ttila tall titactical asset allocation 1.pdf · %r l lgdp h annual gdp growth source: campbell r....

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.


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?


Conditioning Information and Portfolio Conditioning Information and Portfolio ggAnalysisAnalysis

Er Add conditioningAdd conditioninginformation and weightschange through time. Frontier shifts.

Vol


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


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


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.


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 ).


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


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%


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.


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


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


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


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


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


-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


-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


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


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


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.


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.



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.



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.



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.


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


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


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


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


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


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


Here how it looks like...


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


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


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


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


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


∑ ∑∑= == ⎠⎝⎠⎝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


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.


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]


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


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


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


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.


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



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


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


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


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


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


Excess S&P 500 return in previous two months


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


-15 -10 -5 0 5 10

Past one-month excess S&P 500 return


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


1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9

Disagreement of ten-year premium forecasts


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


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.


ttila tall titactical asset allocation 1.pdf · %r l lgdp h annual gdp growth source: campbell r....

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