Asset Pricing Robotti(2)

8/2/2019 Asset Pricing Robotti(2)

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13Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W Second Quarter 2002

Do financial markets offer higher rewardsin the form of average returns for hold-ing risks related to recessions and finan-cial distress in addition to the risks fromoverall market movements? The answer

to this question is related to the wayfinancial economists understand the investmentworld. Fifteen years ago, financial researchers andpractitioners thought that the capital asset pricingmodel (CAPM) provided a reasonable explanation of why different assets, portfolios, funds, and strategiesearn different returns. According to the CAPM, theextra return earned by any risky asset comes frombearing market risk only. There is now considerableevidence against the CAPM, suggesting that variablesother than the rate of return on a market portfolio

proxy command significant risk premia. The inter-temporal CAPM (I-CAPM) theory (Merton 1973) sug-gests that the premium on any risky asset is relatedto the market risk premium as well as to the riskpremia on these additional variables. In this context,economic risk premia represent the compensationfor holding assets that are exposed to prespecifiedsources of economic risk. Merton does not explicitlyidentify these additional sources of risk but showsthat variables affecting a representative investorsrisk-return trade-off should also command signifi-cant risk premia. Hence, the proper selection of additional risk factors has become one of the mostchallenging tasks in modern finance.

Asset Returns andEconomic Risk

CESARE ROBOTTIThe author is a financial economist and assistant policy adviser in

the Atlanta Feds research department. He thanks Tom Cunningham,Gerald Dwyer, and Paula Tkac for helpful comments.

Beginning with Chen, Roll, and Ross (1986), the view that macroeconomic risks systematically affect-ing asset returns should also be significantly pricedhas attracted widespread attention and generated alarge body of empirical work. Chen, Roll, and Ross

argue that in selecting factors one should considerforces that will explain changes in the rate used todiscount future expected cash flows and influencethese cash flows themselves. On the basis of theirintuitive analysis and empirical investigation, theypropose a five-factor model with a maturity premium,expected and unexpected inflation, industrial pro-duction growth, and a default premium. They reachthe striking result that even if the market portfolioexplains a significant portion of the time-series vari-ability of stock returns, it has an insignificant influ-

ence on expected returns when compared to theeconomic risk variables. However, given the lack of theoretical foundations, Chen, Roll, and Ross provideus only with plausible stories about the sign of theeconomic risk premia.

To date, the evidence concerning the sign andsignificance of risk premia of both traded (financial)and nontraded (economic) risk variables is lessthan conclusive. Consider, for example, a marketportfolio proxy. A positive premium on the marketportfolio would reflect the value of insuring againstnondiversifiable market risk. Chen, Roll, and Ross(1986) find that the exposure to the rate of returnon the value-weighted New York Stock Exchange


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14 Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W Second Quarter 2002

investors attempts to hedge against macroeconomicand financial uncertainty.

In addition, this study empirically investigatesthe validity of Mertons (1973) intuition, accordingto which variables that affect the risk-return trade-off (or investment opportunity set) of an investorshould also receive nonzero risk premia and explainequilibrium-expected returns. The analysis measuresthe impact of prespecified economic and financial

variables on the risk-return trade-off by looking athow they affect (or predict) the mean and the vari-ance of asset returns. 1

The objective of the empirical analysis is to ana-lyze the following two related issues: (1) the sourcesof economic risk that investors should track andhedge against and (2) the sign of the risk premiacommanded by economic and financial risks.Specifically, this study establishes a link between a

variables effect on the mean of asset returns andthe sign of the risk premium it commands. This link,also discussed in Balduzzi and Robotti (2001), isnew relative to existing studies and sheds light onprevious results. This issue can be illustrated in ascenario in which an expected inflation variablenegatively affects average returns and positivelyaffects the variance of asset returns. In that case,the effect on the investment opportunity set (orrisk-return trade-off) would be negative, meaningthe investor would receive a lower average return

for a higher level of risk. Lower expected returns fora bigger quantity of risk should translate into a neg-ative risk premium, that is, a negative compensationfor bearing inflation risk.

Finally, this study relaxes the assumption of con-stant risk premia and analyzes the business cyclebehavior exhibited by risk premia associated withdifferent sources of risk in a manner consistentwith the idea that the expected compensation forbearing different sorts of risk is larger at sometimes and smaller at other times, depending on

economic conditions. Hence, it could be misleadingto omit specific risks from a model on the basis of small average premia. 2

Asset Pricing Models

S ince Merton (1973), financial economists havebegun to realize that factors state variablesor sources of priced risk beyond movements inthe market portfolio should be considered as expla-nations of why some average returns are higherthan others. Investors marginal value of wealth is

affected not only by how the stock market performsbut also by how their earnings, bonuses, real estateproperty, and numerous other sources of income or

(NYSE) index commands a negative and statisti-cally insignificant risk premium. On the other hand,Burmeister and McElroy (1988) find that exposureto market risk commands a positive and insignifi-cant premium whereas McElroy and Burmeister(1988) find that the sign of the market premiumchanges depending on whether a January dummyis included. Ferson and Harvey (1991) estimate amarket risk premium that is generally positive andin one case significant. Balduzzi and Robotti (2001)estimate a positive and statically significant pre-mium on the equally weighted NYSE/AMEX/Nasdaqmarket portfolio.

The evidence on the premia associated withmacroeconomic risk variables is equally mixed.For example, a negative premium associated withunexpected inflation would probably indicate that

stock and bond market assets are generally per-ceived to be hedges against the adverse influenceon other assets that are, presumably, relativelymore fixed in nominal terms. If many people preferassets that are less exposed to inflationary pres-sures, they bid up the prices of those assets or,equivalently, are willing to hold the assets at a loweraverage return. Chen, Roll, and Ross (1986) esti-mate negative and often significant risk premiaon unexpected inflation. McElroy and Burmeister(1988) obtain negative and statistically significant

estimates of the unexpected-inflation premiumwhereas Burmeister and McElroy (1988) obtainpositive and significant estimates. Ferson and Harvey(1991) obtain estimates that are negative and mar-ginally significant. In addition, the magnitudes of the estimated risk premia change substantially fromone study to the other.

To demonstrate the importance of economic riskfactors for expected asset returns, this article reviewsand interprets recent advances in the asset pricingliterature. The analysis focuses particularly on the

link between multiple sources of economic risk andpopular asset pricing models and interprets thepremia on traded and nontraded risk variables as

A new generation of empirical research hasfound that there are assets, portfolios, funds,and strategies whose average returns seem tobe better explained by multifactor models witheconomic risks than by the market CAPM.


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1. This article considers asset returns as potentially predictable, in sharp contrast with what financial economists thought untilthe mid-1980s, when stock and bond returns were considered to be essentially unpredictable. According to this earlier view,any apparent predictability pattern would quickly vanish out of sample or would be unexploitable after accounting for trans-action costs. Recent empirical findings show that asset returns have a substantial predictable component, at least over longhorizons.

2. The conditional analysis is also motivated by the empirical finding that expected asset returns seem to be better explainedby time-varying risk premia than by time-varying nondiversifiable risk.

3. See, for example, Campbell (1996), Cochrane (1996), Jagannathan and Wang (1996). Balduzzi and Robotti (2001) propose anovel test of the I-CAPM using mimicking portfolios.

4. Fully developed general equilibrium models with endogenously determined factor prices have not yet been proposed.


wealth change over time. Hence, investors would bemore willing to hold stock and bond market assetsif these represented a good hedge against the pos-sibility of negative developments. In other words,investors would be willing to pay a higher price forthose assets that best hedge against macroeconomicas well as financial risk.

Despite the fact that the I-CAPM was proposedby Merton at the beginning of the seventies, rela-tively little work has been done in the last thirty

years to test the validity of Mertons intuition. 3 Sincethe I-CAPM does not identify the risk factors, manyresearchers have simply disregarded the theoretical

foundations of Mertons model and proposed multi-factor models based on dubious equilibrium argu-ments. The finance profession is still in search of atheoretical link between expected returns and spe-cific sources of economic risk. 4 The CAPM is a one-period model and assumes that the average investorcares only about the performance of his investmentportfolio and chooses assets based on their exposureto nondiversifiable market risk. Box 1 summarizesthe salient features of the CAPM.

Testing unconditional (constant) and conditional

(time-varying) implications of the CAPM has been anongoing effort for several decades. From an uncon-ditional point of view, the CAPM would hold if theintercept term ( ) and the slope coefficient ( ) were

equal to zero and one, respectively. The risk premiumon any asset would then coincide with the marketrisk premium. From a conditional point of view, itseems that the time-varying price of market risk ( )explains expected excess returns better than time-

varying nondiversifiable risk as measured by theCAPM beta ( ). This conditional view is one of thereasons this analysis estimates time-varying riskpremia and disregards time variation associated withthe nondiversifiable risk, . For U.S. stock-marketdata for the past thirty years, the constant and con-ditional implications of the CAPM have been repeat-edly rejected, casting many doubts on whether the

CAPM is a realistic model of asset prices. On oneside, some researchers argue that the evidenceagainst the CAPM is overstated because of mismea-surement of the market portfolio proxy, improperneglect of conditioning information, data snooping,or sample-selection bias. On the other side, somefinancial economists argue that no risk-based modelcan explain the anomalies of stock market behavior.

Finally, some authors argue that multifactormodels such as the I-CAPM perform better than theCAPM in explaining expected excess returns. (See

Box 2 for a description of the I-CAPM.) In the I-CAPM,the market portolio serves as one factor and thestate variables, F A , F B , . . . , serve as additional factors.The additional factors arise from investors demand

T he CAPM uses a time series regression to mea-sure the exposure of asset i to market risk M . R it R f,t 1 = i + iM ( F Mt R f,t 1) + it

for t = 1, 2, . . . , T and i = 1, 2, . . . , N .1 The con-ditional risk premium on asset i is given by

E t1( R it ) R f,t 1 = iM M, t 1

for i = 1, . . . , N , where M,t 1 is the possibly time- varying price of beta risk or market risk premium,

the amount by which expected returns must riseto compensate investors for higher risk.

B O X 1

The Capital Asset Pricing Model (CAPM)

1. R i denotes the return on asset i, R f is the return on a riskless asset f , i is an asset-specific intercept term, i is a meanzero asset-specific error term uncorrelated with the market, F M denotes the return on the market portfolio M , iM rep-resents asset i s exposure to nondiversifiable risk M , R i R f is the excess return on asset i , and F M R f is the excessreturn on the market portfolio.


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obtain negative and statistically significant estimatesof the unexpected-inflation premium whereasBurmeister and McElroy (1988) find positive andstatistically significant estimates. Ferson and Harvey(1991) obtain negative and only marginally statis-tically significant estimates. Balduzzi and Robotti(2001) find a negative and statistically significantpremium associated with anticipated inflation.

Consumption growth rate. The rate of growth inconsumption of nondurables and services representsthe only pricing factor behind the consumption-basedcapital asset pricing model (C-CAPM). According tothe C-CAPM, investors are willing to pay to hedgeagainst a future decline in consumption. Even thoughthe C-CAPM has solid theoretical foundations, it is

unable to empirically identify asset return comove-ments. Specifically, the rate of growth of consumptionis positively but insignificantly priced, as shown, forexample, in Ferson and Harvey (1991) and in Balduzziand Robotti (2001).

Consumption-aggregate wealth ratio. Theratio of consumption to wealth proposed by Lettauand Ludvigson (2001) turns out to be a powerful pre-dictor of asset returns even at short horizons. Thisarticle shows that the consumption-aggregate wealthratio commands a positive and statistically significant

risk premium. A positive risk premium mainly reflectsinvestors attempt to insure against future consump-tion risk. In a similar fashion, Santos and Veronesi(2001) find that the ratio of labor income to con-sumption is significantly priced and is positivelyassociated with stock returns. Moreover, as this ratiofluctuates, the risk premium that investors requireto hold risky assets fluctuates as well.

Industrial production growth rate. The riskpremium associated with the growth rate in indus-trial production is generally positive and statisticallysignificant, reflecting the value of insuring againstreal nondiversifiable production risks (see, for exam-ple, Chen, Roll, and Ross 1986).

to hedge uncertainty about future investment oppor-tunities. Factors do not need to be traded portfoliosof assets. Proposed factors include macroeconomic

variables such as innovations in gross domesticproduct (GDP), changes in bond yields, unantici-pated inflation, and so forth. While the CAPM hasbeen widely tested and repeatedly rejected in itsconditional and unconditional specifications, theI-CAPM has attracted less attention in the literaturemainly because the proper identification of the fun-damental risk factors is still an unresolved issue,leading Fama (1991) to characterize the I-CAPM asa fishing license. 5

The next section presents a survey of the riskfactors that have been proposed so far and derives

implications for premia on pervasive, or nondiversi-fiable, sources of investment risk.

Factor Risk Premia

T here are both academic and practical reasons tomeasure risk premia associated with nontradedrisks. First, these premia are an indication of howimportant an economic variable is for stock returns.Second, if new securities are introduced whosepayoffs track an economic variablefor example, abusiness-cycle indicatorit is important to know

how the new securities should be priced. Giventhe payoff function, the price of such a securitydepends on the risk premium assigned to the eco-nomic risk variable. Box 3 shows how to identifyaverage and conditional risk premia associated withfinancial and economic factors.

The discussion now turns to the financial/economicfactors proposed in the literature and the premia theycommand. Estimated coefficients of the risk premiadiffer from study to study in both size and sign.

Unanticipated and anticipated inflation.Chen, Roll, and Ross (1986) estimate negative andoften statistically significant risk premia on unex-pected inflation. McElroy and Burmeister (1988)

T he I-CAPM uses a time series multipleregression to measure the exposure of asset ito the set of risk factors F M , F A , F B , and so on.

R it R f, t 1 = i + i M ( F Mt R f, t 1 ) + i A F At+ iB F Bt + . . . + it

for t = 1, 2, . . . , T and i = 1, 2, . . . , N , where F M , F A , F B , etc., represent multiple risk factors and the

s represent the factor loadings. The risk premiumon asset i is given by

E t1( R it) R f, t 1 = i M M,t 1 + iA A,t 1 + iB B,t 1 + . . .

for i = 1, . . . , N , where M,t 1 , A,t 1 , B,t 1 , . . .represent the conditional market risk premiumand the conditional premiums on the additionalsources of economic risk, respectively.

B O X 2

The Intertemporal Capital Asset Pricing Model (I-CAPM)


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5. Chen, Roll, and Ross state: A rather embarrassing gap exists between the theoretically exclusive importance of systematicstate variables and our complete ignorance of their identity. The comovements of asset prices suggest the presence of under-lying exogenous influences, but we have not yet determined which economic variables, if any, are responsible (1986, 384).


Innovations in GDP growth rate. Vassalou(forthcoming) argues that a factor that capturesnews related to future GDP growth along with themarket factor can explain expected returns nearly aswell as the Fama-French (1993) three-factor model.

Investment growth. Cochrane (1991, 1996) for-mulates and tests a partial equilibrium model inwhich the factors are returns on physical invest-ment, inferred from investment data via a produc-tion function. He shows that a model that considers

investment growth rates instead of investmentreturns produces similar results. The models do notseem to be rejected by the data, and the investmentreturn factors are priced.

Market portfolio. Equally weighted and value-weighted portfolios on major stock market indexeshave been repeatedly proposed as market portfolioproxies. The discussion in the previous sectionshowed that the importance of the market portfoliois mainly due to its role as the only pricing factor ina CAPM world. The evidence on the sign and signif-

icance of the risk premia on the market portfolio isnot conclusive, as evidenced by the studies cited inthe introduction to this article (see page 13).

Real Treasury bill rate. Ferson and Harvey(1991) find that the real Treasury bill rate com-mands a positive and statistically significant riskpremium consistent with the idea that investorsperceive an increase in the real short-term rate as ahigher real return on any form of capital, includingrisky assets holdings.

Default premium. The default premium is usu-ally calculated as the return spread between corpo-rate bonds rated Baa by Moodys Investor Servicesand a long-term U.S. government bond. Chen, Roll,and Ross (1986) and Ferson and Harvey (1991)estimate a significantly positive default premium.

A positive default risk premium is consistent withinvestors desire to hedge against unanticipatedincreases in the aggregate risk premium occasionedby an increase in uncertainty. The same positive

sign is usually associated with the corporate yieldspread between Baa and Aaa rated bonds. Keim andStambaugh (1986) find that a yield spread has somepredictive power for future bond and stock returns.

Term structure of interest rates. The termstructure of interest rates, as measured by the returnspread between a long-term government bond and aone-month bill, commands a negative and insignif-icant risk premium (Chen, Roll, and Ross 1986).Changes in the term structure command a positiveand nearly statistically significant risk premium

(Ferson and Harvey 1991). This article considersa short-maturity term structure as measured by theone-month return of a three-month Treasury bill lessthe one-month return of a one-month bill. The slopeof this term structure is positively and significantlypriced consistent with the idea that investorsdemand a higher premium to hold risky assets whenthe term structure becomes steeper.

Dividend yield. The dividend yield on majorstock market indexes usually commands positive

T he conditional factor risk premia are calculatedas follows: j, t 1 = E t1[( q t

* 1) F jt ] = j 1 + j M F M, t 1 + j A F A, t 1+ j B F B, t 1 + . . .

for j = M, A, B , . . . , and q t* = 1 [ R t E t1 ( R t)]

T

RR1

, t 1[ E t1( R t) R f,t 11 ].1 This formula simply

states that the conditional factor risk premiumsare given by the negative of the conditional covari-

ance between the pricing function, q *t, and thefactor itself.

Without loss of generality, it is assumed that Var( F j, t 1) = 1 and E(F j, t 1) = 0. Hence, the coeffi-

cients j M , j A , . . . , can be interpreted as thechange in the conditional risk premium for a one-standard-deviation change in the lagged values of the factors. In addition, E ( j,t 1) = j 1 representsthe average or unconditional premium associatedwith the variable j .

B O X 3

Economic Risk Premia

1. R and 1 represent ( N 1) vectors of asset returns and ones, respectively. represents the ( N N ) variance-covariancematrix of asset returns. See Balduzzi and Robotti (2001) for a rigorous explanation of the issues and techniques behindthe risk premium calculations.


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As noted in the introduction, this analysis of pre-dictability helps explain why and how prespecifiedsources of economic and financial risk should bepriced. Specifically, the analysis examines the fac-tors impact on the investment opportunity set andthen relates it to the sign of the factor risk premia.

Box 4 describes the tools needed to understandpredictability patterns in asset returns. This studyconsiders two statistics: (1) the average impactof the lagged value of factor j ( j = M , A , B , . . .) onthe mean of asset returns, j , which represents theaverage slope coefficient in the mean equations, and(2) the average impact of the lagged value of factor jon the volatility of asset returns, v j, which representsthe average slope coefficient in the volatility equa-tions. These statistics provide an indication of thedifferential effect of the lagged values of the factorson the investment opportunity set.

The following section empirically identifies theimpact of the economic/financial factors on the risk-return trade-off and relates it to the sign of the factorrisk premia.

Data

In the empirical analysis, the monthly period con-sidered is January 1960December 1996 for stockand bond returns and December 1959November1996 for economic and information variables.

Asset returns. Using portfolio returns on stocks

listed in the NYSE, AMEX, and Nasdaq, ten stockportfolios are formed according to size deciles on thebasis of the market value of equity outstanding at theend of the previous year. If a capitalization is notavailable for the previous year, the firm is rankedbased on the capitalization on the date with the earli-est available price in the current year. The returns are

value-weighted averages of the firms returns withdividends reinvested. The securities with the smallestcapitalizations are placed in portfolio one. The parti-tions on the Center for Research in Securities Prices

(CRSP) file include all securities, excluding AmericanDepository Receipts (ADRs), that are active onNYSE-AMEX-Nasdaq for each year.

Bond portfolio returns are grouped together withstock returns. The bond portfolios are a long-termgovernment bond, a long-term corporate bond, andthe Treasury bill that is closest to six months tomaturity. The long-term government and corporatebonds are provided by Ibbotson Associates while thesix-month Treasury bill rate is from CRSP (FamaTreasury Bill Term Structure Files). The one-month

Treasury bill rate is from Ibbotson Associates SBBImodule and pertains to a bill with at least one monthto maturity.

but statistically insignificant risk premia (see, forexample, Balduzzi and Robotti 2001).

Price/dividend, price/earnings, and earnings/ dividend ratios. Fama and French (1988) arguethat, at long horizons, a relevant portion of the vari-ation in stock returns is forecastable ahead of timefrom the price/dividend ratio. Ratios formed with

just about any sensible divisor work nearly as well,including earnings, book value, and moving averagesof past prices. These economic factors also seem tobe significantly priced. The earnings/dividend ratioproposed by Lamont (1998) also seems to receive anonzero price of risk and to predict asset returns

relatively well. These measures seem to explain notonly aggregate market movements but also assetreturns of individual firms.

Size and book-to-market factors. Small-cap

stocks and value (or high-book/market) stocks havequite high average returns while large-cap andgrowth (or low-book/market) stocks seem to havelow average returns. Fama and French (1993) showthat the CAPM does a poor job explaining theabnormally high and abnormally low returns onsuch stocks. They propose a multifactor model withthe market portfolio and two additional factors: thereturn of small less big stocks (SMB) and the returnof high-book/market less low-book/market stocks(HML). Size and value factors seem to predict the

rate of growth of GDP (see Liew and Vassalou 2000)and to be significantly priced, reflecting the value of insuring against nondiversifiable production risk.

Most of the variables listed here exhibit strong cor-relations with each other and are correlated with orhelp to forecast business cycles. Hence, the premiaassociated with these economic risks should be higherat the bottom of a business cycle, when investorsrequire a higher excess return to hold risky assets.

Predictability of Asset Returns

T his section describes the statistical and eco-nomic significance of time variation in the firstand second conditional moments of asset returns.

The empirical results on time-varying riskpremia suggest that, during periods of eco-

nomic recessions, there are non-negligiblegains from holding assets whose returns arepositively related to market, term structure,default, and real Treasury bill risks.


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6. See, for example, Chen, Roll, and Ross (1986), Burmeister and McElroy (1988), McElroy and Burmeister (1988), Ferson andHarvey (1991, 1999), Downs and Snow (1996), Kirby (1998), and Lettau and Ludvigson (2001).


All rates of return are deflated using monthlyinflation. The monthly rate of inflation is from SBBIYearbook and is not seasonally adjusted.

Economic variables and instruments. Theanalysis concentrates on a set of seven variablesthat have been previously used in tests of multiple-beta models and/or in studies of stock-return pre-dictability. The factor selection approach used isto specify macroeconomic and financial market

variables that are thought to capture the nondiversifiable risks of the economy. 6 These variablesare statistically significant in multivariate predic-tive regressions of means and volatilities, or theyhave special economic significance.

INF is the monthly rate of inflation (Ibbotson

Associates). XEW represents the equally weighted NYSE-

AMEX-Nasdaq index return (CRSP) less themonthly inflation rate from Ibbotson Associates.

HB 3 is the one-month return of a three-monthTreasury bill less the one-month return of a one-month bill (CRSP, Fama Treasury Bill TermStructure Files).

DIV denotes the monthly dividend yield on theStandard and Poors 500 stock index (CITIBASE).

REALTB denotes the real one-month Treasury bill

(SBBI). PREM represents the yield spread between Baa-

and Aaa-rated bonds (Moodys Industrial fromCITIBASE).

CAY represents the log consumption-aggregatewealth ratio (Lettau and Ludvigson 2001).

The lagged values of the previous seven variablesserve as a proxy for the information investors use toset prices in the market. This choice of instrumentsmainly follows Ferson and Harvey (1991). The reason

for using the lagged values of the economic variablesas instruments is that the variables that explain assetreturns should also help to predict returns.

Study Results

T he following patterns emerge from the analysis,as reported in Table 1: The inflation rate ( INF ) has negative and signif-

icant average impact on returns and a positive andinsignificant average impact on return volatility.Indeed, the inflation rate has the strongest nega-tive effect on average returns.

Lagged stock returns ( XEW ) have a positive andsignificant average impact on returns and a negativeand significant average impact on return volatility.

The slope of the term structure ( HB 3) has anoverall positive and significant impact on returns.The impact on volatility is negative and insignifi-cant. Indeed, the slope of the term structure hasthe strongest positive effect on average returns.

The dividend yield ( DIV ) affects returns posi-tively and significantly. The overall effect on

volatility is also positive but insignificant. The default premium ( PREM ) has a positive

impact on returns and a negative impact on volatil-ity. Both effects are statistically insignificant.

The real rate of interest ( REALTB ) affects returnsnegatively and significantly while the effect on

volatility is positive but insignificant. The effect onaverage returns is negative and large in magnitudealthough smaller than the inflation rate.

The log consumption-aggregate wealth ratio( CAY ) positively affects returns and negativelyaffects volatility.

In summary, INF , XEW , HB 3, DIV , and REALTBsignificantly affect the first conditional moment of

T he mean and volatility of asset returns at timet are modeled as linear functions of the fac-tors at time t 1.

E t1( Ri,t ) = i + iM F M,t 1 + i A F A,t 1 + iB F iB, t 1 + . . .

E t1[| R i,t E t1( R i,t )|] = v i + v iM F M,t 1 + v i A F A,t 1+ v i B F B, t1 + . . .

for i = 1, . . . , N , where i j and v i j , j = M, A, B , . . .represent the coefficients of the mean and vola-tility equations, respectively. || represents theabsolute value operator. The average effects on

the investment opportunity set are based on themean estimated coefficients from the mean and

volatility equations.

B O X 4

Predictability


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These estimations reveal the following patternsreported in Table 2:

The average inflation premium is negative, as onewould expect given the negative impact of infla-tion on the mean of asset returns. The premiumequals 12 basis points. There is also evidence of statistically significant time variation. The infla-tion premium is more negative for higher marketreturns and dividend yield and less negative forhigher consumption-aggregate wealth ratio.

The average market risk premium is positive and

significant, consistent with its positive effect oninvestment opportunities. The premium increaseswith the yield spread between Baa- and Aaa-rated bonds.

The average risk premium on the slope of theterm structure is positive and significant. Thisresult is consistent with the evidence that a steeper

yield curve has a positive effect on investmentopportunities. The premium increases with theinflation rate.

The average risk premium on the dividend yield

is positive and insignificant, consistent with theresults of the predictability analysis. As withother premia, there is significant time variation.The premium becomes less negative as thedefault premium and the real rate increase andmore negative as stock returns increase.

The default premium receives a significant posi-tive average risk premium. This result is consis-tent with the mildly positive effect on investmentopportunities. The premium increases with thedividend yield and with the yield spread between

Baa- and Aaa-rated bonds. The real rate of interest commands a positiveaverage risk premium, consistent with Ferson and

asset returns. The consumption-aggregate wealthratio and the default premium affect averagereturns positively but insignificantly. The value-weighted market index is the only variable that sig-nificantly affects returns volatility. This preliminaryanalysis of predictability is useful for two reasons.First, economic and financial factors that affect thefirst and second conditional moments of assetreturns should also be priced by the market.Second, these predictability patterns make it possi-ble to establish a link between the effect of a vari-able on the risk-return trade-off and the sign of the

risk premium it commands.The previous results are based on an in-sample

investigation of asset returns properties. An out-of-sample analysis is beyond the goal of this article forseveral reasons. First, models that predict well insample are not necessarily the correct models out-of-sample. Second, good in-sample predictors arenot necessarily good out-of-sample predictors.Finally, results are sensitive to the length of thechosen out-of-sample testing windows, to the hori-zon and type of assets considered, and to the fre-

quency of the data.7

Risk Premia

In this section, the average and conditional factorrisk premia are estimated, and the sign of theaverage premia is related to the average impact of each factor on the investors risk-return trade-off.The distinction between average and conditional riskpremia is important because, even if the averagepremium is close to zero, the conditional premia maytake values over time that are quite different from

zero. Moreover, modeling premia as time-varying isconsistent with the empirical evidence that assetreturns fluctuate over the business cycle.

Var INF XEW HB 3 DIV PREM REALTB C AY

j 1.9119 0.7324 1.0273 0.9527 0.3192 1.2082 0.2469(4.34) (3.47) (3.09) (2.84) (1.20) (3.27) (1.23)

v j 0.3701

0.305780.2366 0.3656 0.0521 0.1384 0.1502(1.40) (2.26) (0.94) (1.72) (0.33) (0.62) (1.26)

Note: The table reports estimates of a predictive model of the conditional mean and volatility of the returns on ten size-sorted equity portfo-lios and on three bond portfolios (see Box 4). INF denotes the monthly rate of inflation (percentage points per month). XE W is the equallyweighted NYSE-AMEX-Nasdaq index return less the monthly inflation rate (percentage points per month). HB 3 is the one-month return of athree-month Treasury bill less the one-month T-bill rate (percentage points per month). DIV is the monthly dividend yield on the Standard andPoors 500 stock index (percentage points per month). REALTB is the real one-month Treasury bill rate (percentage points per month). PREM represents the yield spread between Baa- and Aaa-rated bonds (percentage points per month). CAY represents the monthly log consumption-aggregate wealth ratio (percentage points per month). T-statistics, in parentheses, are adjusted for heteroskedasticity and serial correlation.The coefficients that are significant at the 5 percent level are highlighted in bold. The sample period is 1959:121996:11.

T A B L E 1

Average Slope Estimates of Mean and Variance Equations


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7. Daily, weekly, and monthly stock returns are close to unpredictable, and technical systems for predicting such movementsare still nearly useless. Predictability patterns would become weaker when performing an out-of-sample analysis based on thesame predictive model used in its in-sample counterpart. For example, results not reported in the text show that the predic-

tive model that uses the seven factors described above fails to successfully predict directions in up and down markets.8. The corresponding 95 percent exact confidence bounds, not reported in the graphs, are relatively large and indicate that the

time-varying patterns of the economic risk premia should be taken with caution.


Harvey (1991). This result may appear puzzlinggiven the negative effect on average asset returns.Yet investors should care about both the slopeand the position of the risk-return trade-off. Ahigher real rate of interest means higher averagereturns per unit of risk, which may more thancompensate for the negative effect on the slopeof the risk-return trade-off. As with other riskpremia, there is significant time variation. Thepremium increases with the dividend yield.

The consumption-aggregate wealth ratio com-

mands a positive average risk premium. Thisresult is consistent with the positive impact of theconsumption-aggregate wealth ratio on the meanof asset returns. As with other risk premia, there issignificant time variation. The premium increaseswith inflation and the real rate and decreases withthe consumption-aggregate wealth ratio.

A few conclusions can be drawn from the resultsabove: First, the sign and significance of the averagerisk premia associated with the selected economic

variables are largely consistent with the predictabil-ity patterns previously documented. Hence, thereis support for Mertons (1973) I-CAPM intuition.Second, conditional risk premia exhibit significanttime variation. Charts 17 show the time-varyingpatterns of the seven economic risk factors of thisstudy. 8 The vertical bars denote reference businesscycles determined by the National Bureau of

Economic Research (NBER). Overall, economic riskpremia strongly fluctuate over the business cycle.The inflation and the consumption-aggregate wealthpremia exhibit procyclical patternsthat is, theydecrease during periods of recessions and increaseduring economic booms. On the other hand, the mar-ket, term structure, default, and real Treasury bill

Risk Premia INF XE W HB 3 DIV PREM REALTB CAY

Average Premia 0.1168 0.1217 0.1004 0.0118 0.0916 0.1601 0.0341

(6.02) (4.83) (5.27) (0.63) (4.50) (8.16) (2.38)

F INF 0.0347 0.0732 0.1599 0.0261 0.0776 0.0417 0.0598(0.67) (1.31) (2.73) (0.58) (1.72) (0.89) (2.01)

F XE W 0.0720 0.0226 0.0191 0.0536 0.0359 0.0238 0.0105(2.87) (0.66) (0.94) (2.17) (1.74) (0.89) (0.53)

F HB 3 0.0128 0.0420 0.0525 0.0136 0.0363 0.0143 0.0153(0.41) (0.52) (1.16) (0.35) (1.09) (0.43) (1.16)

F DIV 0.0922 0.0071 0.0150 0.0393 0.0724 0.1261 0.0219(3.26) (0.14) (0.46) (0.97) (2.07) (3.75) (1.04)

F PREM 0.0090 0.0776 0.0336 0.0855 0.1055 0.0325 0.0320(0.24) (2.14) (0.89) (2.70) (2.50) (0.89) (1.77)

F REALTB 0.0493 0.0267 0.0762 0.0943 0.0047 0.0089 0.0482

(1.15) (0.55) (1.72) (2.27) (0.11) (0.22) (1.98)

F CAY 0.0369 0.0364 0.0051 0.011 0.0001 0.0316 0.0655(2.09) (1.82) (0.35) (0.72) (0.01) (1.69) (3.03)

Note: The table reports coefficients of the economic risk premia on the economic variables (see Box 3). INF denotes the monthly rateof inflation (percentage points per month). XE W is the equally weighted NYSE-AMEX-Nasdaq index return less the monthly inflation rate(percentage points per month). HB 3 is the one-month return of a three-month Treasury bill less the one-month T-bill rate (percentagepoints per month). DIV is the monthly dividend yield on the Standard and Poors 500 stock index (percentage points per month). REALTB is the real one-month Treasury bill rate (percentage points per month). PREM represents the yield spread between Baa- and Aaa-rated bonds(percentage points per month). C AY is the monthly log consumption-aggregate wealth ratio (percentage points per month). T-s tatistics,in parentheses, are adjusted for heteroskedasticity and serial corr elation. The coefficients that are significant at the 5 percent level arehighlighted in bold. The sample period is 1959:121996:11.

T A B L E 2

Economic Risk Premia


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Jan. 1960

0.4

0.2

0.4

0.2

0

Jan. 1964 Jan. 1968 Jan. 1972 Jan. 1976 Jan. 1980 Jan. 1984 Jan. 1988 Jan. 1992 Jan. 19960.6

I n f l a

t i o n

R i s k P

r e m

i u m

C H A R T 1

Time-Varying Inflation Risk Premium

Jan. 1960

0.2

0.4

0.2

0

Jan. 1964 Jan. 1968 Jan. 1972 Jan. 1976 Jan. 1980 Jan. 1984 Jan. 1988 Jan. 1992 Jan. 1996

M a r k e

t R i s k P r e m

i u m

C H A R T 2

Time-Varying Market Risk Premium

Jan. 1960

0.4

0


T e r m

S t r u c

t u r e

P r e m

i u m 0.8

0.4

C H A R T 3

Time-Varying Term Structure Premium

Note to all char ts: The set of instruments includes a constant and the lagged values of INF , XE W , HB 3, DIV , PREM , REALTB , and C AY .The ver tical lines denote reference business cycles determined by the National Bureau of Economic Research.


11/13


Jan. 1960

0.2

0.2

0


D i v i d e n

d Y i e l d P r e m

i u m

0.4

0.6

0.4

C H A R T 4

Time-Varying Dividend Yield Premium

Jan. 1960

0


D e

f a u

l t P r e m

i u m

0.8

0.4

0.4

C H A R T 5

Time-Varying Default Premium

Jan. 1960

0.6

0


T r e a s u r y

B i l l P r e m

i u m

0.8

0.2

0.4

0.2

C H A R T 6

Time-Varying Treasury Bill Premium


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mia seem to be strongly countercyclical. Finally, thedividend yield premium appears to be procyclicaluntil the mid-1970s and countercyclical afterward.

In summary, this article sheds light on some of the risk factors that investors should track to hedgeagainst financial and economic uncertainty, explainswhere the extra return for holding risky assets comesfrom, and reveals the direction of the compensationfor bearing macroeconomic risk. Investors receivea positive compensation for holding assets whosereturns are positively related to market risk, inter-

est rate risk, and consumption risk. On the otherhand, investors would earn a negative premiumfrom holding stock and bond market assets whosereturns are inversely related to increases in infla-tion. According to this interpretation, stock andbond market assets seem to provide a good hedgeagainst inflation compared to assets that are morefixed in nominal terms.

The empirical results on time-varying risk premiaalso suggest that, during periods of economic reces-sions, there are non-negligible gains from holding

assets whose returns are positively related to market,term structure, default, and real Treasury bill risks.On the other side, the compensation for holdingassets whose returns are inversely related to increasesin inflation becomes smaller during periods of reces-sion, as does the compensation for holding assetswhose returns are positively related to increases inthe consumption-aggregate wealth risk.

Future work should try to investigate more for-mally the link between predictability and risk premiain the context of partial equilibrium and general equi-

librium asset pricing models. An extensive analysis of time-varying risk premia would also be informative.

premia seem to be strongly countercyclical. Indeed,countercyclical variation in expected returns is con-sistent with intertemporal asset pricing models. Withdecreasing risk aversion, high expected returns arerequired in recessions to induce investors away fromcurrent consumption and into risky investments.Until the mid-1970s, the dividend yield premium wasprocyclical and countercyclical afterward.

Conclusion

Anew generation of empirical research has found

that there are assets, portfolios, funds, and strate-gies whose average returns seem to be betterexplained by multifactor models with economicrisks than by the market CAPM. This article showsthat variables affecting the risk-return trade-off are also significantly priced and establishes a linkbetween an economic variables effect on the risk-return trade-off and the sign of the average risk pre-mium it commands. Specifically, variables such asthe market portfolio, the term structure, the defaultpremium, and the consumption-aggregate wealth

ratio positively affect average asset returns andcommand positive risk premia. The inflation port-folio negatively affects average returns and com-mands a negative risk premium.

The article also provides extensive evidence of time variation in economic risk premia, consistentwith the idea that expected compensation for bear-ing different sorts of risk is larger at some times andsmaller at others, depending on economic condi-tions. Specifically, the analysis shows that the infla-tion and the consumption-aggregate wealth premia

exhibit procyclical patterns. In contrast, the market,term-structure, default, and real Treasury bill pre-

Jan. 1960

0.2

0


C o n s u m p

t i o n - A g g r e g a

t e

W e a

l t h P r e m

i u m

0.3

0.2

0.1

0.1

C H A R T 7

Time-Varying Consumption-Aggregate Wealth Premium


13/13

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