Corporate Real Estate Holdings and the Cross Section of Stock Returns∗

Selale Tuzel†

January 2007

Abstract

This paper explores the link between the composition of firm’s capital holdings and stock returns. I develop a general equilibrium production economy where firms use two factors, real estate capital and other capital, and investment is subject to asymmetric adjustment costs that make cutting the capital stock costlier than expanding it. Because real estate depreciates slowly, real estate investment is riskier than investment in other capital, and firmswithhighrealestateholdingsareex- tremely vulnerable to bad productivity shocks. In equilibrium, investors demand a premium to hold these firms. This prediction is supported empirically. I find that the returns of firms with a high share of real estate capital compared to other firms in their industry exceed that for low real estate firms by 3-6% annually, adjusted for exposures to the market return, size, value, and momentum factors. The model also predicts countercyclical variation in the aggregate share of real estate in total capital, which is a state variable in the model economy. A cross sectional investigation of the conditional CAPM, where the change in aggregate share of real estate in total capital is used as the conditioning variable, delivers substantially improved results over its unconditional version.

∗This paper is based on chapter 2 of my UCLA PhD dissertation. I am truly indebted to Mark Grinblatt and Monika Piazzesi for their generous support, guidance, and encouragement. I would like to thank Fernando Alvarez, Tony Bernardo, Michael Brennan, Harold Cole, Lars Hansen, Ayse Im- rohoroglu, Selahattin Imrohoroglu, Chris Jones, Bruno Miranda, Oguzhan Ozbas, Stavros Panageas, Vincenzo Quadrini, Richard Roll, Pedro Santa-Clara, Martin Schneider, Cliﬀord Smith, Avanidhar Sub- rahmanyam, seminar participants at Boston College, Carnegie-Mellon, Chicago GSB, Chicago macro working group, Columbia GSB, Duke, Emory, HBS, Maryland, Notre Dame, Oregon, Rochester, UCLA, UNC, USC, Wharton, and WFA 2005 meeting for their helpful comments and discussions. I gratefully acknowledge ﬁnancial support from the Allstate and UCLA Dissertation Year Fellowships. †Corresponding Address: USC Marshall School of Business; 701 Exposition Blvd., Los Angeles, CA, 90089; Phone: (323)304-3363; Email: [email protected]. 1 Introduction

Firms own and use many different capital goods. Capital is heterogeneous; a building is not a computer. Even if in some extreme cases one can be substituted with the other in the firm’s production (Barnes & Noble versus Barnes & Noble.com), other characteristics still distinguish them, such as the rates of depreciation. Commercial real estate and equipment naturally emerge as two major classes of capital goods. Their dollar values in the U.S. economy are comparable. The Bureau of Economic Analysis (BEA) estimates approximately 8.8 trillion dollars worth of nonresidential structures (value of buildings excluding the value of the land) and 4.7 trillion dollars worth of nonresidential equipment at the end of 2005. While most firms own and use both capital types in their operations, there is considerable variation in firms’ capital composition. When firms are sorted on the share of buildings and capital leases in their total physical capital (PPE), for the firms in the first quintile the average share of buildings and capital leases is 22% lower than the average firm in that industry, whereas it is 25% higher for the firms in the fifth quintile. In addition to the obvious differences in their roles in the firm’s operations, structures and equipment are different in their durability. Structures, on the average, depreciate much more slowly than equipment. Bureau of Economic Analysis rates of depreciation for private nonresidential structures range between 1.5-3%, whereas the depreciation rates for private nonresidential equipment are in the range of 10-30% (Fraumeni, 1997). Glaeser and Gyourko (2005) point out the extremely durable nature of residential real estate. Therefore, structures require less replacement investment than equipment. This introduces significant heterogeneity into the capital stock of firms. The value of a firm depends on the underlying value of its assets, i.e. its capital stock. Therefore, the dynamics of a firm’s value (return) is fundamentally linked to the changes in the firm’s capital stock, both its size and composition. In this paper, I study the link between the composition of the firm’s capital holdings1 and stock returns. I specifically explore the role of real estate holdings in the firm’s investment decisions and capital. I develop a general equilibrium model, where a representative agent invests in the firms in the economy and consumes their dividends. The firm uses two factors, real estate capital (buildings/structures)2 and other capital (equipment); stochastic productivity shocks lead to heterogeneity among firms. Investment in either form of capital is subject to convex adjustment costs, which are asymmetric; i.e., cutting the capital stock is costlier than expanding it. Numerical solutions of the model predict a "real estate premium", i.e. in equilibrium, investors demand a premium to hold a firm that owns a lot of real estate as part of its capital. I consequently verify this prediction with firm level data. I find that the returns of firms with a high share of real estate compared to other firms in their industry exceed that for low real estate firms by 3-6% annually, adjusted for exposures to the market return, size, value, and momentum

1 The composition of the ﬁrm’s capital is diﬀerent from the composition risk in Piazzesi, Schneider, and Tuzel (2006). The composition risk, measured by the changes in the expenditure share of housing in household’s consumption, is part of the pricing kernel in that paper. 2 Throughout this paper, I use the real estate/buildings/structures terms interchangibly. The BEA reports the quantity of structures, whereas Compustat reports the value of buildings.

1 factors. The model also predicts countercyclical variation in the aggregate share of real estate in total capital. This prediction is also supported by the data. A cross sectional investigation of the conditional CAPM, where the change in aggregate share of real estate in total capital is used as the conditioning variable, delivers substantially improved results over its unconditional version. Firms accumulate capital through real investment. In the presence of capital heterogeneity, the real investment decisions determine not only the size of the firm’s capital but also its composition. If the capital holdings can be costlessly adjusted at any time, then the composition of the firm’s capital becomes trivial. The firm always holds the optimal capital mix for a given level of output, i.e. the mix of capital inputs that minimizes the firm’s costs for a given level of output. Nevertheless, capital adjustment is rarely costless, and the frictions in capital adjustment can distort the firm’s investment decisions together with its capital composition. Costless adjustment of the capital holdings allows firms to pay a smooth dividend stream, thereby reducing their risk. Firms can accommodate exogenous productivity shocks by increasing/decreasing their investments and capital holdings, keeping their dividends relatively smooth. Frictions in capital adjustment reduce the flexibility of the firms in accommodating exogenous shocks. If capital is heterogeneous, the implications of frictions can vary among capital types. For a simple example, take a manufacturing firm with two types of capital: a plant, which depreciates very slowly, and cutting tools, which wear out (depreciate completely) after a few hours of heavy use. If there are frictions to reduce the capital stock, these frictions will have an impact on plant investment, whereas they will have almost no impact on investment in cutting tools. I assume a particular form of friction in capital adjustment that investment is subject to convex but asymmetric adjustment costs. This form of friction captures the idea that it is more costly to cut the existing capital stock (reverse investment) than to add new capital to the current stock. For the manufacturing firm portrayed above, the implications of costly reversibility are starkly asymmetric: The firm with a big plant dreads bad exogenous shocks and tries to mitigate the effect of a bad shock by decreasing the investment in short-lived cutting tools. This change in investment policy distorts the capital composition of the firm, increasing the share of plant in the firm’s capital holdings. Positive exogenous shocks have the opposite effect, reducing the share of plant in the firm’s capital. As the share of plant increases, the firm becomes more vulnerable to bad productivity shocks; therefore, the investors demand a premium to hold them in equilibrium. The presence of costly reversibility leads the firm, on average, to invest less and hold less capital than it would otherwise. The firm anticipates that a decision to cut the capital stock in the future can be very costly and is therefore more hesitant to invest. In addition, the asymmetric depreciation rates of the factors distort the composition of capital holdings in favor of the one that depreciates faster, i.e. equipment. When a firm receives bad productivity shocks, its capital holdings go down; however, the composition of factors get closer to their "optimal" mix (the mix that would be chosen if factors of production could be costlessly adjusted). This unintentional move in factor composition

2 actually makes the firm slightly more productive, especially when the good shocks arrive. Frictions make the firm riskier, however, because high real estate holdings make the firm extremely vulnerable to bad shocks. Investment in the slowly depreciating factor (real estate) becomes a sunk cost in bad times and pays off well in good times; therefore, investorswoulddemandapremiumtoholdafirm with high real estate holdings. The risks associated with investing in and holding real estate capital are well under- stood and frequently mentioned in the business press:

A number of analysts express concerns about Hilton and Starwood in particular, because the two companies’ real estate poses additional recession risks ... Owning hotels is more risky than managing or franchising them because of the cost of carrying and maintaining property ... Hilton in particular could be hard hit by the economic slowdown. Hilton owns many of its hotels, unlike Marriott, which mostly franchises and manages properties owned by others. - WSJ, 3/26/01

Diﬀerent business cycle implications of investment in real estate capital and other, less durable capital types are also cited in the business press:

Yet the aftereffects of overinvestment in technology are likely to be less pronounced than those of previous investment busts. In the 1980s, a frenzy of real estate investment saddled the U.S. with commercial office space that took years to fill. During that time, new investment in such properties almost ground to a halt. By contrast, business equipment and software depreciate in just a few years, if not months. Rapid depreciation means that any excess capacity should be eliminated relatively quickly. - WSJ, 1/5/01

The paper proceeds as follows. Section 2 discusses the key elements of the model and related work. Section 3 presents the model and derives the pricing equations. Section 4 brieﬂy explains the computational solution, which is detailed in Appendix A. Section 5 explains the quantitative results. Section 6 ties the quantitative results to the data. The paper is concluded in Section 7.

2 Key Elements and Related Work

2.1 Capital Heterogeneity

Many different capital inputs enter the firm’s production process. Nevertheless, capital is overwhelmingly modeled as homogeneous. Even though it is convenient to assume homogeneity of capital, this assumption implies that different capital goods are perfect

3 substitutes; i.e. personal computers can be replaced by forklifts. The perfect substitutability assumption is typically rejected by the data, and the degree of substitutability is different across capital types (Denny and May, 1978). There is a small literature on investment with capital heterogeneity. In a highly styl- ized economy where the same ratio of inputs are maintained across consumption and capital goods industries, Samuelson (1962) finds that heterogeneous capital goods can be reduced to a homogeneous capital good. Garegnani (1970) shows that the equal propor- tions of inputs assumption is crucial for Samuelson’s (1962) results, and this assumption practically turns the heterogeneous capital economy to an economy with homogeneous capital and consumption good, the two being perfectly substitutable. Several papers study the aggregation problem of multiple capital goods in the presence of adjustment costs (Blackorby and Schworm, 1983; Epstein, 1983; Wildasin, 1984). Their common result is that one has to impose a very stringent set of assumptions in order to aggregate heterogeneous capital inputs into a homogeneous input as a weighted sum of multiple capital inputs. Wildasin (1984) extends the q theory of investment to the general case of multiple capital goods and derives a relationship between q and the vector of investments in multiple capital goods. Chirinko (1993) uses Wildasin’s (1984) result to estimate an investment equation relating q to investment in multiple capital goods. Epstein (1983) provides a model of optimal capital allocation with the assumption that the capital inputs are weakly separable, where multiple capital inputs can be aggregated into a capital aggregate in the form of a scalar index of multiple capital inputs. Hayashi and Inoue (1991) use this measure of capital aggregate, as opposed to the sum of nominal capital stocks, to estimate the relation between investment and q using a panel of data disaggregated to capital types from Japanese manufacturing firms. Goolsbee and Gross (1997) use firm level data disaggregated to capital types from the airline industry to study the adjustment costs. They find that airlines have a significant region of inaction while adjusting their capital stocks, and aggregating at the firm level leads to the disappearance of the inaction region and an upward bias in adjustment costs. Doms and Dunne (1998) and Nilsen and Schiantarelli (2003), using plant level data disaggregated to capital types from a diverse set of industries from the U.S. and Norway, respectively, have similar conclusions with respect to the smoothing effects of aggregating data at the firm level. Cummins and Dey (1998), using firm level data from Compustat, also find that when capital heterogeneity is ignored, estimates of adjustment costs are upward biased and estimates of factor substitution in production are downward biased. Abel and Eberly (2002) also use panel data from Compustat to estimate several models of optimal investment, one of which incorporates capital heterogeneity and fixed adjustment costs. They find that firms do not choose to invest in all types of capital every period. Finally, Jermann (2006) studies asset prices in the presence of a multi-input aggregate production technology. In his model, sectoral investment (structures, equipment) plays the key role; asymmetries across these sectors are crucial in matching the first two moments of the risk free rate and the aggregate equity returns.

4 2.2 Costly Reversibility

It is widely accepted that firms cannot sell capital at the price they can purchase it. The sale price of used capital is generally substantially lower than its replacement cost, even after taking depreciation into account. Ramey and Shapiro (2001), by collecting and analyzing data from aerospace industry auctions, find that reallocating capital entails substantial costs due to the loss of value and time. They estimate that the average market value of equipment sold in auctions is 28 cents per dollar of replacement cost. Many factors contribute to the low resale prices for capital, including installation costs, capital specificity, thin markets, and adverse selection problems. Furthermore, Eisfeldt and Rampini (2006) find that capital reallocation is procyclical, even though the benefits to reallocation are countercyclical, implying substantial countercyclical costs of reallocation. Firms are stuck with excess capital when they most need to reverse their investments, which is during economic downturns. Traditional capital theory cannot accommodate a difference between the price of installed capital and its replacement cost. In these models, investment is costlessly reversible, and the firms can buy and sell capital at the same price. A more recent stream of literature goes to the opposite extreme and models investment as "irreversible" (Pindyck, 1988; Dixit, 1989; Dixit and Pindyck, 1994; and many others), implying that the sale price of used capital is essentially zero. Recently, several papers have studied the asset pricing implications of models with irreversible investment (Cooper, 2006; Gomes, Kogan, and Zhang, 2003; Kogan, 2004; Berk, Green, and Naik, 1999). Irreversible investment is a special case of the investment frictions considered in another group of papers, including this one, that model investment with costly reversibility (Abel and Eberly, 1996; Hall, 2001; Zhang, 2005). Abel and Eberly (1996) model costly reversibility by directly introducing a difference between the price at which the firm can purchase capital and the price at which it can sell it. Hall (2001) and Zhang (2005), like this paper, introduce costly reversibility through a piecewise quadratic adjustment cost function, which allows cutting capital to be costlier than expanding the capital stock through parameter asymmetry. Real estate is different from equipment due to the presence of more established secondary markets3 for real estate. Yet investment in real estate can be very costly to reverse. Ramey and Shapiro (2001), in one of the examples to motivate their study, report that the (now relocated) building of the Department of Economics at the University of California, Riverside had been converted from a motel. Complete bathrooms in each office and a swimming pool in the courtyard certainly contribute less to the productivity of an educational institution than they would to the value of a lodging; the value of these amenities to the Economics department will naturally be lower than their replacement value. In this example, capital is reallocated across sectors (from hotels to educational services), but in many cases, this is not an option, either. Toward the end of 1981, Ford Motor Company announced that it would close its huge Michigan Casting Center in Flat

3 Some types of equipment, such as photocopy machines, laboratory equipments, microscopes, etc. have relatively established secondary markets.

5 Rock, which was built only 12 years previously at a cost of more than $150 million. The company spokesman said that, "Slow sales of large cast-iron auto engines and the fact that the plant cannot easily be adapted to newer products have forced the closing" (New York Times, Sep. 15, 1981). The spokesman added that the plant would be kept on standby. After staying idle for more than three years, in 1985, the Ford casting plant was demolished, and Mazda Motor Manufacturing Corporation built a factory on the same site.

2.3 Related Work

The main contribution of this paper is to investigate the implications of capital heterogeneity within the firm in the asset pricing context. A somewhat related line of literature is concerned with intangible capital (Hall, 2001; Hansen, Heaton, and Li, 2004; Cum- mins, 2003; Li, 2004). Even though the existence and importance of intangible capital is widely agreed upon, interpreting and accounting for intangible capital is inherently difficult. Interpretations of intangible capital range from being a capital input in addition to physical capital to being a form of adjustment cost. Several papers attempt to measure the aggregate value of intangible capital in the U.S. economy (Atkeson and Kehoe, 2002; Hall, 2001; Li, 2004). Considering the difficulties with interpreting, measuring, and modeling intangible capital, I choose to concentrate on heterogeneity in physical capital. The interactions between business cycles and asset returns are studied in a strand of papers with production economies. The early studies (Danthine, Donaldson, and Mehra, 1992; Rouwenhorst, 1995) find that standard one-sector business cycle models have counterfactual asset pricing implications despite their relative success at explaining key business cycle facts. Jermann (1998) introduces capital adjustment costs to the standard business cycle model to mitigate the endogenous consumption smoothing mech- anism inherent in production economies. Boldrin, Christiano, and Fisher (2001) consider a two sector economy with limited labor mobility. The two sector model is designed to make the short term supply of capital completely inelastic, limiting the firm’s ability to smooth its dividend stream. Both of these papers consider habit formation preferences, generating a time varying risk premium. The link between real investment and stock returns is explored by Cochrane (1991, 1996). Cochrane considers a production based asset pricing model with quadratic adjustment costs in which the first order conditions of the producers describe the relationship between asset returns and real investment returns in a partial equilibrium framework. Cochrane (1991) predicts a contemporaneous relationship between asset returns and investment returns, acknowledging that if there are lags in the investment process, then the investment plans (rather than current investment returns) should covary with asset returns. Lamont (2000) reports that due to lags in investment, contemporaneous investment returns and stock returns have a strong negative covariation; however, the investment plans strongly covary with asset returns. In their empirical analysis, Cochrane (1991) uses private domestic investment and Lamont (2000) uses private nonresidential investment data; neither of them distinguishes between investment in different types of

6 capital. Cochrane (1996) considers a two factor asset pricing model where the factors are returns to residential and nonresidential investment and tries to explain the cross sectional differences in asset returns. Based on Cochrane’s production based model, Li, Vassalou, and Xing (2005) perform an empirical investigation of asset returns with a four factor model, where the factors are investment growth rates in different sectors of the economy. Recently, several papers have investigated production based models with capital adjustment frictions in an attempt to link stock returns to the book-to-market ratio (Cooper, 2006; Zhang, 2005; Kogan, 2004; Gourio, 2004). Their general idea is that firms with high B/M ratios are burdened with excess capital in bad times. Frictions in capital adjustment mechanisms (irreversibilities, costly reversibility) prevent the firms from achieving their desired capital holdings, leading to discrepancies between the market and book values of assets and time varying stock returns. These papers mainly differ along the frictions they assume in capital adjustment mechanisms. Kogan (2004) assumes that investment is irreversible and subject to convex adjustment costs. Cooper (2006) considers the nonconvex (fixed) adjustment costs in addition to irreversible investment. Zhang (2005) assumes convex but asymmetric adjustment costs; firms face higher adjustment costs while cutting their capital compared to capital expansions. Gourio (2004) works with a putty clay model where investment is irreversible and the ratio of factors used in production is fixed once the capital is installed. Even though real estate is an important component of aggregate wealth, it is generally omitted from the empirical and theoretical work in the asset pricing literature. There are a few notable exceptions, including Stambaugh (1982); Kullman (2003); Flavin and Yamashita (2002); Piazzesi, Schneider, and Tuzel (2006); and Lustig and Nieuwerburgh (2006). Stambaugh (1982) constructs market portfolio as a combination of several asset groups, some of which includes proxies for residential real estate. Kullman (2003) includes measures of both residential real estate returns and commercial real estate returns (as measured from REITs) in addition to proxies for returns to human capital and stock market returns in the market portfolio. Stambaugh (1982) finds that the ability of the CAPM to explain the cross section of returns is insensitive to the construction of the market portfolio. Kullman (2003), on the other hand, finds that returns to residential real estate are significant in explaining the cross section of stock returns, whereas the returns to commercial real estate is insignificant. Flavin and Yamashita (2002) consider portfolio choice with exogenous returns in the presence of housing. Piazzesi, Schneider, and Tuzel (2006) construct an equilibrium asset pricing model with housing and show that the composition of the consumption bundle appears in the pricing kernel, and matters for asset pricing. The expenditure share of housing predicts stock returns. Lustig and Nieuwerburgh (2006) find that the ratio of housing wealth to human wealth is related to the market price of risk and therefore has asset pricing implications. Deng and Gyourko (1999) study the empirical relationship between real estate ownership by non-real estate firms and firm returns. They find that firms with high degrees of real estate concentration and high levels of risk as measured by beta experience lower returns. However, their measure of real estate concentration, PPE/Assets, does not mea-

7 sure the share of real estate in the firm’s physical capital. Their ratio measures the ratio of physical assets in the firm’s total assets; this is what Braun (2003) calls the "tangibility" of a firm. Braun (2003) finds that tangibility of firms is related to their financing possibilities and leverage; tangible firms find it easier to raise debt financing and have higher leverage.

3Setup

The economy is populated with many firms and many infinitely lived identical agents who maximize expected discounted utility. There is a single consumption/investment good that is produced by the firms that use two types of capital. The investment is subject to convex adjustment costs.

3.1 Firms

There are many firms that produce a homogeneous good. The firms use two types of capital: structures and equipment. The firms are subject to different productivity shocks. The investment in either form of capital is subject to convex adjustment costs. Structures depreciate at rate µ and equipment depreciates at rate δ. I assume that structures depreciate more slowly than other capital (µ<δ), consistent with the depreciation rates in the BEA tables (1-3% for nonresidential structures, 10-30% for nonresidential equipment, annually). The production function for firm i is given by:

Yit = F(At,Zit,Kit,Hit,Lit) α1 α2 α 1 α = AtZit(Kit Hit ) Lit− .

Hit and Kit denote the beginning of period t stock of structures and equipment of ﬁrm i, respectively, α, α1 and α2 (0, 1).Lit denotes the labor used in production by ﬁrm i ∈ during period t. at =log(At) denotes aggregate productivity. at has a stationary and monotone Markov transition function, denoted by pa (at+1 at), as follows: | a at+1 = ρaat + σaεt+1 (1)

a where εt+1 is an IID normal shock. The ﬁrm productivity, denoted zit =log(Zit),hasa stationary and monotone Markov transition function, denoted pz (zi,t+1 zit), as follows: i | z zi,t+1 = ρzzit + σzεi,t+1 (2)

z z z where εi,t+1 is IID normal shock. εi,t+1 and εj,t+1 are uncorrelated for any pair (i, j) with i = j. 6

8 The capital accumulation rule is

k Ki,t+1 =(1 δ)Kit + Iit (3) − h Hi,t+1 =(1 µ)Hit + I − it k h where Iit and Iit denote investment in equipment and structures, respectively. k h The investment is subject to quadratic adjustment costs, git and git:

k k k 1 k Iit k g Iit,Kit = η Iit (4) 2 Kit h h ¡ h ¢ 1 h Iit h g Iit,Hit = η Iit 2 Hit and ¡ ¢ ηj if Ij > 0 ηj = low it , j = h, k. ηj otherwise ½ high ¾ j j The adjustment costs are allowed to be asymmetric ηlow ηhigh , j = h, k as in Zhang (2005), Hall (2001), and Abel and Eberly (1996) to capture≤ the intuition that reversing an investment is costlier than expanding the capital¡ stock of the ﬁrm. ¢ Firms are equity ﬁnanced. The dividend to shareholders is equal to

k h k h Dit = Yit I + I + g + g witLit, (5) − it it it it − where wit is the wage payment to£ labor services. Labor¤ markets are competitive, so wage payments are determined by the marginal product of labor. Labor is free to move between ﬁrms; therefore, the marginal product of labor is equalized among ﬁrms.

At each date t, firms choose Ki,t+1,Hi,t+1 to maximize the net present value of their expected dividend stream, { } k ∞ β Λt+k Et Di,t+k , (6) Λt "k=0 # k X subject to (Eq.1-4), where β Λt+k is the marginal rate of substitution of the firm’s owners Λt between time t and t + k. The pricing equations that come out of the firm’s optimization problem are:

k 2 k 1 k Ii,t+1 FK +(1 δ)q + η i,t+1 − i,t+1 2 Ki,t+1 Λt = βΛt+1 k pzi (zi,t+1 zit)pa(at+1 at)dzi da qit ³ ´ × | | ZZ (7) h 2 h 1 h Ii,t+1 FH +(1 µ)q + η i,t+1 − i,t+1 2 Hi,t+1 Λt = βΛt+1 h pzi (zi,t+1 zit)pa(at+1 at)dzi da qit ³ ´ × | | ZZ (8)

9 where

FKit = FK(At,Zit,Kit,Hit,Lit)

FHit = FH(At,Zit,Kit,Hit,Lit) and

k k k Iit qit =1+η (9) Kit h h h Iit qit =1+η . Hit

k h qit and qit are Tobin’s q, the consumption cost of capital.

Multiplying both sides of pricing equations with Ki,t+1 and Hi,t+1, respectively, rear- ranging, and adding the equations leads to:

k h qitKi,t+1 + qitHi,t+1 (10)

βΛt+1 k h k h = αYi,t+1 +(1 δ)Ki,t+1qi,t+1 +(1 µ)Hi,t+1qi,t+1 + gi,t+1 + gi,t+1 Λt − − ZZ £ pz (zi,t+1 zit)pa(at+1 at)dz da¤. × i | | i

The (end of period) value of a ﬁrm’s equity (Vit)isequaltothemarketvalueofits assets in place:

Vit = qkitKi,t+1 + qhitHi,t+1. (11)

Replacing equations (11) and (5) in (10) gives the standard Euler equation:

βΛt+1 Vi,t+1 + Di,t+1 1= pzi (zi,t+1 zit)pa(at+1 at)dzi da. (12) Λt Vit | | ZZ

3.2 Households

The households maximize expected discounted utility. Preferences over consumption take the standard form:

1 γ ∞ C − E βku(C ) , with u(C )= t . (13) t t+k t 1 γ "k=0 # X −

I assume that a complete set of contingent claims are marketed. Risk averse agents trade in claims to their individual labor income so that their intertemporal marginal rate of substitutions are equated. Therefore, the households can be aggregated into a representative agent. The representative agent invests in a one-period riskless discount

10 bond in zero net supply and the risky assets, the equity of ﬁrms. At every date t,the representative agent satisﬁes the following budget constraint:

rf bt+1qt + si,t+1Vit + Ct sit(Vit + Dit)+bt + wit (14) i ≤ i i X X X where bt+1and si,t+1 denote period t acquisition of riskless bond and risky asset i;and rf qt and Vit denote their prices, respectively. Dit denotes period t dividend of the risky asset i as defined in the previous section. At each date t, the agent chooses bt+1,si,t+1 for each firm, and Ct to maximize (13) subject to (14). The first order conditions for the representative agent’s optimization problem are:

f βu (C ) qr = E C t+1 (15) t t u (C ) ∙ C t ¸ βu (C ) V + D 1=E C t+1 i,t+1 i,t+1 . t u (C ) V ∙ C t it ¸

3.3 Equilibrium

The state of the economy is characterized by the aggregate productivity a and by the distribution of capital holdings across firms, S. The state variables for any given firm are its own asset holdings (Ki,Hi) and firm productivity, zi; and the economy wide state (S, a). A competitive equilibrium consists of consumption function C(S, a); invest- 0 ment functions b0(S, a) and si0 (Ki,Hi,zi,S,a); policy functions Ki (Ki,Hi,zi,S,a) and 0 k Hi (Ki,Hi,zi,S,a); price functions for installed capital qi (Ki,Hi,zi,S,a) and h f qi (Ki,Hi,zi,S,a); price functions for firms Vi(Ki,Hi,zi,S,a);andariskfreerater (S, a) that solve the firms’ optimization problems (maximize Eq.6 subject to Eq.1-4), solve the representative agent’s optimization problem (maximize Eq.13 subject to Eq.14), and sat- isfy the aggregate resource constraint:

0 0 k C(S, a)+ Ki (Ki,Hi,zi,S,a)+ Hi (Ki,Hi,zi,S,a)+ gi (Ki,Hi,zi,S,a) i i i X h X X + gi (Ki,Hi,zi,S,a) Yi +(1 δ) Ki +(1 µ) Hi. i ≤ i − i − i X X X X 4 Computational Solution

The model cannot be solved analytically. I therefore use numerical techniques. The main difficulty in solving the model is in accounting for the distribution of capital holdings across firms. I follow the approximate aggregation idea of Krusell and Smith (1998) and assume that the firms use a small number of moments of the capital distribution when they make their investment decisions. I solve the Euler equations (Eq.7-8) using the parameterized expectations algorithm (PEA) by Marcet (1988). The basic idea in

11 the PEA is to substitute the conditional expectations that appear in the equilibrium conditions with parameterized functions of the state variables. The conditional expectation is parameterized using an exponentiated polynomial, where the exponential guarantees nonnegativity. Once the conditional expectation function is approximated, the policy variables can be expressed as functions of the approximated conditional expectations. The details of the solution are explained in Appendix A.

5 Quantitative Results

I consider asset pricing in a simple production economy with two types of capital (structures and equipment) and adjustment costs. I am particularly interested in whether the composition of the capital bundle matters for asset pricing. The presence of heterogeneous firms in the economy allows me to study the cross sectional implications. The firms receive different productivity shocks, which, over time, lead to heterogeneity between them. Through simulations of the model economy, I show that the productivity shocks effect firms’ investment decisions and lead to changes in firms’ capital compositions. The composition of the capital bundle determines the flexibility of firms to accommodate future productivity shocks. As the share of buildings in the capital bundle of a firm increases, the firm becomes less flexible to accommodate bad shocks in the future, i.e. gets riskier. I demonstrate that these riskier firms indeed have higher expected returns in equilibrium. Table 1 presents the parameters used in the simulations of the model economy. For the parameters that previous empirical studies guide us, I use the suggestions of those studies. The model is not calibrated to match any benchmark result. Following Cooley and Prescott (1995), the capital share α is set to 0.36. Similarly, the time discount factor β is set to 0.99 (annually), and the coefficient of relative risk aversion γ is set to 2. The depreciation rates, δ and µ, are set to 0.12 and 0.02 for equipment and buildings, respectively. These are roughly the average BEA depreciation rates for equipment and structures. The persistence and the conditional volatility of the aggregate productivity process, ρa and σa, are set to 0.815 and 0.014, respectively, which are consistent with the quarterly parameters used in Cooley and Prescott (1995). I set the share of equipment α1 and the share of buildings α2 to 0.5. The persistence and the conditional volatility of the firm productivity process, ρz and σz, are set to 0.5 and 0.05, respectively. I set the adjustment cost parameters for increasing the capital stock for equipment and k h structures, ηlow and ηlow , to 1, consistent with the annual estimates in Whited (1992). In the baseline parameterization, I set the adjustment cost parameters for decreasing the k h capital stock for equipment and structures, ηhigh and ηhigh , to 25 and allow them to vary in different specifications. I do not impose any differences between the adjustment cost parameters of the two types of capital.

12 Panel A: Equipment Panel B: Structures 1.15 1.04 low H/K low H/K high H/K high H/K

1.14 1.03

1.13 1.02

q q

1.12 1.01

1.11 1.00

1.10 0.99 -0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1 Aggregate Productivity Aggregate Productivity

Figure 1: Simulated Tobin’s q vs. Aggregate Productivity

Table 1: Parameter Values k,h k,h αα1 α2 δµβγρa σa ρz σz ηlow ηhigh 0.36 0.5 0.5 0.12 0.02 0.99 2 0.815 0.014 0.5 0.05 1 25

Figure 1 plots the average Tobin’s q (consumption cost of capital) for equipment and structures as functions of the aggregate productivity. For every period, I compute the structures/equipment (H/K) ratios for firms using quantities of capital and sort firms based on their H/K ratios. Low H/K firms are the firms that are in the lowest quintile with respect to their H/K ratios, and high H/K firms are the firms in the highest H/K quintile. I plot the average Tobin’s q for low H/K and high H/K firmsineachperiod with respect to the aggregate productivity in that period. There is a very strong positive relationship between the average consumption cost of capital and aggregate productivity, reflecting the strong link between investment and productivity. Investment (and resale) prices are high during economic booms, and resale (and investment) prices are depressed during recessions, consistent with the conclusion of Eisfeldt and Rampini (2006) that costs of reallocation are substantially countercyclical. Low H/K firms have a slightly higher consumption cost of equipment than the high H/K firms. The difference between the Tobin’s q for structures of low H/K firms and high H/K firms is bigger, and the gap widens as the aggregate productivity gets lower. The widening gap is due to costly disinvestment of many high H/K firms, which already hold disproportionately high shares of their capital in structures when the aggregate productivity is low. These firms also reduce their equipment investment, but they do not have to disinvest since a considerable portion of their equipment diminishes through

13 depreciation. Therefore, when a ﬁrm receives bad productivity shocks, its equipment stock diminishes quickly with little reduction in its stock of buildings, leading to a higher H/K ratio. Few low H/K ﬁrms disinvest their structures when they are hit by bad productivity shocks; they have fewer structures compared to equipment to start with.

s f I am interested in the rate of return ri on ﬁrms and the riskless borrowing rate r in the economy. These are deﬁned as:

V + D rs =log i,t+1 i,t+1 i,t+1 V µ it ¶ rf = log qrf t − t βuC (Ct+1) = log Et − u (C ) ∙ C t ¸ In addition to these standard asset returns, I am interested in the expected returns of firms sorted based on their H/K ratios and the "real estate premium" generated in this model economy. For every period, I compute the structures/equipment (H/K) ratios for firms and label the firms that are in the highest quintile with respect to their H/K ratios as high H/K firms and the firms that are in the lowest quintile with respect to their H/K ratios as low H/K firms. I present the first two moments of the asset returns in Table 2.

Table 2: Model Implied Moments of Asset Returns (%, annualized) H/K quintile rf rs low 234high 5 1 mean 0.950 0.981 0.975 0.979 0.983 0.987 1.005 0.030− std 0.068 0.245 0.259 0.259 0.259 0.261 0.273 0.147

Note: The table reports the means and standard deviations of the risk free rate (rf ), the raw stock returns (rs), and the returns to the portfolios sorted on H/K.

The preferences in this model are standard, so the model implies a small equity premium. My focus here is generating the qualitative features of the data rather than matching the observed moments of returns quantitatively. The model generates cross sectional differences in the expected returns of firms sorted based on the H/K ratio, namely that expected returns of firms in the highest H/K quintile exceed those of firms in the lowest H/K quintile, confirming that high H/K firms are riskier than the low H/K firms. The standard deviations of returns follow a similar pattern. Furthermore, the expected return premium of high H/K firms over low H/K firms is countercyclical. During recessions, firms with a high ratio of structures to equipment (H/K) are hit particularly hard, making them riskier than the firms with H/K ratio. Therefore, investors expect higher premium from such firms during recessions. Figure 2 demonstrates this feature of the economy. In Figure 2, I plot the expected returns of the high H/K low H/K zero − 14 High H/K - Low H/K

0.6

0.5

) 0.4

(

t e

R 0.3

e p

x 0.2 E

0.1

-0.1 -0.10 -0.05 0.00 0.05 0.10 Aggregate Productivity

Figure 2: Simulated Expected Return Spread vs. Aggregate Productivity investment portfolio (expected return spread) against the aggregate productivity. The negative correlation coefficient between the expected return spread and the aggregate productivity ( 0.4) confirms that the expected real estate premium is countercyclical. ∼− The strong positive relationship between the price of capital (Tobin’s q) and productivity (Figure 1) is due to the positive response of investment to productivity shocks for both types of capital. Investment in equipment is more responsive to productivity shocks than investment in structures. When firms receive positive productivity shocks, they invest in both equipment and structures, but their equipment stock increases more than their structures stock, leading to a lower H/K ratio. When firms receive bad productivity shocks, their equipment stock diminishes quickly due to fast depreciation, with little reduction in their stock of buildings (since disinvestment is very costly), leading to ahigherH/K ratio. Figure 3 plots the changes in the aggregate structures / equipment H ratio i i against the changes in output, indicating that the aggregate H/K ratio is Ki Pi highly³ countercyclical.P ´ In the numerical solution, the aggregate H/K ratio shows up as a state variable in the economy. Later, empirical results will confirm that aggregate H/K ratio indeed captures important information about the economy. In Figure 4, I simulate the economy for 100 periods and plot the changes in model generated aggregate H/K ratio against time. In Section 6, I calculate and plot the changes in empirical aggregate H/K ratio using quarterly data over 1947-2005. The shaded areas in the Figure represent periods in which the output growth is more than one standard deviation below its mean (to proxy for recessions). The aggregate H/K ratio rises during recessions, since the firms find it difficult to reduce their structures holdings, whereas equipment depreciates and hence decreases faster.

15 0.8

0.6

) 0.4

(

a R

0.2

e t

a 0

n -0.2

n a

h -0.4 C

-0.6

-0.8 -6 -4 -2 0 2 4 6 Output Growth (%)

Figure 3: Simulated Changes in Aggregate H/K vs. Output Growth

0.5

0.4

0.3

)

(

o 0.2

/ 0.1

e t

a 0

g g

A -0.1

e g

n -0.2

h C -0.3

-0.4

-0.5 10 20 30 40 50 60 70 80 90 100

Figure 4: Simulated Series of Changes in Aggregate H/K ratiofora100PeriodSample. The shaded areas indicate periods in which output growth is more than one standard deviation below its mean.

The quantitative results presented so far are generated using the parameters in Table 1. The main feature of the adjustment costs considered in this benchmark case is that they are asymmetric; i.e, reversing an investment is costlier than expanding the capital

16 stock. Table 3 presents the basic results for alternative adjustment cost parameters, where I change the degree of asymmetry in adjustment costs, starting with the symmetric case (so that reversing an investment is no more costly than increasing the capital stock). Table 3 shows that both the excess returns and the high H/K -lowH/K returns go up and become more volatile as the asymmetry in adjustment costs increases.

Table 3: Model Implied Moments of Asset Returns for Alternative Adjustment Cost Parameters (%, annualized)

k,h k,h f s (H/K)high (H/K)low ηlow ηhigh r r r − 1 1 mean 0.949 0.975 0.007 std 0.067 0.239 0.131 1 5 mean 0.949 0.976 0.009 std 0.067 0.240 0.131 1 25 mean 0.950 0.981 0.030 std 0.068 0.245 0.147

Note: The table reports the means and standard deviations of the risk free rate (rf ), the raw stock returns (rs), and the returns to the zero cost portfolio that is formed by buying the high H/Kportfolio and selling the low H/Kportfolio (H/K) (H/K) (r high− low ) generated by the model economy using alternative adjustment cost parameters.

6 Empirical Results

In this section, I examine the empirical relationship between the composition of firms’ physical capital (equipment and the real estate related items that proxy for structures) and stock returns. In the first part, I study the relationship at the firm level. I look at the capital composition of individual firms and try to understand whether there are any cross sectional differences in firm returns with respect to their capital composition. In the second part, I consider the composition of the aggregate capital in the economy. This variable comes out as a state variable in my model economy and therefore is economically meaningful. I use the aggregate H/K ratio as a conditioning variable and try to explain the cross sectional differences in the returns of size and B/M sorted portfolios via the conditional CAPM.

6.1 Data

In order to measure the capital composition of ﬁrms, I use data from Compustat. Com- pustat Industrial Annual provides a breakdown of property, plant, and equipment (PPE) into buildings, capitalized leases, machinery and equipment, natural resources, land and

17 improvements, and construction in progress. Among these items, buildings and capitalized leases are the closest counterparts to "structures" in the model. "Buildings" is the cost of all buildings included in a company’s PPE account. "Capital leases" represents the capitalized value of leases and leasehold improvements included in PPE.4 A capital lease (as opposed to an operating lease) is quite similar to property ownership. In a capital lease, the lessee is exposed to most of the risks and benefits of ownership; therefore, the lease is recognized both as an asset and as a liability on the balance sheet. In addition to buildings and capitalized leases, "construction in progress" and "land and improvements" are also real estate related components of PPE, but they do not have counterparts in the model economy. Construction in progress is not a productive capital for the firm yet, and land cannot be reproduced.5 The Compustat data on the composition of the PPE is "net"6 over 1969-1997 and "historical cost" over 1984-2003. These values are the book values of the assets. In order to make the capital compositions comparable between firms, I calculate a real estate ratio for each firm in every year by dividing the real estate components of PPE that proxy for structures by total PPE. Since neither net nor historical cost series span throughout the whole 1969-2003 period, I use net values until 1984 and switch to historical cost values starting in 1984.7 My choice of using net versus historical cost values over 1984-1997 is somewhat arbitrary, but the results are insensitive to the choice. In the base case, I measure the real estate holdings of the firm as the sum of buildings and capitalized leases. Buildings and capitalized leases are the two biggest real estate relatedcomponentsofPPE;onaverage,they account for approximately 16% and 10% of PPE, respectively, measured at historical cost over 1984-2003. Construction in progress and land and improvements are much smaller in size; together they account for about 5% of PPE on average. I repeat the analyses including construction in progress and land and improvements in the real estate holdings (in addition to buildings and leases) and report those results as well. Including construction and land components in real estate holdings does not have a material affect on my results. The capital composition of firms differ among industries. For example, health service firms (hospitals) and hotels tend to invest heavily in structures, whereas transportation firms tend to hold a lot of equipment. The model assumes that all firms use the same production technology, though in reality the natural composition of capital varies among

4 Capitalized leases can be leases of property or equipment. The data does not allow me to distinguish property leases from equipment leases. However, I compared the capital lease data provided by Compu- stat to the breakdown of PPE in the annual reports for a number of firms and realized that a significant part of the capitalized leases reported by Compustat are leasehold improvements, which are changes to leased property that increase its value. By using data from Census of Manufactures, Eisfeldt and Rampini (2006) find that the fraction of capital leased is much higher for structures than for equipment. 5 In the model, all capital is reproducible capital, and the consumption goods can be converted into investment goods (capital) in the next period. The model does not have a time to build feature; therefore, there is no construction in progress in the model. Likewise, there is no land in the model because land is not reproducible capital. 6 "Net" is "at cost" - "accumulated depreciation." 7 If I have net (gross) real estate holdings in the nominator, I use net (gross) PPE in the denominator.

18 industries due to their different business needs. In the absence of an industry adjustment, the firms with extremely high or low real estate ratios tend to reflect the characteristics of specific industries, and their returns reflect these industry effects. In order to cancel out industry effects and make firms from different industries comparable, I calculate industry adjusted real estate ratios for firms. Every year, I form industry portfolios using two digit Standard Industrial Classification (SIC) codes and calculate the average real estate ratio within each portfolio. The industry adjusted real estate ratios of firms are the real estate ratios in excess of their industry averages. Throughout the rest of the paper, the "real estate ratio" refers to the "industry adjusted real estate ratio," and it is denoted by RER. My sample consists of all non-real estate firms with data on buildings and capitalized leases from Compustat Industrial Annual (1969-2003) and stock return data from CRSP (July 1971 - June 2005).8 Firms that do not have data on assets or net and gross PPE are excluded from the sample. There must be at least 5 firms from each two digit SIC code in order to include firms from that industry in my sample. To ensure that accounting information is already impounded into stock prices, I match CRSP stock return data from July of year t to June of year t +1 with accounting information for fiscal year ending in year t 1,asinFamaandFrench(1992,1993),allowingforaminimumofa six month gap between− fiscal year-end and return tests. In addition to my original sample, I consider a subsample for empirical tests. In the model presented in this paper, there are no rental markets, i.e., productive assets that are deployed by the firms are owned by the firms. In practice, firms can deploy productive assets through leasing. Accounting rules distinguish between an operating lease and a capital lease,9 the latter of which is similar to property ownership and is therefore included in firm assets. However, operating leases is a potential concern and might be contaminating the results, hence I present the results for a subset of firms that do not have a significant amount of operating leases. In this subsample, I normalize the rental expense from Compustat Industrial Annual (which includes only rental payments for operating leases) with the gross PPE and exclude firmsthathavemorethan3% normalized rental expense from the sample.10 The aggregate ratio of structures to equipment (H/K) is constructed using the quantity indexes for real private fixed investment on nonresidential structures and equipment by the Bureau of Economic Analysis (NIPA Table 5.3.3). I first construct quarterly quantity indexes for stocks of nonresidential structures and equipment using the perpet- ual inventory method. The quarterly investment data starts in 1947. As the benchmark stock and investment values, I use current cost net stock of nonresidential structures and equipment in 1946 and historical cost investment in 1947 (Fixed Assets Tables 2.1

8 Iidentifyrealestatefirms as firms with two digit SIC code 65. Including these firms in my sample does not change any of the results. 9 Eisfeldt and Rampini (2006) point out the similarities between the classification of leases for accounting, tax, and legal purposes. Commercial law distinguishes between a "true lease" and a "lease intended as security;" and the tax law distinguishes between a "true lease" and a "conditional sales contract." 10Since this refinement requires data on rental expenses, the firms with missing rental expense data are also excluded from this subsample.

19 and 2.7). I use 0.5% and 3% quarterly depreciation rates for structures and equipment, respectively. The aggregate H/K ratio is calculated by dividing the quantity index for nonresidential structures by the index for equipment. The ratio is trending downward over time (i.e. the quantity of structures relative to equipment is decreasing); therefore, I use the quarterly percentage change in the ratio as the scaling (conditioning) variable. The test assets in Fama-MacBeth regressions are the 25 value weighted size and B/M sorted portfolios (FF portfolios). FF portfolio returns, FF factors, and the momentum factor are taken from Kenneth French’s website.

6.2 Firm Level Analysis

This section investigates whether a stock’s expected return is related to its capital composition, the share of its real estate related items in its total capital. I follow a straight- forward portfolio based approach by sorting the firms in my sample every year according to their real estate ratio (RER) and grouping them into quintile portfolios. Table 4 reports the descriptive statistics for RER sorted portfolios. There is significant dispersion in real estate ratios of portfolios. For the firms in the first quintile, the share of real estate-related items in the firms’ total physical capital is 22% lower than the average firm in that industry, whereas it is 25% higher for the firms in the fifth quintile. Vari- ation in real estate ratios implies that there is considerable heterogeneity in the capital composition of firms, even within the same industry. The returns of the portfolios are dispersed as well. Table 4 presents the excess returns (firm return - risk free rate) and the industry adjusted returns (firm return - industry return) for RER sorted portfolios. Since the real estate holdings are measured with respect to the firm’s industry, I report industry adjusted returns in addition to the standard excess returns. Both excess returns and industry adjusted returns of portfolios increase monotonically with the real estate holdings of firms. I risk adjust the monthly excess and industry adjusted returns of RER sorted portfolios using a four factor model, where the factors are the three Fama-French factors (MKT, excess market returns; SMB, returns of portfolio that is long in small, short in big firms; HML, returns of portfolio that is long in high B/M,shortinlowB/M firms) and the momentum factor (MOM, returns of portfolio that is long in short term winners, short in short term losers). The intercepts of the regressions (alphas) represent pricing errors. If the four factor model can account for all the risk in RER sorted portfolios, the alphas should be indistinguishable from zero. Tables 5 and 6 present the alphas and betas of RER sorted portfolios with respect to MKT, SBM, HML,and MOM factors using value and equally weighted portfolios. Betas are estimated by re- gressing the portfolio excess returns and industry adjusted returns on the four factors. The alphas are estimated as intercepts from the regressions of excess portfolio returns and industry adjusted returns on the same factors. Monthly alphas are annualized by multiplying by 12. If real estate risk is priced, risk-adjusted returns (i.e. alphas) should exhibit systematic differences. This is indeed the case in the data. Like the excess returns, risk adjusted returns (alphas) increase monotonically as the RER increases. The

20 value weighted portfolios that are long in high RER portfolios and short in low RER portfolio (5-1) have alphas around 3% over the 1971-2005 period. The equally weighted portfolios produce smaller alphas, which are not statistically signiﬁcant. Table 7 reports the descriptive statistics and risk adjusted returns for portfolios sorted on an alternative measure of RER, where real estate components are more broadly deﬁned as the sum of buildings, capitalized leases, construction, and land. These results are quite similar to the base case results.

Table 4: Descriptive Statistics for RER Sorted Portfolios (%, annualized) July 1971 - June 2005 RER quintile low 2 3 4 high 5-1

RER -0.22 -0.09 -0.01 0.07 0.25 0.47 N 435 440 443 442 439 Average Excess Returns e rVW 4.64 5.32 5.49 5.30 7.56 2.93 (1.27) (1.78) (1.84) (1.71) (2.16) (1.80) e σVW 21.27 17.40 17.42 18.06 20.47 9.51

e rEW 11.10 11.19 10.58 10.42 12.37 1.28 (2.49) (2.65) (2.74) (2.76) (3.05) (1.28) e σEW 25.98 24.61 22.52 22.02 23.64 5.82 Average Industry Adjusted Returns IA rVW -1.15 -0.26 -0.15 -0.11 2.15 3.30 (-0.95) (-0.46) (-0.27) (-0.21) (2.76) (2.28) IA σVW 7.09 3.24 3.29 3.11 4.55 8.43

IA rEW -0.39 0.03 -0.13 -0.49 0.99 1.38 (-0.50) (0.07) (-0.26) (-0.87) (1.90) (1.38) IA σEW 4.52 2.76 2.86 3.32 3.04 5.82

Note: For RER, equal-weighted averages are ﬁrst taken over all ﬁrms in that

portfolio, then over years. RER is defined as [(buil.+cap. leases) /PPE]firm [(buil. + cap. leases) /P PE]industry. N is the average number of firms in each − e portfolio. rVW is value-weighted monthly excess returns (excess of risk free rate), e rEW is equal-weighted monthly excess returns, annualized; averages are taken over IA time (%). rVW is value-weighted monthly industry adjusted returns (in excess of industry returns, where industry returns are calculated by value weighting the IA firms in that industry), rEW is equal-weighted monthly industry adjusted returns (in excess of industry returns, where industry returns are calculated by equally weighting the firms in that industry), annualized; averages are taken over time e e IA IA (%). σVW, σEW , σVW, σEW are the corresponding standard deviations. All returns are measured in the year following the portfolio formation and annualized (%). t statistics are in parentheses. − 21 Table5:AlphasandBetasofPortfoliosSortedonRER Dependent Variable: Excess Returns July 1971 - June 2005 RER quintile low 2 3 4 high 5-1 Value Weighted Portfolios alpha -0.64 -0.17 1.37 1.59 2.94 3.58 (-0.47) (-0.16) (1.05) (1.50) (2.40) (2.24) MKT 1.05 0.98 0.96 0.99 1.05 0.00 ( 32.20 ) ( 40.99 ) ( 37.04 ) ( 40.56 ) ( 37.07 ) ( 0.00 ) SMB 0.35 0.04 0.04 0.03 0.21 -0.14 (5.30) (1.34) (1.21) (0.92) (4.89) (-1.69) HML -0.30 -0.13 -0.13 -0.24 -0.32 -0.01 (-4.87) (-3.67) (-3.31) (-5.82) (-6.64) (-0.20) MOM 0.01 0.04 -0.07 -0.07 -0.01 -0.03 (0.28) (1.53) (-1.87) (-2.66) (-0.47) (-0.56) Equal Weighted Portfolios alpha 4.92 5.95 4.33 4.08 5.46 0.54 (2.15) (2.70) (3.09) (2.93) (3.39) (0.48) MKT 1.00 1.01 1.02 1.00 1.00 -0.01 ( 24.51 ) ( 27.54 ) ( 31.86 ) ( 32.96 ) ( 30.87 ) ( -0.32 ) SMB 1.23 1.08 0.97 0.94 1.11 -0.11 ( 17.19 ) ( 18.98 ) ( 19.93 ) ( 17.98 ) ( 22.09 ) ( -3.55 ) HML 0.02 -0.01 0.15 0.15 0.13 0.11 ( 0.21 ) ( -0.07 ) ( 2.56 ) ( 2.70 ) ( 2.10 ) ( 2.87 ) MOM -0.23 -0.28 -0.25 -0.23 -0.19 0.04 ( -2.72 ) ( -3.21 ) ( -5.02 ) ( -4.46 ) ( -3.54 ) ( 1.06 )

Note: Regressions of value and equal weighted excess portfolio returns on FF and momentum factor returns. Alphas are annualized (%). t statistics are in parentheses. −

22 Table6:AlphasandBetasofPortfoliosSortedonRER Dependent Variable: Industry Adjusted Returns July 1971 - June 2005 RER quintile low 2 3 4 high 5-1 Value Weighted Portfolios alpha -1.81 -0.17 0.27 0.27 1.19 3.00 ( -1.65 ) ( -0.30 ) ( 0.45 ) ( 0.49 ) ( 1.53 ) ( 2.23 ) MKT 0.04 0.00 -0.02 -0.01 0.04 0.00 ( 1.49 ) ( -0.19 ) ( -1.52 ) ( -0.68 ) ( 2.54 ) ( 0.05 ) SMB 0.26 -0.01 0.01 -0.04 0.03 -0.22 (4.71) (-0.65) (0.33) (-2.05) (1.31) (-3.42) HML -0.09 -0.02 0.01 -0.01 0.00 0.09 ( -1.99 ) ( -0.79 ) ( 0.32 ) ( -0.36 ) ( 0.08 ) ( 1.57 ) MOM 0.04 0.00 -0.03 -0.02 0.06 0.02 (1.11) (0.32) (-2.04) (-1.46) (3.47) (0.56) Equal Weighted Portfolios alpha -0.160.57-0.24-0.630.480.64 ( -0.18 ) ( 1.02 ) ( -0.45 ) ( -1.07 ) ( 0.91 ) ( 0.55 ) MKT 0.00 0.01 0.01 0.00 -0.01 -0.01 ( -0.13 ) ( 0.62 ) ( 1.03 ) ( -0.14 ) ( -1.28 ) ( -0.57 ) SMB 0.15 0.01 -0.07 -0.12 0.04 -0.11 (5.88) (0.50) (-4.26) (-6.68) (2.31) (-3.25) HML -0.07 -0.05 0.04 0.05 0.03 0.10 ( -2.11 ) ( -3.72 ) ( 2.11 ) ( 2.39 ) ( 2.03 ) ( 2.47 ) MOM -0.01 -0.03 0.00 0.01 0.03 0.04 ( -0.45 ) ( -1.70 ) ( -0.21 ) ( 0.68 ) ( 2.58 ) ( 1.19 )

Note: Regressions of value and equal weighted industry adjusted portfolio returns on FF and momentum factor returns. Alphas are annualized (%). t statistics are in parentheses. −

23 Table 7: Descriptive Statistics, Alphas, and Betas of Portfolios Sorted on Alternative RER July 1971 - June 2005 RER quintile low 2 3 4 high 5-1 Descriptive Statistics RER -0.25 -0.10 -0.01 0.08 0.27 0.52 N 405 407 410 410 408

e rVW 4.51 4.61 6.48 4.56 7.77 3.26 (1.37) (1.47) (2.10) (1.49) (2.30) (1.97) e σVW 19.11 18.28 18.00 17.90 19.72 9.63

IA rVW -1.22 -0.58 0.68 -0.89 2.08 3.30 ( -1.14 ) ( -1.01 ) ( 1.18 ) ( -1.33 ) ( 3.11 ) ( 2.50 ) IA σVW 6.26 3.36 3.36 3.88 3.91 7.71 Dependent Variable: Excess Returns alpha -1.70 -0.35 2.35 1.13 3.32 5.02 (-1.38) (-0.29) (1.84) (0.93) (2.69) (2.99) MKT 1.02 0.99 0.98 0.97 1.03 0.00 ( 34.26 ) ( 37.16 ) ( 42.67 ) ( 35.72 ) ( 34.43 ) ( 0.09 ) SMB 0.21 0.10 0.10 0.00 0.14 -0.07 (3.74) (2.18) (2.97) (0.00) (3.08) (-0.87) HML -0.14 -0.21 -0.13 -0.24 -0.31 -0.17 (-2.97) (-3.78) (-3.09) (-5.51) (-6.22) (-2.48) MOM 0.06 0.02 -0.10 -0.08 -0.01 -0.06 (1.76) (0.57) (-3.07) (-2.51) (-0.19) (-1.36) Dependent Variable: Industry Adjusted Returns alpha -2.24 -0.74 1.13 -0.50 1.96 4.20 ( -2.19 ) ( -1.15 ) ( 1.82 ) ( -0.77 ) ( 2.75 ) ( 3.13 ) MKT 0.03 -0.01 -0.02 0.01 0.03 0.00 (1.13) (-0.96) (-1.11) (0.43) (1.55) (-0.04) SMB 0.20 0.03 0.04 -0.10 0.02 -0.17 ( 3.99 ) ( 1.35 ) ( 2.07 ) ( -3.66 ) ( 0.98 ) ( -2.84 ) HML 0.00 0.00 -0.03 0.03 -0.07 -0.07 ( -0.07 ) ( 0.07 ) ( -1.07 ) ( 1.00 ) ( -2.66 ) ( -1.25 ) MOM 0.04 0.01 -0.03 -0.03 0.03 -0.01 (1.44) (0.90) (-1.96) (-1.94) (2.28) (-0.33)

Note: Descriptive statistics and regressions of value weighted excess and industry adjusted portfolio returns on FF and momentum factor returns. For RER,equal- weighted averages are ﬁrst taken over all ﬁrms in that portfolio, then over years.

RER is deﬁned as [(buil.+cap. leases+land+const.) /PPE]firm [(buil.+cap. leases+land+const.) /PPE]industry. N is the average number of − e ﬁrmsineachportfolio. rVW is value-weighted monthly excess returns (excess of

24 IA risk free rate), annualized; averages are taken over time (%). rVW is value-weighted monthly industry adjusted returns (in excess of industry returns, where industry returns are calculated by value weighting the ﬁrms in that industry), annualized; e IA averages are taken over time (%).σVW and σVW are the corresponding standard deviations. All returns are measured in the year following the portfolio formation; returns and alphas are annualized (%). t statistics are in parentheses. −

The general equilibrium model considered in this paper does not allow for the sepa- ration of ownership and control of the assets. Productive assets that are deployed by the firms are owned by the firms. In practice, the firms can deploy productive assets through leasing. The finance literature primarily focuses on tax related incentives for leasing. Smith and Wakeman (1985) identify eight non-tax incentives to lease or buy, including asset specificity (assets highly specialized to the firm are generally owned), expected use period compared to asset life (if the expected use period is short compared to the life of the asset, there is an inclination to lease), and comparative advantage in asset disposal (if the lessor has a comparative incentive in disposing of the asset, this provides an incentive to lease). The Financial Accounting Standards Board requires that leases be classified as either capital or operating leases. Appendix B of Statement of Financial Accounting Standards No.13, Basis for Conclusions states that (page 28):

... a lease that transfers substantially all of the benefits and risks incident to the ownership of property should be accounted for as the acquisition of an asset and the incurrence of an obligation by the lessee and as a sale or financing by the lessor. All other leases should be accounted for as operating leases. In a lease that transfers substantially all of the benefits and risks of ownership, the economic effect on the parties is similar, in many respects, to that of an installment purchase.

Therefore, capital leases are similar to property ownership, whereas the nature of operating leases can be quite different. It may be argued that firms that inherently need more flexibility in their capital holdings may self select into leasing with relatively flexible terms rather than owning because leased capital may be more easily redeployed than owned capital and hence be more reversible (Eisfeldt and Rampini, 2006).11 Slovin, Sushka, and Poloncheck (1990) report that firms that engage in sale-leaseback transactions experience positive abnormal returns following their announcement. This result is consistent with the view that leasing provides more flexibility than ownership; therefore,

11Eisfeldt and Rampini (2006) test this hypothesis by looking at the likelihood of low cash flows for firms; they find that firms with a higher likelihood of low cash flow realizations lease more. I look at the volatility of firm returns and find evidence for the same hypothesis. I find that the sample of firms that do not have a significant amount of operating leases have less volatile returns than the sample of all firms (Table 8 and Table 4), implying that the firms that engage in lots of operating leases have much more volatile returns than the firms that do not have a significant amount of operating leases. In unreported results, I find that the volatility of stock returns is significantly positively related to the normalized rental expense and negatively related to the firm size.

25 firms that engage in sale-leasebacks effectively become less risky and hence experience a positive price response.12 Besides this argument, some of the operating leases can still look like ownership in the short run and can be even more inflexible than ownership if the lease contract puts a lot of restrictions on how the asset can de deployed or utilized. Therefore, operating leases is a potential concern and might be contaminating the results. I present the results for a subset of firms that do not have a significant amount of operating leases. In this subsample, I normalize the rental expense from Compustat Industrial Annual (which includes only rental payments for operating leases) with the gross PPE, and exclude firmsthathavemorethan3%normalizedrentalexpensefrom the sample. It is not practical to exclude all the firms that have positive rental expense; in the data, almost all firmshavesomerentalexpenseinagivenperiod.Evenexcluding firms with more than 3% normalized rental expense leads to a 75% loss in my sample size, yet I still have on average about 110 firms in each quintile portfolio. Table 8 presents the descriptive statistics on the excess returns and the industry adjusted returns for the RER sorted portfolios of these non-lessee firms. The dispersion in the real estate ratios of these non-lessee firms is quite similar to the dispersion in real estate ratios of all firms. However, the dispersion in both the excess returns and the industry adjusted returns of value and equally weighted portfolios is much bigger. The returns of the high RER firms exceed the returns of the low RER firms (5-1) by about 4-5% per annum, and the difference in returns is statistically significant for all return measures. Most of the change is in the returns of the low RER portfolio: The returns of the non-lessee low RER firms is about 2% lower than the returns of the low RER firms from the whole sample, which can be interpreted as these non-lessee, low RER firms being less risky than the low RER firms that have a lot of operating leases. Similar observations are made for the volatility of returns. The volatility of returns for the non-lessee, high RER firms generally exceed the volatility of low RER firms. The RER sorted portfolios of non-lessee firms typically have lower volatility, where the biggest decreases in volatility are observed for the low RER portfolios. Tables 9 and 10 present the alphas and betas of RER sorted portfolios of non-lessee firms using the four-factor model. Like the excess returns, risk adjusted returns (alphas) increase monotonically as the RER increases. The portfolios that are formed by going long in the high RER portfolios and short in low RER portfolios (5-1) have alphas around 4-5% over the 1971-2005 period (both value and equally weighted). Excluding the firms that lease heavily from my sample increases the alphas of the 5-1 portfolios by more than 2%. Excluding firms that lease heavily leads to a major improvement in the results for equally weighted portfolios. The explanation for this improvement comes from the nature of the lessee firms: The firms that lease heavily tend to be smaller firms. Even though their returns do not constitute a big part of the value weighted portfolio returns, they are well represented in the equally weighted portfolios; hence, they contaminate equally weighted portfolio results more than the results for the value weighted portfolios.

12The authors interpret the positive market reaction to sale-leaseback transactions through the traditional ﬁnance view of leases as a result of an overall reduction in the present value of expected taxes.

26 Therefore, removing heavily leasing ﬁrms from the sample leads to a stark improvement in equally weighted portfolio results.

Table 8: Descriptive Statistics for RER Sorted Portfolios (%, annualized) Non-lessee Firms July 1971 - June 2005 RER quintile low 2 3 4 high 5-1

RER -0.20 -0.08 -0.02 0.06 0.24 0.44 N 110 110 111 110 109 Average Excess Returns e rVW 2.63 5.52 6.64 4.10 8.43 5.81 ( 0.86 ) ( 1.76 ) ( 2.28 ) ( 1.26 ) ( 2.52 ) ( 2.88 ) e σVW 17.85 18.27 16.98 19.07 19.49 11.77

e rEW 8.43 10.91 10.58 10.93 12.46 4.03 ( 2.19 ) ( 3.19 ) ( 3.13 ) ( 3.11 ) ( 3.27 ) ( 2.66 ) e σEW 22.41 19.95 19.70 20.50 22.25 8.84 Average Industry Adjusted Returns IA rVW -1.88 0.82 0.89 -0.58 2.49 4.37 ( -1.90 ) ( 1.25 ) ( 1.28 ) ( -0.80 ) ( 2.23 ) ( 2.84 ) IA σVW 5.77 3.85 4.03 4.23 6.50 8.96

IA rEW -2.25 0.50 0.02 -0.25 1.97 4.22 ( -2.49 ) ( 0.72 ) ( 0.02 ) ( -0.32 ) ( 2.17 ) ( 2.81 ) IA σEW 5.28 4.09 4.00 4.48 5.28 8.74

Note: Descriptive statistics of non-lessee firms, sorted on RER. I exclude firms with more than 3% normalized rental expense (rental expense / PPE) from my sample. For RER, equal-weighted averages are first taken over all firms in that

27 Table9:AlphasandBetasofPortfoliosSortedonRER, Non-lessee Firms Dependent Variable: Excess Returns July 1971 - June 2005 RER quintile low 2 3 4 high 5-1 Value Weighted Portfolios alpha -4.26 -0.31 1.90 0.41 1.63 5.89 (-2.88) (-0.18) (1.29) (0.25) (0.90) (2.87) MKT 1.01 1.00 0.90 0.95 1.01 -0.01 ( 30.55 ) ( 31.12 ) ( 26.22 ) ( 24.16 ) ( 22.45 ) ( -0.15 ) SMB 0.07 -0.05 0.00 -0.13 0.15 0.09 ( 1.61 ) ( -1.28 ) ( 0.07 ) ( -2.53 ) ( 2.34 ) ( 1.61 ) HML 0.07 -0.03 -0.07 -0.25 -0.02 -0.10 ( 1.32 ) ( -0.53 ) ( -1.35 ) ( -3.45 ) ( -0.33 ) ( -1.35 ) MOM 0.04 0.03 -0.01 -0.01 0.07 0.03 ( 1.08 ) ( 0.64 ) ( -0.31 ) ( -0.25 ) ( 1.38 ) ( 0.58 ) Equal Weighted Portfolios alpha 1.59 3.01 3.14 4.13 4.98 3.39 (0.86) (2.63) (2.39) (2.96) (3.10) (2.09) MKT 1.04 1.00 0.98 0.98 0.97 -0.07 ( 28.50 ) ( 34.78 ) ( 29.70 ) ( 32.66 ) ( 28.09 ) ( -2.18 ) SMB 0.87 0.78 0.76 0.80 1.00 0.13 ( 13.65 ) ( 14.18 ) ( 12.71 ) ( 14.87 ) ( 18.19 ) ( 2.46 ) HML 0.22 0.32 0.34 0.24 0.21 0.00 (3.17) (6.88) (6.38) (5.00) (3.50) (-0.06) MOM -0.22 -0.13 -0.17 -0.19 -0.14 0.07 ( -3.21 ) ( -4.20 ) ( -4.28 ) ( -4.47 ) ( -3.27 ) ( 1.74 )

Note: Regressions of value and equal weighted excess portfolio returns on FF and momentum factor returns. Alphas are annualized (%). t statistics are in parentheses. −

28 Table 10: Alphas and Betas of Portfolios Sorted on RER, Non-lessee Firms Dependent Variable: Industry Adjusted Returns July 1971 - June 2005 RER quintile low 2 3 4 high 5-1 Value Weighted Portfolios alpha -2.84 0.81 1.11 -0.26 1.63 4.47 ( -2.88 ) ( 0.92 ) ( 1.45 ) ( -0.34 ) ( 1.55 ) ( 3.07 ) MKT 0.05 0.00 -0.03 0.00 0.04 0.00 ( 2.19 ) ( 0.17 ) ( -1.80 ) ( 0.00 ) ( 1.34 ) ( -0.12 ) SMB 0.11 -0.03 0.03 -0.06 0.11 0.00 (3.07) (-1.18) (1.06) (-1.86) (2.21) (0.10) HML 0.07 -0.01 0.02 -0.07 0.04 -0.03 (1.78) (-0.54) (0.64) (-2.20) (0.77) (-0.52) MOM 0.01 0.01 -0.02 0.02 0.02 0.01 ( 0.19 ) ( 0.50 ) ( -0.77 ) ( 0.97 ) ( 0.48 ) ( 0.23 ) Equal Weighted Portfolios alpha -2.18 0.14 0.01 0.38 1.59 3.77 ( -2.17 ) ( 0.20 ) ( 0.02 ) ( 0.44 ) ( 1.79 ) ( 2.37 ) MKT 0.05 0.00 0.00 -0.01 -0.03 -0.08 (2.36) (-0.02) (-0.28) (-0.58) (-1.69) (-2.47) SMB 0.02 -0.04 -0.07 -0.04 0.14 0.12 ( 0.73 ) ( -1.83 ) ( -4.07 ) ( -1.79 ) ( 3.90 ) ( 2.27 ) HML 0.01 0.03 0.02 -0.05 -0.01 -0.01 (0.27) (1.32) (0.86) (-1.96) (-0.17) (-0.26) MOM -0.04 0.03 0.01 -0.02 0.03 0.07 ( -1.36 ) ( 1.39 ) ( 0.40 ) ( -0.83 ) ( 1.53 ) ( 1.66 )

Note: Regressions of value and equal weighted industry adjusted portfolio returns on FF and momentum factor returns. Alphas are annualized (%). t statistics are in parentheses. −

Overall, the results of the firm level analysis are interesting. I find that the firms with higher RER indeed earn higher returns after adjusting for common risk factors, suggest- ing that the owners of these firms are compensated for their real estate risk exposure. This empirical result is consistent with the predictions of the model economy (Table 2).

6.3 Implications of Aggregate Capital Composition

I construct an aggregate measure of capital composition, aggregate H/K,usingquantity indexes of aggregate capital by dividing the quantity index for nonresidential structures by the quantity index for equipment. Aggregate H/K ratioisastatevariableinthe model economy and is therefore economically meaningful.

29 0.5

) -0.5

(

/ -1

r g

g -1.5

a h

C -2

-2.5

-3 1950 1960 1970 1980 1990 2000

Figure 5: Change in Aggregate H/K Ratio, 1947-2005. The shaded areas indicate NBER recession periods.

Figure 5 plots the quarterly change in aggregate H/K ratio over the 1947-2005 period. The yellow (darker) columns in the Figure indicate NBER recession periods. The aggregate H/K ratio increased during all recessions in the postwar period. This empirical observation is consistent with the predictions of the model economy (Figure 4); the aggregate H/K ratio increases in bad times. I utilize the information content of the aggregate H/K ratiobyusingitasacondi- tioning variable and undertake a cross sectional investigation of the conditional CAPM using the 25 size and B/M sorted Fama-French portfolios. The unconditional (static) version of CAPM has been unable to explain the cross sectional differences in firm returns. The first column in Figure 6 plots the average realized returns of the 25 portfolios against their CAPM fitted counterparts. The plots are almost flat, indicating that there is virtually no relationship between the realized and expected mean returns based on CAPM. In standard applications of CAPM, the parameters of the discount factor are constant, i.e. the discount factor is of the form mt+1 = a brvw,t+1. By scaling the CAPM, I model the dependence of the parameters in the discount− factor on variables in time t information set, at = a(zt), bt = b(zt). My choice of conditioning variable (zt) is the change in the aggregate H/K ratio, ∆H/Kt, which is a state variable in the model economy described above. The idea behind conditioning the CAPM with the aggregate H/K is that the risk of an asset is determined by the covariance of the asset’s return with the market return conditional on the time t information set of investors, which is approximated by the aggregate H/K ratio. The assets with returns that are more tightly correlated with market returns when the aggregate H/K ratiogoesuptradeatadiscount.Thediscount

30 factor takes the form

mt+1 = a0 + a1∆H/Kt +(b0 + b1∆H/Kt)rvw,t+1

= a0 + a1∆H/Kt + b0rvw,t+1 + b1(∆H/Kt rvw,t+1). · My estimation is in the spirit of Cochrane (1996) and Lettau and Ludvigson (2001). Cochrane (1996) estimates unconditional and conditional factor models using returns on physical investment as factors and term premium and dividend/price ratio as conditioning variables. Lettau and Ludvigson (2001) estimate conditional versions of CAPM and consumption CAPM. Their conditioning variable cay is a cointegrating residual between the logarithms of consumption, asset wealth, and labor income.

e E(mt+1ri,t+1)=0implies

e 0=E (a0 + a1∆H/Kt + b0rvw,t+1 + b1(∆H/Kt rvw,t+1))r , · i,t+1 which can be written¡ as ¢

e a1var(∆H/Kt) b0var(rvw,t+1) E(ri,t+1)= β∆H/Kt βrvw,t+1 − E(mt+1) − E(mt+1) b1var(∆H/Kt rvw,t+1) · β∆H/Kt rvw,t+1 , − E(mt+1) ·

e cov(x,ri,t+1) where βx = var(x) . I estimate the following cross sectional regression:13

e E(ri,t+1)=β∆H/Kt λ∆H/Kt + βrvw,t+1 λrvw,t+1 + β∆H/Kt rvw,t+1 λ∆H/Kt rvw,t+1 · · Table 11 reports the estimates for factor loadings (λ) from the cross sectional Fama- MacBeth regressions using the returns of 25 size and B/M sorted Fama-French portfolios, together with t-statistics, Shanken corrected t-statistics and R2s. I report the results for the unconditional CAPM, FF 3-factor model and the conditional CAPM, where CAPM is scaled by the change in aggregate H/K ratio. Figure 6 plots the average realized returns of the 25 portfolios against their model fitted counterparts. The unconditional CAPM has very little power in explaining the cross section of average returns over both sample periods, starting in 1947 and 1964. The adjusted R2s of the cross sectional regressions are in the 16 - 28% range. Furthermore, the loading on market return is insignificant and has the wrong sign (negative). By contrast, the conditional CAPM performs relatively well in both subperiods. The adjusted R2 of the cross sectional regression are slightly above 50%. The loadings on the market return scaled by the aggregate H/K ratio (H/Kt rvw,t+1)andtheaggregateH/K ratio are both positive and statistically significant. The· fit of the model is comparable to that of the Fama-French 3 factor model, even though the latter model produces slightly higher adjusted R2s.

13 I demean the scaling variable, change in aggregate H/Kt, in my empirical analysis.

31 Table 11: Fama-MacBeth Regression Results Using 25 Size and B/M Sorted Portfolios

2 Row Model Constant λH/Kt λrvw,t+1 λSMBt+1 λHMLt+1 λH/Kt rvw,t+1 R 1947 2005 · 1 CAPM 5.33 -2.01− 0.31 (6.67) (-2.09) (0.28) (6.47) (-1.79) 2 Cond. CAPM 2.47 0.08 0.31 4.64 0.58 (2.55) (0.67) (0.28) (3.38) (0.52) (1.79) (0.46) (0.18) (2.35) 3 FF 5.40 -2.73 0.14 1.34 0.77 (5.80) (-2.52) (0.38) (3.77) (0.74) (5.37) (-2.12) (0.26) (2.59) 1964 2005 4 CAPM 4.75 -1.52− 0.20 (5.59) (-1.42) (0.16) (5.51) (-1.19) 5 Cond. CAPM 2.84 0.21 -0.49 3.78 0.59 (2.81) (2.14) (-0.41) (3.37) (0.54) (2.03) (1.50) (-0.27) (2.38) 6 FF 5.67 -3.25 0.41 1.54 0.78 (4.84) (-2.35) (0.90) (3.36) (0.75) (4.36) (-1.94) (0.61) (2.27)

Note: The table reports the cross sectional regression coefficients, t statistics, and R2s. In each row, the first line reports the regression coefficients− and the R2s, the second line reports the t-statistics and adjusted R2s, the third line reports the t statistics after Shanken (1992) correction. −

32 CAPM Scaled CAPM FF3 5 5 5

1947 - 2005 1947 - 2005 1947 - 2005

4 4 4 45 35 15 54 53 14 33 44 34 35 34 24 25 55 55 43 25 54 13 45 52 44 44

43 34 54 24 55 33 23

) ) 42 22 ) 51 33 45 24 35 23 15 53 43

42 23 14 13 14

% %

32 25 %

( (

13 15 51 53 (

3 3 52 3 42 22 12 32

n n

22 n 52

r r

41 32 r

u u

12 12 u

t t

31 t

e e 21 e

R R R

11 31 11 51

d d

d 41 21

e e

e 31 41

t t

t 2 2 11 2

t t t

i i i

F F F

1 AdjR2: 0.28 1 AdjR2: 0.52 1 AdjR2: 0.74

0 0 0 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 Realized Return (%) Realized Return (%) Realized Return (%)

5 5 5

1964 - 2005 1964 - 2005 1964 - 2005

15 4 4 4 14 4534 25 35 25 13 54 35 34 24 53 55 33 43 23 24 15 45

52 13 33 23

) ) 44 55 14 ) 54 44 43 4534 35 42 22 44

51 33 24 55 12 43

% %

42 25 32 %

( (

23 14 54 ( 53 22

3 32 13 15 3 3

n n

22 n 32

r r

41 53 r 42

u u

12 52 u

t t

31 12 t 52

e e 51 e

R R R

11 21 31

d d

d 11 11

e e e

t t

t 2 2 2

t t

t 21

i i i 51

31 41

F F F

1 AdjR2: 0.16 1 AdjR2: 0.54 1 AdjR2: 0.75

0 0 0 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 Realized Return (%) Realized Return (%) Realized Return (%)

Figure 6: Actual vs. Predicted Mean Excess Returns of 25 Size and B/M Sorted Portfolios

33 7Conclusion

I introduce a general equilibrium production model where the firms use two factors, real estate capital and other capital, and investment is subject to asymmetric adjustment costs, where cutting the capital stock is costlier than expanding it. Slow depreciation of real estate capital makes real estate investment riskier than investment in other capital. Due to costly reversibility, the firm will find it difficult to reduce its real estate holdings when it would like to do so, whereas the other capital depreciates and hence decreases faster. Therefore, recessions hurt firms with high real estate holdings particularly badly. In equilibrium, investors demand a premium to hold these firms. This prediction is also empirically supported. Using a portfolio based approach, I find that the returns of firms with a high share of real estate capital compared to other firms in the same industry exceed that for low real estate firms by 3-6% annually, adjusted for exposures to the market return, size, value, and momentum factors. The model also predicts countercyclical variation in the aggregate share of real estate in total capital, which is a state variable in the model economy. The empirical evidence is also consistent with this prediction. I undertake a cross sectional investigation of the conditional CAPM, where the change in aggregate share of real estate in total capital is used as the conditioning variable. The conditional CAPM delivers substantially improved results over its unconditional version. The capital breakdown I consider is limited to real estate and other physical capital. Nevertheless, this breakdown excludes at least one big class of capital, which is referred to as intangible or organizational capital. Accounting for intangible capital is inherently difficult; neither is there a consensus on how intangible capital is defined nor on how it is measured. Its definition involves a variety of concepts, such as organizational culture, copyrights, and research and development. Further research integrating intangible capital into the firm’s capital composition would provide a more realistic and comprehensive view of the firm than what this simple model portrays.

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39 Appendix A: Computational Solution

I solve the Euler equations (Eq.7-8) using a modiﬁed version of the parameterized expectations algorithm (PEA) by Marcet (1988). In order to use the PEA, the system should be "invertible", i.e., once the parameterized expectation is substituted in the equilibrium condition, one should be able to construct the policy function. The Euler equations that will be solved (Eq.7-8) are not "invertible" in the sense that the policy functions,

[Ki0,Hi0], cannot be retrieved by substituting the parameterized expectations in the right hand side. A value for C can be found from any one of the many Euler equations, but there is no way to compute individual policy functions. In order to make the system invertible, following Marcet and Lorenzoni (1988), I slightly modify the Euler equations by premultiplying both sides of the Euler equations by Ki0 and Hi0, respectively. Since capital levels are never zero in equilibrium, the new equations are satisfied if and only if the original Euler equations are satisfied. The modified Euler equations are as follows, where the primes denote next period’s values14:

2 k k 2 k 1 k Ii 0 1 k I 0 FK0 +(1 δ)qi 0 + η + ξ i 2 K 2 K − i0 0 u K0 = βu K0p (z0 z )p (a0 a)d d C i C0 k µ ¶ ³ ´ i zi i i a zi a qi 0 | | ZZ 2 h h 2 h 1 h Ii 0 1 h I 0 FH0 +(1 µ)qi 0 + η + ξ i 2 H 2 H − i0 0 uCH0 = βuC µ ¶ H0pz (z0 zi)pa(a0 a)dz da i 0 qh ³ ´ i i i| | i ZZ i 0 where u = u (C ), F = F (K ), F = F (H ). C0 C 0 Ki0 K i0 Hi0 H i0

Thesolutionisafunctioneψ(Ki,Hi,zi,S,a),withaﬁnite set of parameters, ψ :

2 2 Ik k 0 k 1 k i 0 1 k I 0 FK +(1bδ)qi 0+ 2 η + 2 ξ i0 − K K βu Ã i0 ! µ 0 ¶ K p (z z )p (a a)d d C0 qk i0 zi i0 i a 0 zi a ¯ i 0 | | ¯ exp (eψi) ¯ 2 2 ¯ . (16) Ih h ≈ ¯ h 1 h i 0 1 h I 0 ¯ RR FH +(1 µ)qi 0+ 2 η + 2 ξ ¯ i0 − H H ¯ ¯ βu Ã i0 ! µ 0 ¶ H p (z z )p (a a)d d ¯ ¯ C0 qh i0 zi i0 i a 0 zi a¯ b ¯ i 0 | | ¯ ¯ ¯ ¯RR ¯ ¯ ¯ The relations linking the policy functions, sˆ (K ,H,z,S,a)=[K , H ] and the ψ0 i i i i0ψ i0ψ consumption function, Cψ to eψ(Ki,Hi,zi,S,a) areasfollows: b b b b sˆ0 =exp e /u ψ iψ Cˆψ ¡ ¢ k b I = K0 (1 δ)Ki iψ iψ − − h I = H0 (1 µ)Hi biψ biψ − − 14 When the time subscript is dropped,b primesb denote next period’s values.

40 k k 1 Ii 1 I gk = ηk ψ Ik + ξk ψ Ik iψ iψ iψ 2 Ki 2 K bh bh 1 Ii 1 I gbh = ηh ψ Ibh + ξk ψ Ibh iψ iψ iψ 2 Hi 2 H b b b b b C = Y + K + H K H gk gh ψ i i i i0ψ i0ψ iψ iψ i − − − − X ³ ´ b b b b b The procedure to estimate the parameter set, ψ, starts with generating series for a and zi,i =1,...,n, of length T ,wheren is the number of firms in the economy, and coming up with an initial guess for ψ, ψ0. The standard PEA algorithm (Marcet, 1988, Den Haan and Marcet, 1990) has two steps. In the first step, the economy is simulated using the series for productivity, initial capital levels, and initial guess, ψ0,and T Ct (ψ0) ,Kit (ψ0) ,Hit (ψ0) ,i=1, ..., n t=1 is generated (simulation step). In the second { } k 2 k 2 T k 1 k Iit 1 k It FK +(1 δ)q + η + ξ it − it 2 K 2 K µ it ¶ µ t ¶ step, a non-linear least squares regression of βuCt qk Kit ⎧ it ⎫ ⎨ ⎬t=1 h 2 h 2 T h 1 h Iit 1 h It FHit +(1 µ)qit+ 2 η + 2 ξ − H Ht ⎩ ⎭ µ it ¶ µ ¶ and βuCt qh Hit is run on the power function of e and ⎧ it ⎫ ⎨ ⎬t=1 ψ1 is estimated (regression step). If ψ1 is sufficiently close to ψ0, the program stops; otherwise,⎩ ψ0 is updated and the two steps⎭ are repeated. I make several changes in the implemantation of the algorithm. The standard PEA concentrates observations on points of high probability. Marcet and Marimon (1992) observed that greater dispersion in the state variables is desirable while studying the far-from-steady-state properties of a model. Christiano and Fisher (2000) suggest that this observation still applies when the object of interest is the steady state properties of the distribution, since high variance in explanatory variables implies greater precision in regression estimates. Marcet and Marimon (1992) overcome this problem by exogenously oversampling from the tails of the state variable distribution in their simulations. Christiano and Fisher (2000) suggest an alternative to the standard PEA, the Chebyshev PEA. Chebyshev PEA considers a fixed distribution of state variables in the simulation step, which is more widely dispersed than the ones in the standard PEA. I modify the standard algorithm in the following way: In order to ensure that there is sufficient dispersion in aggregate productivity, I find 2 (a aj ) − Na 5 periods from the simulated productivity series a that minimizes a2 , where × j a =exp([ 2σa σa 0 σa 2σa]). After simulating the economy for T periods as in the first− step explained− above, I evaluate the conditional expectations in Eq. 16 at 15 these Na 5 periods using Monte Carlo simulation . Next, in order to ensure sufficient × dispersion in firm level productivity, I find Nz 5 firmsineachoftheNa 5 periods × × 15Unlike the model presented in Christiano and Fisher (2000), the distribution of capital over firms is not trivial in this model. Therefore, I still have to simulate the economy for a long time to get a

41 2 (zi zj ) − that minimizes z2 , where z =exp([ 2σzi σzi 0 σzi 2σzi ]). So,Iendupwith j − − 16 Na Nz 5 5 [time, firm] pairs that I will use in the regression stage. Finally, I run a non-linear× × least× squares regression of the conditional expectations in Eq. 16 evaluated for these Na Nz 5 5 [time, firm] pairs on the power function of eψ(Ki,Hi,zi,S,a). × × × The functional form I use for e is a second order polynomial of the aggregate productivity, first two moments of the capital distribution and firm level stateb variables (firm’s capital holdings and productivity).

reasonable distribution of capital, even though I do not evaluate the conditional expectations at every period. 16 Like the simulated series for a and zi, I ﬁx these [time, ﬁrm] pairs once and use the same set during each iteration.