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T ti l A t All tiT ti l A t All tiTactical Asset Allocation Tactical Asset Allocation sessionsession 55
Andrei Simonovd e S o ov
8/30/2007Tactical Asset Allocation1
AgendaAgenda
What is tactical asset allocation?M i i TAA d SAAMean-variance perspective on TAA and SAA Predictability– January dummy– Business cycle variables– Explaining risk premia: US, World, Sweden.– Currency risk premia– Caveats: data snooping, statistical issues.
8/30/2007Tactical Asset Allocation2
What is TAA?What is TAA?What is TAA?What is TAA?Exists since early-to-mid- 80-ies.By now $100-200 bln are under management by TAA managersA TAA managers’s investment objective is to obtain better-than-expected return with (possibly) lower-than-b h k l l b f h fbenchmark volatility by forecasting the returns of two or more asset classes and varying asset class exposure in systematic manner (Phillips Rogers & Capaldi 1996)systematic manner (Phillips, Rogers & Capaldi, 1996)Can TAA funds be interpreted as stand-alone asset class?class?
8/30/2007Tactical Asset Allocation3
Conditioning Information and Portfolio Conditioning Information and Portfolio ggAnalysisAnalysis
Er Add conditioningAdd conditioninginformation and weightschange through time. Frontier shifts.
Vol
8/30/2007Tactical Asset Allocation4
Optimal portfolio for riskOptimal portfolio for risk--averse investoraverse investor
⎟⎞
⎜⎛
=− 1wVwwRw
111 ..
1 t.s. 2
)(max
N
TTT E
σσ
γ
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=== V1w
1
111
21
........
..),1,...,1,1,1(,...),,(
NNN
NTT wwHere
σσ
σσ
( )−+−=
⎠⎝
1wVwwRw
1
12
)(min TTT
NNN
EL λγ
( )−=⇒
⎩⎨⎧
=−=−− − 1RVw
1w1VwR 1
:up Summing .)(01
0)(T
EEγ
λλγ
⎞⎛
⇒−=
−−−
−−
−
RV1V1V1V11V1
RV1
111
11
1
)(
)(
T
TT
T
E
E γλ
⎟⎟⎠
⎞⎜⎜⎝
⎛−+= −− 1V1
RV11RV1V1
1Vw 1
11
tf limin var
1
1* )()( T
T
Global
T
EEγ321
8/30/2007Tactical Asset Allocation5
portfolio
Equilibrium and TAAEquilibrium and TAAEquilibrium and TAAEquilibrium and TAAL t th t th i t l tLet us assume that there exists long-term expected returns vector e. However, due to
di t bilit f t t E(R)predictability of asset returns, e≠E(R)
( ) ( )Δ−Δ− −−−−− 11111 TTTT V11VV1ee1V1V ( ) ( )Δ−Δ+
−+= −−− 11
portfoliomin var
1*
tTacticalBe
T
etStrategicB
T
Global
T 11V1
V11V11V1
V1ee1V1V1
1Vw444 3444 21444 3444 21321 γγ
( )( ) ( )
( ) ( ) ⎥⎥⎤
⎢⎢⎡
−−−−−−
=Δ−Δ 0)()(0
11
11
portfolio
nnTT erEerE
erEerE11( ) ( ) ( )
( ) ( ) ⎥⎥⎦⎢
⎢⎣ −−−
ΔΔ0)(
0)(
11
11
nn
jj
erEerEerEerE11
8/30/2007Tactical Asset Allocation6
How to do it?How to do it?
We need a model that explains the ti b t t d ’ i bl dconnection between today’s variables and
tomorrow returns.Candidates: economic business cycle variables and Jan. Effect.
8/30/2007Tactical Asset Allocation7
E l I dibl J EffE l I dibl J EffExample: Incredible January EffectExample: Incredible January Effect
Excess returns associated with small firms w.r.t. Large-cap stocksg pRitter: Tax effect. Is it so?Incredibly Shrinking January EffectIncredibly Shrinking January Effect (William J. Bernstein ).
8/30/2007Tactical Asset Allocation8
Example: dividend yieldExample: dividend yield
Fama-French (1988). 1927-1986Fama French (1988). 1927 1986Holding period
Coeff. t(coeff) R2
M 0 21 1 40 0 00M 0.21 1.40 0.00Q 1.07 2.10 0.011 2.47 1.27 0.012 7 38 2 04 0 092 7.38 2.04 0.093 9.94 2.21 0.134 12.86 2.43 0.19
• May not be sustained out of sample
8/30/2007Tactical Asset Allocation9
Risk and return over the business cycleRisk and return over the business cycleRisk and return over the business cycleRisk and return over the business cycle( ) ( )tttt RrRE varθλ =−= ????( ) ( )mtmtmttm RrRE var, θλ == ????
G-7 output 1973Q2 to 1996Q2G 7 output, 1973Q2 to 1996Q2output level
potential line
end. recess beg. expan end. expan beg. recess Average 15 23% 10 36% 6 96% 2 86%Average returns
15.23% 10.36% 6.96% 2.86%
Return 12.59% 10.63% 16.85% 26.98%Return volatility
12.59% 10.63% 16.85% 26.98%
8/30/2007Tactical Asset Allocation10
Evaluation of RecentEvaluation of RecentEvaluation of Recent Evaluation of Recent RecessionRecessionRecessionRecession
In July 2000, the Yield Curve inverted forecasting recession to begin in June 2001recession to begin in June 2001.Official NBER Peak is March 2001 (Yield Curve within one quarter accurate).In March 2001, the Yield Curve returned to normal forecasting the end of the recession in November 2001.O J l 17 2003 h NBER d h ffi i l d fOn July 17, 2003 the NBER announced the official end of the recession was November 2001.
8/30/2007Tactical Asset Allocation11
Exhibit 1
N t l f lid d t C HLead Lag Analysis in Months
Next couple of slides are due to Cam Harvey
NBER NBER Length Length of Business Cycle 5-Year Yield Spread
Peak Trough of Cycle Inversion Lead Normal Lead InversionDec-69 Nov-70 11 Oct-68 14 Feb-70 9 16Nov-73 Mar-75 16 Jun-73 5 Jan-75 2 19Nov 73 Mar 75 16 Jun 73 5 Jan 75 2 19Jan-80 Jul-80 6 Nov-78 14 May-80 2 18Jul-81 Nov-82 16 Oct-80 9 Oct-81 13 12Jul-90 Mar-91 8 May-89 14 Feb-90 13 9Jul-90 Mar-91 8 May-89 14 Feb-90 13 9
Average last four 11 11 7 15
R t R iRecent RecessionMar-01 Nov-01 8 Jul-00 8 Mar-01 8 8
8/30/2007Tactical Asset Allocation12
Exhibit 2
Forecast evaluation
Term Structure Inversion
Average Lead to
Forecast Beginning
Actual RecessionInversion
DateLead to Recession
Beginning of Recession
Recession Begins Error
Jul-2000 11 Jun-2001 Mar-2001 3
Term Structure Normal Date
Average Lead
Forecast End of Recession Actual End ErrorNormal Date Lead Recession Actual End Error
Mar-2001 8 Nov-2001 Nov-2001 0
8/30/2007Tactical Asset Allocation13
Yield Curve Inverts Before Last Six RecessionsYield Curve Inverts Before Last Six Recessions(5(5--year Treasury note minus 3year Treasury note minus 3--month Treasury bill yieldmonth Treasury bill yield--secondary)secondary)(5(5 year Treasury note minus 3year Treasury note minus 3 month Treasury bill yieldmonth Treasury bill yield secondary)secondary)
% R l l GDP h
AnnualGDP growth
Source: Campbell R. Harvey.
8% Real annual GDP growthGDP growth
or Yield Curve %
4
6
0
2Yield curve
-2
0
RecessionRecessionCorrect Yield curve accurate
in recent recessionRecessionCorrect
Recent flattening
-6
-4
8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6
RecessionCorrect 2 Recessions
Correct
in recent recessionCorrect
Data though April 11, 2006
8/30/2007Tactical Asset Allocation14
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
Yield Curve Inverts Before Last Six RecessionsYield Curve Inverts Before Last Six Recessions(5(5--year Treasury note minus 3year Treasury note minus 3--month Treasury bill yieldmonth Treasury bill yield –– constant maturity)constant maturity)(5(5 year Treasury note minus 3year Treasury note minus 3 month Treasury bill yield month Treasury bill yield constant maturity)constant maturity)
% R l l GDP h
AnnualGDP growth
8% Real annual GDP growthGDP growth
or Yield Curve %Source: Campbell R. Harvey.
4
6
0
2Yield curve
-2
0
RecessionRecessionCorrect Yield curve accurate
in recent recessionRecessionCorrect
Recent flattening
-6
-4
8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6
RecessionCorrect 2 Recessions
Correct
in recent recessionCorrect
Data though April 11, 2006
8/30/2007Tactical Asset Allocation15
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
Recent Annualized OneRecent Annualized One Quarter GDP GrowthQuarter GDP GrowthRecent Annualized OneRecent Annualized One--Quarter GDP Growth Quarter GDP Growth (10(10--year and 5year and 5--year Yield Curvesyear Yield Curves--secondary market)secondary market)
Annualized
8 4% Real annualized one-quarter GDP growth
Annualized1-quarter
GDP growth 10-year Yield curve
6 3
% Real annualized one quarter GDP growth
2
4
1
2
0
2
0
1
4
-2
2
-1Both curvesinvert 2000Q3
5-yearData though April 11, 2006
8/30/2007Tactical Asset Allocation16
-4
Mar-95
Sep-9
5Mar-
96Se
p-96
Mar-97
Sep-9
7Mar-
98Se
p-98
Mar-99
Sep-9
9Mar-
00Se
p-00
Mar-01
Sep-0
1Mar-
02Se
p-02
Mar-03
Sep-0
3Mar-
04Se
p-04
Mar-05
Sep-0
5Mar-
06
-2
Recent Annualized OneRecent Annualized One Quarter GDP GrowthQuarter GDP GrowthRecent Annualized OneRecent Annualized One--Quarter GDP Growth Quarter GDP Growth (10(10--year and 5year and 5--year Yield Curvesyear Yield Curves--constant maturity)constant maturity)
Annualized
8 4% Real annualized one-quarter GDP growth
Annualized1-quarter
GDP growth 10-year Yield curve
6 3
% Real annualized one quarter GDP growth
2
4
1
2
0
2
0
1
4
-2
2
-1Both curvesinvert 2000Q3
5-yearData though April 2006
8/30/2007Tactical Asset Allocation17
-4
Mar-95
Sep-9
5Mar-
96Se
p-96
Mar-97
Sep-9
7Mar-
98Se
p-98
Mar-99
Sep-9
9Mar-
00Se
p-00
Mar-01
Sep-0
1Mar-
02Se
p-02
Mar-03
Sep-0
3Mar-
04Se
p-04
Mar-05
Sep-0
5Mar-
06
-2
What shall we expect now?What shall we expect now?US yield curves, 2006
5.4
5
5.2
4.6
4.8
42
4.4
1/3/20064/3/2006
4
4.2
1 mo 3 mo 6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr 30 yr
4/3/20067/3/20068/29/2006
8/30/2007Tactical Asset Allocation18
May 2007: Practically flatMay 2007: Practically flat
5
5.1
4.7
4.8
4.9
5
5-5.1
4.3
4.4
4.5
4.6 4.9-5
4.8-4.9
4.7-4.8
4.6-4.7
4.25/1/20075/3/2007
5/7/20075/9/2007
4.5-4.6
4.4-4.5
4.3-4.4
4.2-4.3
2yr 3yr 5yr 7yr 10yr 20yr 30yr
5/11/2007
5/15/2007
5/17/2007
5/21/2007
8/30/2007Tactical Asset Allocation19
1mo 3mo 6mo 1yr 2yr y5/21/2007
August 2007August 20075-6
5
64-53-42-31-20 1
2
3
40-1
0
1
2
8/30/2007Tactical Asset Allocation20
Current Situation: Economic growthCurrent Situation: Economic growth•The economy expanded at an annual pace of 4 1% the most in•The economy expanded at an annual pace of 4.1%, the most in more than a year, according to the median estimate of 81 economists surveyed by Bloomberg News. The Commerce y y gDepartment last month calculated the growth rate at 3.4%. • But the outlook for the second half of 2007 has soured in recent
k h b i i i h i dweeks as the subprime mortgage crisis has restricted access to credit. The Federal Reserve this month said risks to growth had ``increased appreciably'' and economists at JPMorgan andincreased appreciably and economists at JPMorgan and Lehman are among those that have reduced forecasts. •There are growing signs of a housing slowdown; new home g g g gsales down, housing prices down, and homeowners with ARMs facing much higher interest rates.
8/30/2007Tactical Asset Allocation21
Current SituationCurrent Situation
Inflation perceptions. The long-term rate is a combination of expected inflation expected real interest rates and anexpected inflation, expected real interest rates and an inflation risk factor. Long-term inflation expectations have decreased mainly due to the glut of cheap labor resulting f l b li tifrom globalization.
8/30/2007Tactical Asset Allocation22
Current SituationCurrent Situation
Strong buying of long term bonds by foreigners For the pastStrong buying of long-term bonds by foreigners. For the past few years, strong buying by Asian central banks have pushed up the Treasury bond prices. However, there is a debate as to whether this has had a large impact on bond prices. In addition, this buying has flattened out recently. A recent Fed study estimated that the foreign buying pushedrecent Fed study estimated that the foreign buying pushed yields down by 150bp. Subprime crisis does not end buying of T-debt by foreigners. Demand for 5yr TB last
k hi hweek was very high.
8/30/2007Tactical Asset Allocation23
Current SituationCurrent Situation
Hedge funds. There has been a recent increase in demand for U S bonds from the Caribbean area indicating hedge fundU.S. bonds from the Caribbean area indicating hedge fund activity. With long-rates above short rates, many managers do “carry trades” (borrow short-term and buy long-term b d h i th l ti b t t i t bl )bonds hoping the relation between rates remains stable). As the term structure flattens, many of these managers increase their leverage which means more buying pressure g y g pon the long-term bonds.
8/30/2007Tactical Asset Allocation24
Current SituationCurrent Situation
Demographic forces. As the population ages, more money is allocated into fixed income and long-term bond yields mayallocated into fixed income and long term bond yields may decrease.
Inflation risk. The long-rate rates contain expected inflation, expected real rates and an inflation risk factor. It is widely perceived that inflation risk (an unexpectedis widely perceived that inflation risk (an unexpected episode of inflation turbulence) has decreased.
8/30/2007Tactical Asset Allocation25
A l R l E i G th AftA l R l E i G th AftAnnual Real Economic Growth After Annual Real Economic Growth After Yield Curve InversionsYield Curve Inversions
4.50%
3.00%3.50%4.00%
1 50%2.00%2.50%
0 00%0.50%1.00%1.50%
0.00%Up to one year after
inversionsOther quarters
8/30/2007Tactical Asset Allocation26
Stock Returns and U S Yield CurveStock Returns and U S Yield CurveStock Returns and U.S. Yield CurveStock Returns and U.S. Yield CurveAverage Monthly Returns in %
2.5
3
1.5
2
0 5
1
0
0.5
-0.5
AU AT BE CA DK FR DE HK IT JP NL NO SG ES SE CH UK US
WO
Inversion NormalData through
8/30/2007Tactical Asset Allocation27
Inversion NormalNovember 2000
A M thl St k R t AftA M thl St k R t AftAverage Monthly Stock Returns After Average Monthly Stock Returns After Yield Curve InversionsYield Curve Inversions
1.40
1.00
1.20
0.60
0.80Equally weighted
Value weighted
0 00
0.20
0.40
0.00After first month of
inversionNormal
Based on 19 countries
8/30/2007Tactical Asset Allocation28
Based on 19 countries.
Trader’s calendarTrader’s calendar (from thestreet com)(from thestreet com)Trader s calendar Trader s calendar (from thestreet.com)(from thestreet.com)Time(EST)
Indicator(click for definition)
Source(click for press release) Actual Forecast Previous
(revised)Previous(original)
Monday, May 21No releases.Tuesday, May 22
9 a.m. ICSC-UBS Weekly Chain Store Sales Snapshot for the week ended May 19
International Council of Shopping Centers and UBS -1.5% n.a. +0.8% +0.8%
9 a.m. Johnson Redbook Retail Sales Index for the week ended May 19, vs. April Redbook Research +2.0% n.a. +2.2% +2.5%*
Wednesday, May 239 a.m. Mortgage Applications Survey for the week ended
May 18 -- Market Composite Index Mortgage Bankers Association-- n.a. -- 675.5y p Mortgage Bankers Association
Purchase Index -- n.a. -- 432.39 a.m. Consumer Comfort Index for the week ended May
20 ABC News and Washington Post -- n.a. -- -7
Thursday, May 248:308:30 a.m. Initial Jobless Claims for the week ended May 19
Labor Department-- +305,000 -- +293,000
Four-week average -- n.a. -- +306,0008:30 a.m.
Durable goods orders for April Census Bureau
-- +0.9% -- +3.7%Ex-transportation -- n.a. -- +1.5%
10 a.m. New home sales for April Census Bureau -- .860M -- .858M
2:30 p.m.
Treasury auction announcement Bureau of the Public Debt The Treasury announces the size of its next monthly two-year note auction, next Tuesday.
Friday, May 2510 a m
8/30/2007Tactical Asset Allocation29
10 a.m. Existing Home Sales for April National Association of Realtors -- 6.10M -- 6.12M
10:30 a.m.
Weekly Leading Index for the week ended May 18 Economic Cycle Research Institute -- n.a. -- +6.1%
What variables matter?What variables matter?Methodology: 1 Exploratory: regressing1. Exploratory: regressing
returns at t on informational variables at t-1
2. ”Correct one”: first fi di i i kfinding economic risk premia (a la APT) and then regressing it onthen regressing it on informational variables at t-1
8/30/2007Tactical Asset Allocation30
Do informational variables haveDo informational variables haveDo informational variables have Do informational variables have predictive ability?predictive ability?p yp y
Info variables:– January dummyJanuary dummy– Past excess return on Equally
weighted CRSP indexweighted CRSP index– Spread between 1 and 3 mo T-
bills– Dividend yield– Spread between Baa and Aaa p
corporate bonds– 1-mo T-bill rate
8/30/2007Tactical Asset Allocation31
Here how it looks like...
8/30/2007Tactical Asset Allocation32
Performance & Business CyclePerformance & Business CyclePerformance & Business CyclePerformance & Business CycleAverage Annual Returns During U.S. Business Cycle Phases
20
30
0
10
-10
0
30
-20
-30
Austral
ia Aust
ria
Belgium
Can
ada
Den
mark
Finlan
d Fran
ce G
erman
y
Hon
g Kon
gIre
land
Italy
Japan
Netherl
ands
New Zeal
and
Norway
Port
ugal
Spain
S
weden
Switzerl
and
UK USW
orld
Worl
d ex-U
S EAFE
8/30/2007Tactical Asset Allocation33
N W
Expansion geometric mean Recession geometric meanData through June 2002
Performance & Business Cycle (2)Performance & Business Cycle (2)Performance & Business Cycle (2)Performance & Business Cycle (2)
60Average Annual Volatility During U.S. Business Cycle Phases
50
60
30
40
20
0
10
Austral
ia Aust
ria
Belgium
Can
ada
Den
mark
Finlan
d Fran
ce G
erman
y
Hon
g Kon
gIre
land
Italy
Japan
Netherl
ands
New
Zealan
dNorw
ay
Portug
al Spa
in
Swed
en
Switzerl
and
UK USW
orld
Worl
d ex-U
S EAFE
8/30/2007Tactical Asset Allocation34
Expansion std.dev. Recession std.dev.Data through June 2002
Performance & Business Cycle (3)Performance & Business Cycle (3)Performance & Business Cycle (3)Performance & Business Cycle (3)
1Correlations During U.S. Business Cycle Phases
0.8
1
0.4
0.6
0.2
-0.2
0
Austral
ia Aust
ria
Belgium
Can
ada
Den
mark
Finlan
d Fran
ce G
erman
y
Hon
g Kon
gIre
land
Italy
Japan
Netherl
ands
New
Zealan
dNorw
ay
Portug
al Spa
in
Swed
en
Switzerl
and
UK USW
orld
Worl
d ex-U
S EAFE
8/30/2007Tactical Asset Allocation35
Expansion correlation with US Recession correlation with USData through June 2002
3. Performance & Business Cycle (4)3. Performance & Business Cycle (4)3. Performance & Business Cycle (4)3. Performance & Business Cycle (4)
45Covariances During U.S. Business Cycle Phases
35
40
20
25
30
10
15
20
0
5
a a m a k d y g d y n s d y l n n d K S d S E
Austral
ia Aust
ria
Belgium
Can
ada
Den
mark
Finlan
d Fran
ce G
erman
y
Hon
g Kon
gIre
land
Italy
Japan
Netherl
ands
New
Zealan
dNorw
ay
Portug
al Spa
in S
weden
Switzerl
and
UK USW
orld
Worl
d ex-U
S EAFE
E i i ith US R i i ith US
8/30/2007Tactical Asset Allocation36
Expansion covariance with US Recession covariance with USData through June 2002
How important are global factors?How important are global factors?How important are global factors?How important are global factors?Based on Ferson-Harvey RFS95Based on Ferson-Harvey RFS95Question here is: what is more important, local or global factors for predictability of asset returns.Global Informational variables: : ”old friends”: 1 mo t-bill, div. Yield on MSCI World index, spread between 10yr and 3 mo T-bills, Eurodollar/US treasury spread, lagged market , y p , ggreturn, January dummy.Local informational variables: Country x div. Yield, 30-day t-bill rate term spread lagged MSCI country x market returnbill rate, term spread, lagged MSCI country x market return.
( ) ( ) ( ) ( ) ∑∑ −−−−− +=+=L
lltl
K
tjtijttit ZZZZZRE1
,101
11101 λλβλ
∑ ∑∑ −−
==
⎟⎠
⎞⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛+
K L
mtjm
L
ltijl
lj
ZZ ,1,1
11
λβ
8/30/2007Tactical Asset Allocation37
∑ ∑∑= == ⎠⎝⎠⎝j m
mtjml
ltijl1 1
,11
,1β
So, what So, what ,,matters?matters?
”Global only” d l i l dmodel is already
good enoughAdding local factors increases explanatory power of the model
8/30/2007Tactical Asset Allocation38
Changes in Changes in ββ vs changes in risk premiumvs changes in risk premiumgg ββ g pg p( )[ ] ( )[ ]
( )[ ] )()'(
)()'('
λβλ
βλβλβ
EZEVE
EZEVarEZEVar +=
( )[ ] )()'( λβλ EZEVarE
O l 2 4% f i ti i d t b t ’Only 2-4% of variation is due to beta’s.
8/30/2007Tactical Asset Allocation39
Sweden (Robertsson, 2000):Sweden (Robertsson, 2000):
Swedenbond bill mat def fx irs ey mb irw R2
Market Index –2.05 –1.02 –0.42 3.19 1.26 1.24 0.35 0.01 –6.50 6.1-1.09 -0.64 -0.62 -2.27 -0.5 -0.58 -0.29 -0.03 -11.5 [0.00]
Small Stocks 2 91 0 75 1 19 0 65 0 05 0 02 0 67 0 08 13 6 16 8Small Stocks –2.91 –0.75 1.19 0.65 –0.05 –0.02 –0.67 0.08 –13.6 16.8-1.27 -0.5 -0.65 -2.17 -0.58 -0.61 -0.34 -0.05 -10 [0.00]
Bond Index –1.18 0.37 0.02 0.7 0.14 0.32 0.1 –0.01 4.19 13.1-0.32 -0.18 -0.13 -0.56 -0.14 -0.14 -0.08 -0.01 -2.41 [0.00]
8/30/2007Tactical Asset Allocation40
Wh t b t i k i ?Wh t b t i k i ?What about currency risk premium?What about currency risk premium?
Currency specificiyy: zero-sum gameDumas-Solnik: currency risk premia exists. It is time-varying and predictabley g p
8/30/2007Tactical Asset Allocation41
Caveats:Caveats:Caveats:Caveats:iData snooping
– Foster, Smith and Whaley (98): by choosing to , y ( ) y gmax R2 via choice of instruments one can get significance when there is none.g
– Not clear how to use as list of instruments already exists...exists...
In-sample vs. Out-of-sample validation
8/30/2007Tactical Asset Allocation42
Caveats(2)Caveats(2)
Statistical biases: t l ti h t d ti it ( iautocorrelation, heteroscedastisity (via
Monte-Carlo simulations).Non-normality, excess skewness and kurtosis
8/30/2007Tactical Asset Allocation43
How to deal with statistical issues?How to deal with statistical issues?How to deal with statistical issues?How to deal with statistical issues?
Bootstrap methodology:– Form empirical distribution of returns – Generate time series of returns (length T).( g )– Perform the regression of interest
See how many times there exists significance– See how many times there exists significance on level α.
8/30/2007Tactical Asset Allocation44
U.S. Risk PremiumU.S. Risk Premium
Survey BackgroundSurvey Background
Graham/Harvey: Survey CFOs every quarterQ2 2000 through Q4 2003 (15 quarters)Current survey attracts about 400 respondents
Wh CFOs?Why CFOs? – We know from previous surveys and interviews that the
CFOs use the risk premium for their capital budgetingCFOs use the risk premium for their capital budgeting– Hence, they have thought hard about risk premium
Sho ld not be biased the a that anal st forecasts might– Should not be biased the way that analyst forecasts might be
8/30/2007Tactical Asset Allocation45
U.S. Risk PremiumU.S. Risk Premium
OneOne--Year PremiumYear PremiumOneOne Year PremiumYear PremiumOne-year risk premium variable. Currently, about 7%
8
A. One-year risk premium
6
7
4
5
prem
ium
2
3
4
Mea
n p
1
2
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0 Jun., Sept., Dec., Mar., Jun., Sept., Dec., Mar., Jun., Sept., Dec., Mar., Jun., Sept., Dec., 00 00 00 01 01 01 01 02 02 02 02 03 03 03 03
U.S. Risk PremiumU.S. Risk Premium
TenTen--Year PremiumYear PremiumTenTen Year PremiumYear PremiumTen-year risk premium is stable. Currently, about 3.7%
7
B. Ten-year risk premium
5
6
3
4
an p
rem
ium
2
3
Mea
0
1
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Jun., Sept., Dec., Mar., Jun., Sept., Dec., Mar., Jun., Sept., Dec., Mar., Jun., Sept., Dec., 00 00 00 01 01 01 01 02 02 02 02 03 03 03 03
U.S. Risk PremiumU.S. Risk Premium
Momentum in Expectations for 1Momentum in Expectations for 1--year year pp yyPremiumPremium
7
8
5
6
ar p
rem
ium
y = 0.1912x + 3.8912R2 = 0 5242
3
4
an o
ne-y
ea
R = 0.5242
1
2Mea
0-15 -10 -5 0 5 10 15
Excess S&P 500 return in previous two months
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Excess S&P 500 return in previous two months
U.S. Risk PremiumU.S. Risk Premium
E t R t C Di tE t R t C Di tExtreme Returns Cause DisagreementExtreme Returns Cause DisagreementA. Disagreement over the one-year premium and past returns
y = 0.0194x2 + 0.0247x + 3.3696R2 = 0.58926
m
5
ar p
rem
ium
3
4
the
one-
yea
y = -0.0614x + 3.9079R2 = 0.1684
2
emen
t ove
r
0
1
Disa
gree
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-15 -10 -5 0 5 10
Past one-month excess S&P 500 return
U.S. Risk PremiumU.S. Risk Premium
Positive Relation Between Disagreement Positive Relation Between Disagreement ggand Expected 10and Expected 10--year Returnsyear Returns
B. Ten-year premium and disagreement
8
6
7
8
um
4
5
6
year
pre
miu
2
3
Mea
n te
n-y
y = 0.9777x + 1.5936R2 = 0.3165
0
1
1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9
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1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9
Disagreement of ten-year premium forecasts
U.S. Risk PremiumU.S. Risk Premium
Example Confidence Intervals: September Example Confidence Intervals: September 16, 200216, 2002
Standard 95%
Confidence Mean deviation Interval Median Min Max Total
Over the next 10 years, I expect the averageannual S&P 500 return will be: There is a 1-in-10 chance it will be less than: 3.65 2.35 3.40 - 3.89 4 -3 10 351
Over the next 10 years, I expect the averageannual S&P 500 return will be: Expected return: 7.81 2.19 7.58 - 8.03 8 0 15 373
Over the next 10 years I expect the averageOver the next 10 years, I expect the averageannual S&P 500 return will be: There is a 1-in-10 chance it will be greater than: 11.5 3.33 11.15 - 11.84 11 4 20 355
Over the next year, I expect the averagey , p gannual S&P 500 return will be: There is a 1-in-10 chance it will be less than: -2.98 6.86 -3.7 - -2.26 0 -20 10 348
Over the next year, I expect the averageannual S&P 500 return will be: Expected return: 4.95 2.78 4.66 - 5.24 5 0 12 345
Over the next year, I expect the averageannual S&P 500 return will be: There is a 1-in-10 chance it will be greater than: 9 96 4 56 9 47 10 44 10 0 20 343
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10 chance it will be greater than: 9.96 4.56 9.47 - 10.44 10 0 20 343
Notes: 10-year bond yield 3.9%; 1-year bill yield 1.6%. Confidence interval based on standard deviation of the mean.
Conclusion:Conclusion:
TAA can be an important tool in asset ll ti th d lallocation methodology.
It is based on time variation of real economic risk premia.Selection of predictors is important.Selection of predictors is important.We are still in ”top-down” paradigm.D il i i h d il i l iDevil is in the details= implementation matters.
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