfolio
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Capital Asset Pricing Model (CAPM) It is the equilibrium model that underlies all modern financial theory. Derived using principles of diversification with simplified assumptions. Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development.
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Figure - The Efficient Frontier and the Capital Market Line
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Slope and Market Risk Premium Market risk premium
Market price of risk, Slope of the CML
fM rrE )(
M
fM rrE
)(
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The Security Market Line Expected return – beta relationship
The security’s risk premium is directly proportional to both the beta and the risk premium of the market portfolio
All securities must lie on the SML in market equilibrium
])([)( fMifi rrErrE )()(
2,
M
Mii R
RRCov
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Figure - The Security Market Line
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Sample Calculations for SML Suppose that the market return is
expected to be 14%, and the T-bill rate is 6% Stock A has a beta of 1.2
If one believed the stock would provide an expected return of 17%
%6.15%)6%14(2.1%6)( ArE
%4.1%6.15%17
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Do security prices reflect information ?
Why look at market efficiency? Implications for business and
corporate finance Implications for investment
Efficient Market Hypothesis (EMH)
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Random Walk Stock prices are random Randomly evolving stock prices are
the consequence of intelligent investors competing to discover relevant information
Expected price is positive over time Positive trend and random about the
trend
Random Walk and the EMH
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Random Walk with Positive Trend
Security Prices
Time
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Why are price changes random? Prices react to information Flow of information is random Therefore, price changes are
random
Random Price Changes
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Figure - Cumulative Abnormal Returns before Takeover Attempts: Target Companies
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EMH and Competition Stock prices fully and accurately
reflect publicly available information.
Once information becomes available, market participants analyze it.
Competition assures prices reflect information.
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Forms of the EMH Weak form EMH Semi-strong form EMH Strong form EMH
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Information Sets