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Unformatted text preview: Outlines of Lecture 5 Objectives
1. Learn motivations of using multifactor models
2. Apply multifactor models in managing risk,
timing factor bets, and creating neutral strategies References
Chapter 16, EGBG; Chapter 10, BKM; Handouts
(Ludwig Chincarini & Daehwan Kim, Quantitative
Equity Portfolio Management, McGrawHill ;
ISBN 0071459391)
Hsiulang Chen Portfolio Analysis 1 Factor Models Single Factor Models
Multi Factor Models
Factor Surprises and Risk Premia
Applications of the Factor Model
― Risk Control
― Factor Timing
― Tracking Portfolios
(LongShort or Neutral Strategies)
A factor is any variable that may predict stock returns.
Hsiulang Chen Portfolio Analysis 2 Introduction
Recall the SCL from the CAPM theory: ri,trf,t = αi + βi (rm,trf,t) + εi,t If the market were the only systematic driver (a.k.a.
factor) you’d expect that εi,t and εj,t would be
uncorrelated
Empirically the hypothesis that cov(εi,t,εj,t)=0 if i≠j is
most often rejected for portfolios and especially
individual stocks.
This leads us to consider Multi Factor Models.
– Factor models describe asset returns as
dependent on several sources of risk
(factors) apart from “market” risk.
Hsiulang Chen Portfolio Analysis 3 Single Factor Models
The single factor model states a return generating process:
ri,t=ai + biF1,t+ εi,t.
where F1 is the single pervasive factor driving all returns.
bi is called the factor loading/sensitivity of asset i.
εi,t is a purely firm specific shock, e.g. cov(εi,t,εj,t)=0.
<Implicit assumption> Two securities covary exclusively
through common reactions to the underlying factor.
The single factor model is agnostic with respect to the
underlying behavior of investors. Instead it relies on the
highlevel assumption that F1 is the unique pervasive source
of risk in the economy.
Hsiulang Chen Portfolio Analysis 4 What are potential important
COMMON factors? Hsiulang Chen Portfolio Analysis 5 Introduction
Our focus will mainly be on portfolios (or asset
classes) rather than individual stocks.
Returns on large portfolios are random variables
conditional mainly upon:
1. Economy
2. (Industry)
These observations are the main motivation
behind factor models.
The main analysis tool is multivariate regression
analysis.
Hsiulang Chen Portfolio Analysis 6 Introduction
The purpose of factor models in portfolio
allocation is to
Forecast of volatility of portfolio returns,
absolute as well as relative to a benchmark
Characterize investment styles of managers
Attribute portfolio risk and return to the
exposure to a set of underlying systematic
risk factors.
Hsiulang Chen Portfolio Analysis 7 Common Risk Factors
In practice you will want to consider more than one
source of pervasive risk (= undiversifiable risk).
You want to consider types of risk which you think
are being rewarded by the market. 1. Observable Economic/Market Factors:
(Thus, factor risk premium can be measured!)
the “market” (i.e. your favorite stock index)
Long/Short Term Inflation
Default Risk Premium
Michigan Consumer Sentiment Index (growth
rates)
Hsiulang Chen Portfolio Analysis 8 Other Candidates for Macro Economic Risk Factors
[Chapter 17, BKM] Hsiulang Chen Portfolio Analysis 9 Regular Releases of Indicators [Chapter 17, BKM] Hsiulang Chen Portfolio Analysis 10 Reliable Engine of Recovery Loses Steam
Manufacturing Sectors Across the World Slow Down in September; Germany and
Taiwan Shed Pace, U.S. Output Ticks Up ; WSJ; 10/04/2011; A14
Hsiulang Chen Portfolio Analysis 11 Common Risk Factors 2. Unobservable Fundamental Factors
(Factor risk premium needs to be estimated!)
An approach of creating a zeroinvestment portfolio
SIZE: Ret(Small)Ret(Big)
HML (distress factor): Ret(Value)Ret(Growth)
Momentum (?): Ret(Up)Ret(Down)
An approach of using observable firm characteristics
The factor risk premium is estimated from panel
regression of the stock returns on the observed
characteristics. 3. Statistical Factors
Principal Component Analysis
Hsiulang Chen
Portfolio Analysis 12 Construction of FamaFrench Factors
Year t1 Year t





Q1 Q2 Q3 Q4

Rank all firms using NYSE breakpoints SIZE: ME June t; BE/ME: BE t1, ME Dec t1
Hsiulang Chen Portfolio Analysis 13 MultiFactor Models
The nfactor model:
ri,t = ai + bi,1F1,t + … + bi,nFn,t + εi,t
tries to explain the return on stock i by its sensitivity to
n underlying sources of pervasive risk.
We often assume that the factors are uncorrelated
(this leads to a simpler formula but is otherwise not
required)
The expected return and covariances can be found
analogously to the single factor model using the
assumption that the εi,t are firm specific:
E(ri)= ai + bi,1E(F1) + … + bi,n E(Fn)
σi2=bi,12σf12+…+bi,n2 σfn2 + σεi2
σi,j = bi,1bj,1σf12+…+ bi,nbj,nσfn2
i≠j
Hsiulang Chen Portfolio Analysis 14 MultiFactor Models K R = β + ∑ β f +e
it
it
i0
j = 1 ij jt
⇒ E ( R) N ×1 = B F
N × K K ×1 = BΩ
V
B′ + D
N×N
K×K
This is a general expression in which factors may not be independent!
Hsiulang Chen Portfolio Analysis 15 ~ E ( R1 ) β10 β11 • • • ~ E ( R ) = β i0 + β i1
i • • •
~ E ( R ) β β N N 0 N1
Hsiulang Chen β12
•
βi2
•
βN2 Portfolio Analysis •
•
•
•
• •
•
•
•
• β1K E ( F1 ) E F • ( 2)
β iK • • • β NK E ( FK ) 16 VN × N = β11 β12 •
• β i1 β i 2 • •
β N1 β N 2 σ 2 ε1
0
+ 0 0
0 0 •
•
•
•
• 0
• 0
0 σ ε2
i
0 0
0 0 Hsiulang Chen • β1K σ F1F1 σ F1F2 • • σ F2 F1 σ F2 F2 •
• β iK • •
• • •
• β NK σ FK F1 σ FK F2 0 0 0 0 0 0 • 0 0 σ ε2 N •
•
•
•
• • σ F1FK β11
• σ F2 FK β12 •
• • •
• •
• σ FK FK β1K Portfolio Analysis • β i1
• βi2
• •
• •
• β iK • β N1 • βN2 • • • • • β NK 17 Validity of MultiFactor Models Use historical data for UAL and GE
• Period: 1990/1 – 1999/12 (10 years)
• Monthly returns Step 1: Compute residual returns using zero, one, and
three factor models Step 2: Regress GE residual return on UAL residual return What R2 in Step 2 would you expect to find? What does the finding of this R2>0 indicate?
Rsquare
Zero Factors
13.50%
Can you replicate this
One Factor
6.41%
experiment?
Three Factors
1.63%
Hsiulang Chen Portfolio Analysis 18 MultiFactor Models
(Results from the residual regression) Hsiulang Chen Portfolio Analysis 19 MultiFactor Models
Clearly the multifactor model has greater potential for
explaining returns than a single factor model
– Why? What happens to R2 if I add an additional factor? Fit diagnostic
– How do you detect a missing factor? Why not throw everything in?
– R2 caveat
– Overfitting/stability
– Number of factor covariances How do we know which model is better empirically?
Hsiulang Chen Portfolio Analysis 20 OutofSample Tests To test if a proposed parameter model
works in the future.
By construction, the parameters are
estimated so the model can fit the data
well over the past. 
OutofSample Test

Parameters estimated here CHECK forecasting ability HERE ˆ
Y = Xβ +ε Yt +1− X t +1β
Hsiulang Chen Portfolio Analysis 21 MultiFactor Models
This discussion raises two crucial questions:
1.How many factors should be used?
2.Which ones? Each firm has its own preferred set of factors
and put a lot of effort into identifying factors and
factor sensitivities. Much like CAPM betas, factor sensitivities can
be time varying and need to be reestimated
regularly.
Hsiulang Chen Portfolio Analysis 22 Controlling Portfolio Risk Using the Factor Model
Each source of systematic risk has its own
volatility and its own reward .
A well diversified portfolio's longterm return
and its volatility are largely determined by its
factor loadings.
By measuring and controlling a portfolio's
relative systematic risk exposures, one can
produce the highest possible return for a
given level of risk.
Hsiulang Chen Portfolio Analysis 23 Controlling Portfolio Risk Using the Factor Model Suppose you are the manager of funds of domestic
equity mutual funds.
– You have no stock picking ability
– You do have factor forecasting/timing ability Consider investing in six portfolios, formed by sorting
all stocks according to their market capitalization and
booktomarket ratio. The data is in “fundret.xls.” Hsiulang Chen Portfolio Analysis 24 Controlling Portfolio Risk Using the Factor Model
You believe the following fourfactor model holds:
ri,t – rf = ai+bi,MFM,t+bi,TSFTS,t+bi,YSFYS,t+bI,OIFOI,t+εi,t
– FM is the excess return on the stock market index
– FTS is the change in the slope of the term structure
– FYS is the change in the yield spread between Baa and
Aaa bonds.
– FOI is Oil inflation (percentage change in Oil price).
Note: Y is an excessreturn format when Xs are risk factors!
Hsiulang Chen Portfolio Analysis 25 Controlling Portfolio Risk Using the Factor Model
Your analysts have come up with the following sample
estimates on a monthly basis. E(r) is in % while Cov is in 104 Sample Period:
Jan 1979 ~ Dec 2010
Hsiulang Chen Portfolio Analysis 26 Controlling Portfolio Risk Using the Factor Model
Suppose you form a portfolio
rP = w1 r1 + w2 r2 + … + w6 r6
Then the portfolio factor loadings will be the
weighted average of the factor loadings of the
constituent assets:
bP,M = w1 b1,M + w2 b2,M + w3 b3,M + w4 b4,M + w5 b5,M + w6 b6,M
bP,TS =w1 b1,TS +w2 b2,TS +w3 b3,TS +w4 b4,TS +w5 b5,TS +w6 b6,TS
bP,YS =w1 b1,YS +w2 b2,YS +w3 b3,YS +w4 b4,YS +w5 b5,YS +w6 b6,YS
bP,OI = w1 b1,OI +w2 b2,OI +w3 b3,OI + w4 b4,OI + w5 b5,OI + w6 b6,OI Number of equations? Number of variables?
Hsiulang Chen Portfolio Analysis 27 Controlling Portfolio Risk Using the Factor Model
Suppose that you want to target at least a 1% expected
return per month, but
1. You would not take oilprice risk.
2. You would like your portfolio to move onetoone with the
market. This means we would like to set 1.bP,OI=0 or Cov(rP,t,FOI,t) /σOI2 =0 ?
2.bP,M=1 or Cov(rP,t,FM,t)/σM2 =1 ? Why? This can be solved using Markowitz optimization in
Excel Solver.
Hsiulang Chen Portfolio Analysis 28 Controlling Portfolio Risk Using the Factor Model
Portfolio 4 Systematic Risk Factors 1
FM 2
3 FYS 4 FTS 5
6
Hsiulang Chen X
Portfolio Analysis FOil
29 Controlling Portfolio Risk Using the Factor Model
The covariances above can be expressed in terms of
factor loadings and covariances between factors,
Cov(rP,FOI) = bP,MCov(FM,FOI)+bP,TSCov(FTS, FOI)
+bP,YSCov(FYS,FOI)+bP,OICov(FOI,FOI)
Cov(rP,FM) = bP,MCov(FM,FM)+bP,TSCov(FTS, FM)
+bP,YSCov(FYS,FM)+bP,OICov(FOI,FM)
Your analysts estimate the following factor covariances:
Unit: 104 Hsiulang Chen Portfolio Analysis 30 Controlling Portfolio Risk Using the Factor Model Is this construction of inputs
consistent with the model? Sample Period: Jan 79 ~ Jun 10
Sample Period: Jan 1979 ~ Dec 2010
Hsiulang Chen Portfolio Analysis 31 Controlling Portfolio Risk Using the Factor Model This is a consistent way! Sample Period: Jan 1979 ~ Dec 2010
Hsiulang Chen Portfolio Analysis 32 A Common Mistake ri,t – rf = ai+bi,MFM,t+bi,TSFTS,t+bi,YSFYS,t+bI,OIFOI,t+εi,t
The risk of security i is determined by the factor
loadings on FM, FTS, FYS, FOI simultaneously. ri,t – rf =αi+βI,YSFYS,t+εi,t
The risk of security i is determined by βYS, the
factor loading on FYS only. Note: bI,YS ≠ βI,YS
Hsiulang Chen Portfolio Analysis 33 You believe the CAPM and you are a passive
manager. Since your benchmark is Russell 1000
Index, you prefer your risky portfolio perfectly vary
with Russell 1000 Index. In other words, you prefer
both of your portfolio and Russell 1000 Index have
the same risk sensitivity to the market factor. After
running regressions, your assistant has provided
you the following information:
RRussell 1000 = 2% + 0.9 RMarket + eRussell 1000 R2 = 0.8
RStock Fund = 2% + 1.2 RMarket + eStock Fund R2=0.64
RBond Fund = 3% + 0.2 RMarket + eBond Fund
R2=0.07
σMarket = 20%
How do you construct such a portfolio based on the
stock fund and the bond fund you can select? Hsiulang Chen Portfolio Analysis 34 Factor Surprises and Risk Premia
Consider rewriting the nfactor model as ri,t = E(ri) + bi,1 f1,t + … + bi,n fn,t + εi,t (*).
where fi,t = Fi,t – E[Fi,t] is the realized ith factor
surprise at time t. How did we arrive at (*) from the nfactor model (**) below? ri,t = αi + bi,1 F1,t + … + bi,n Fn,t + εi,t (**). Thus the realized return on an asset equals the exante
expected return plus factor loadings time factor surprises plus
idiosyncratic noise. If the nfactor model holds, then (*) holds for all stocks and
cov(εi,t, εj,t)=0 for j≠i.
Hsiulang Chen Portfolio Analysis 35 Factor Surprises and Risk Premia
We require that, for each of the factors, E(fk)=0, (why?).
For example: fk is the deviation of economic growth from
what was expected rather than economic growth itself.
bi,k denotes the loading of the i’th asset on the k'th factor.
The εi,t is nonsystematic, idiosyncratic,
or residual risk, which is the security
movement that is not associated with
any of the systematic factors.
For example, εi,t will be negative when a
firm's CEO dies (assuming he was any
good), or a firm loses a big contract.
WSJ, 09/05/2007, A1
Hsiulang Chen Portfolio Analysis 36 Test on Arbitrage Pricing Theory (APT) Step 1: Run the timeseries regression on individual stocks ri,t = E(ri) + bi,1 f1,t + … + bi,n fn,t + εi,t Step 2: Run the cross sectional regression: E(ri) = λ0 + bi,1 λ1 + … + bi,n λn + ui (**). λj is called the market price of factor j risk since it tells us
how much extra expected return the average investor (i.e. the
market) requires to take on an extra unit of factor j risk.
In a one factor model where the factor is the realized excess
return on the market, (**) is just the CAPM SML regression
we’ve seen.
If the nfactor model is correctly specified and only
systematic risk (e.g. factor risk) is priced, then λ0=rf and ui=0.
Hsiulang Chen Portfolio Analysis 37 Factor Surprises and Risk Premia
Example 1: Factor models → Expected returns. Suppose that two factors have been identified for the U.S.
economy:
– the growth rate of industrial production, IP.
– the inflation rate, IR.
– IP is expected to be 4%, and IR 6%. A stock with a factor loading of 1.0 on IP and 0.4 on IR
currently is expected to provide a rate of return of 14%. If industrial production actually grows by 5%, while the
inflation rate turns out to be 7%, what is your revised estimate
of the return on the stock?
Hsiulang Chen Portfolio Analysis 38 Factor Surprises and Risk Premia
Example 1: Factor models → Expected returns. We know E(IP) = 4% and bIP = 1, E(IR) = 6%, bIR = 0.4,
and E(ri) = 14%
The two factor surprises are therefore:
fIP=(0.050.04)=0.01 and fIR=(0.070.06)=0.01
Plug these into the return generating process gives the
expected return conditional on these realization of the
industrial production growth rate (IP) and the inflation
rate (IR):
E(rifIP=0.01,fIR=0.01) = 0.14 + 1x0.01 + 0.4x0.01 = 0.154
Hsiulang Chen Portfolio Analysis 39 Example 2 Hsiulang Chen Portfolio Analysis 40 Factor Surprises and Risk Premia
Example 3: Factor Timing Your analyst gives you the following information
on three securities that are correctly priced
according to a 2 factor model
rA = 0.06 + 1 f1 + 1 f2 + eA
rB = 0.04 + 1 f1 + 2 f2 + eB
rC = 0.10 + 3 f1 + 2 f2 + eC
– Here, the E[r]’s (constants) are what the market
expects – not what we expect!
Hsiulang Chen Portfolio Analysis 41 Factor Surprises and Risk Premia Example 3: Factor Timing
Factor 1 is a foreign income factor
Factor 2 is a U.S. earnings price ratio factor. Assumptions:
– The way the model is constructed these factors are uncorrelated.
– You believe very strongly that Japan will finally come out of its
recession in the next few months and therefore exports of U.S.
produced goods will rise more than the market expects.
– Moreover, you believe the earnings price ratio factor will not change
at all in this time period, consistent with what analysts expect. Using the above three securities, you wish to construct a portfolio
that takes advantage of all of these facts.
What are
(i) the composition of the portfolio?
(ii) the b's of the portfolio?
(iii) the expected return on the portfolio?
Hsiulang Chen Portfolio Analysis 42 Factor Surprises and Risk Premia
Example 3: Factor Timing
We want to construct a portfolio with a lot of factor 1 exposure and no
factor 2 exposure.
– Let’s assume we want a loading of 10 on factor 1 and 0 on factor 2.
– Therefore we solve the three equations.
1 wA + 1 wB + 3 wC = 10. (Is 10 reasonable?)
in excel this is solved as:
1 wA + 2 wB + 2 wC = 0.
1 wA + 1 wB + 1 wC = 1. so wA=2, wB=5.5, wC=4.5 and the portfolio
rp = 2 rA – 5.5 rB + 4.5 rC.
will have the desired factor loading: bp,1=10, bp,2=0.
Hsiulang Chen Portfolio Analysis 43 Factor Surprises and Risk Premia
Example 3: Factor Timing Assuming that you believe that the foreign income factor
will rise by 2%, the expected return on this portfolio is:
2 · 0.06 – 5.5 · 0.04 + 4.5 · 0.1 + 10 · 0.02 = 55%
Is this the highest SharpeRatio portfolio possible? No reason why this portfolio should be the optimal one.
Need to know the idiosyncratic variances, then we can
solve Markowitz with
E(rA)=0.06+1·0.02, E(rB)=0.04+1·0.02, E(rC)=0.10+3·0.02
Hsiulang Chen Portfolio Analysis 44 Tracking Benchmarks; Hedging Liability
Most institutional investors, e.g. pension funds, insurance
companies etc. have to worry about their liabilities when
investing.
Mutual funds have to worry about their benchmarks too.
– Losing money when the benchmark is down is OK.
– Losing money when markets are up can be fatal for a
money manager.
This suggests that the relevant return measure is the
tracking error vis á vis the benchmark, not the actual
return.
Similarly, the relevant risk measure is the standard
deviation of the tracking error.
Hsiulang Chen Portfolio Analysis 45 Discussion on Tracking Error
Consider a BENCHMARK called B. You can invest in
two risky assets stock1 and stock2.
The aim is to construct a portfolio of stock1 and
stock2 that mimics the benchmark B as closely as
possible subject to achieving a target level of
expected return.
Define the TRACKING ERROR = Assets  Liabilities
rTE=wr1+(1w)r2rB
Your expected TE: E(rTE)=wE(r1)+(1w)E(r2)E(rB)
The variance of the TE: σ2TE=w2σ12+(1w)2σ22+σ2B
+2w(1w) cov(r1,r2)2w cov(r1,rB)2(1w) cov(r2,rB)
Hsiulang Chen Portfolio Analysis 46 Discussion on Tracking Error
Setting up the Tracking Error Problem using Markowitz
If you look closely at the equations above, it is really as if
– there are three assets
– the weight on the last asset (B) is fixed at 1
– the weights on the first two assets (stock1&2) add up to 1
– We want to minimize σTE for each given level of E(r)
Let’s do an example:
– Consider the inputs – And lets draw the best possible E(r) vs. σTE tradeoffs
This is just like an efficient frontier!
Hsiulang Chen Portfolio Analysis 47 Discussion on Tracking Error
Note the change in the constraints, reflecting
– Fixed weight of 1 on the benchmark
– The sum of all weights equal 0 instead of 1 [Excel] Formula? – As in the standard setup, we minimize the std.dev. (here
the TE std.dev) for each level of expected return (here the
expected TE)
Hsiulang Chen Portfolio Analysis 48 Apply Tracking Error Discussion to
the Creation of a LongShort Strategy
Portfolio
P Benchmark
B Minimize σ2 (rTE) ≡ σ2 (rP – rB )
rP,t = αP + bP,1 F1,t + … + bP,n Fn,t + εP,t
rB,t = αB + bB,1 F1,t + … + bB,n Fn,t + εB,t Exposure
Neutral
Strategy The Aggregated Portfolio (AP)
Long
+1 Portfolio
p Short
1 Benchmark
B Minimize σ2 (rAP ) ≡ σ2 (rP – rB )
Hsiulang Chen Portfolio Analysis 49 Tracking Benchmarks Hsiulang Chen Portfolio Analysis 50 Tracking Benchmarks
 Hedging systematic component of tracking error risk  Suppose you want use the factor model to create a
portfolio of A, B and C which tracks the Market with no
systematic tracking error risk What should the factor loadings of your tracking portfolio
be? You want your portfolio to react to factor surprises in the
same way as the market.
– This implies that your portfolio should have the same
factor loadings as the market: Hsiulang Chen Portfolio Analysis 51 Tracking Benchmarks
 Minimize total tracking error risk  Suppose you create an optimal tracking portfolio earning
1% above the expected return on the market, i.e. 9%
– What is the optimal portfolio?
– What is the factor sensitivity of your tracking error? This is a standard tracking error problem
– We now care about the entire tracking error, not
just the systematic part
– We wish to know how the tracking error will
respond to changes in the factors
– This will enable us to predict in which scenarios the
tracking error will be exacerbated
– We may want to eliminate one type of factor risk
from the tracking error if we have a view.
Hsiulang Chen Portfolio Analysis 52 Tracking Benchmarks
 Minimize total tracking error risk  We solve using Markowitz. Q. How does the surprise of systematic risk factors affect
your portfolio performance relative to the benchmark? Formula? Hsiulang Chen Portfolio Analysis 53 Tracking Benchmarks
S&P500 Index published in 1957
www.standardandpoors.com; 10/04/2011
captures 75% coverage of U.S.
equities. It has over US$ 4.83 trillion
Number of Constituents
500
benchmarked, with index assets
comprising approximately US$ 1.1 Adjusted Market Cap ($ Billion)
10,233.14
trillion of this total.
Constituent Mkt. Cap(Adjusted $ Billion)
 Average 20.47  Largest 354.11  Smallest .70  Median 9.45 % Weight Largest Constituent 3.46% Top 10 Holdings(% Market Cap Share) 20.52% As of 8/31/2011, Vanguard 500 Index Fund (VFINX) has total
asset $97.9b (504 stocks) with expense ratio of 0.17%, while
Vantagepoint 500 Index I Fund (VPFIX) has total asset $367m
(8/31/2011) with expense ratio of 0.43%. How to effectively mimic
54
S&P 500 Index? Discussions on Tracking Portfolios When the factors are correlated, will this
affect the construction of tracking
portfolios in slides 50~53? The example in slides 50~53 has three
underlying assets and two factors, we
cannot neutralize the factor exposures and
achieve higher returns at the same time.
Can you accomplish both if there are more
underlying assets? Conclusion
Factor models introduce multiple sources of systematic risk.
Each source of risk has a “market price”.
The market price tends to be negative on counter cyclical
factors and positive on pro cyclical factors.
Factor models can be used to decompose volatility as well as
expected returns.
Factor models can be used to take bets on future factor
realizations and to manage risk.
It is easy to incorporate factor models in creating tracking
portfolios into the Markowitz framework.
Hsiulang Chen Portfolio Analysis 56 Further References in Factor Models Chen, NaiFu, Richard Roll, and Stephen Ross,
1986, Economic Forces and the Stock Market,
Journal of Business 59, 383403.
Fama, Eugene F., and K. R. French, 1996,
Multifactor explanations of asset pricing
anomalies, Journal of Finance 51, 55−84.
Chan, Louis K.C., Jason Karceski, and Josef
Lakonishok, 1999, On portfolio optimization:
Forecasting covariances and choosing the risk
model, Review of Financial Studies 12, 937974.
Patton, Andrew J., 2009, Are “market neutral”
hedge funds really market netural? Review of
Financial Studies 22, 22952330. Hsiulang Chen Portfolio Analysis 57 ...
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This note was uploaded on 10/07/2011 for the course FIN 512 taught by Professor Hengchen during the Fall '11 term at Ill. Chicago.
 Fall '11
 HengChen

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