Implicit Forward Rents as Predictors of Future Rents

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Implicit Forward Rents as Predictors of Future Rents

ENGLUND, Peter, et al.

Abstract

The paper investigates the relation between the term structure of rents and future spot rents.

A rich database of office rental agreements for various maturities is used to estimate the term structure of rents, and from this structure implicit forward rents are extracted. The data pertain to commercial properties in the three largest Swedish cities for the period 1998-2002. A positive relation between forward and spot rents is found in some regions, but forward rents underestimate future rent levels. Another contribution of the paper lies in the area of rental index construction. We provide evidence that rental indices should not only be quality-constant (i.e. control for characteristics), but should also be maturity-constant.

ENGLUND, Peter, et al. Implicit Forward Rents as Predictors of Future Rents. 2003

Available at:

http://archive-ouverte.unige.ch/unige:5794

Disclaimer: layout of this document may differ from the published version.

Implicit Forward Rents as Predictors of Future Rents

Peter Englund^*, Åke Gunnelin^**, Martin Hoesli^*** and Bo Söderberg^****

This version: May 16, 2003

Abstract

The paper investigates the relation between the term structure of rents and future spot rents. A rich database of office rental agreements for various maturities is used to estimate the term structure of rents, and from this structure implicit forward rents are extracted. The data pertain to commercial properties in the three largest Swedish cities for the period 1998-2002. A positive relation between forward and spot rents is found in some regions, but forward rents underestimate future rent levels.

Another contribution of the paper lies in the area of rental index construction. We provide evidence that rental indices should not only be quality-constant (i.e. control for characteristics), but should also be maturity-constant.

* Stockholm Institute for Financial Research and Stockholm School of Economics, [email protected]

** Stockholm Institute for Financial Research and Royal Institute of Technology, Stockholm, [email protected]

*** University of Geneva (HEC and FAME) and University of Aberdeen (Business School), [email protected]

**** Royal Institute of Technology, Stockholm, [email protected]

Address correspondence to: Peter Englund, Stockholm Institute for Financial Research, Saltmätargatan 19A, SE-113 59 Stockholm, Sweden.

This paper was written while Martin Hoesli was the Hans Dalborg visiting professor of financial economics, Stockholm Institute for Financial Research, Sweden. We gratefully acknowledge financial support from the Bank of Sweden Tercentenary Foundation (Englund and Gunnelin) and the Jan Wallander and Tom Hedelius Foundation (Söderberg).

The paper has benefited from comments from two anonymous referees and from participants at the research seminars of the Royal Institute of Technology (section of building and real estate economics), Stockholm, and of the University of Geneva (HEC). We are grateful to the Board of Directors of the SFI/IPD Swedish Property Databank for providing the data used in the analysis.

Implicit Forward Rents as Predictors of Future Rents

1. Introduction

Commercial leases are signed for a variety of maturities (terms). If rent levels for different terms are observable, then it should be possible to construct the term structure of rents in analogy with the term structure of interest rates. In most instances, one would expect very short leases to have high rent levels due to the transaction costs associated with such leases for the owner, while the longer end of the term structure curve can be either upward- or downward-sloping. Consideration of the term structure of existing rental contracts is obviously important when valuing individual properties. It should also matter for our picture of overall market movements. Rental indices that are constructed without controlling for the term structure may be biased if the composition of leases over different terms changes through time. Further, and this is the main focus of the paper, just like the term structure of interest rates is hypothesized to contain information that is useful in predicting future spot interest rates, the term structure of rents may offer important insights about market expectations of future rent levels.

In analogy with fixed-income securities one may formulate an “expectations hypothesis” of the term structure of rents, stating that forward rents are unbiased estimates of future spot rents. It is well known that such a hypothesis holds for interest rates under very restrictive conditions only. It can be shown that similar assumptions as in interest rate theory regarding risk aversion and the stochastic nature of interest rates (and of rents) are required in the case of rental contracts as well.¹ The expectations hypothesis is conveniently formulated in terms of forward rates. There is no explicit forward market for leases, but it is possible to extract implicit forward rents from the spot rents at different maturities. For instance, the one-year forward rent for a one-year lease is implied by current spot rents on one-year and two-year contracts. These implicit forward rents may not be directly relevant for trading, since it is not possible to construct synthetic forward contracts, but it is still relevant to investigate if they are able to predict future spot rents. The mechanism that would bring about such a relation operates even in the absence of explicit or implicit forward contracts: In signing a lease, tenants could be expected to weigh the cost of a long contract against the expected costs (and uncertainty) of a sequence of shorter contracts. In other words, implicit forward rents

should reflect market expectations of future spot rates. Under idealized conditions, they may even be unbiased predictors of future spot rates.

Despite the importance for actors on real estate markets of considering the term structure of rents, research in this area is limited. Grenadier (1995, 2002) has put forth equilibrium models of lease valuation that account for the term structure. Gunnelin and Söderberg (2003) report that differences in lease terms have a statistically significant impact on commercial rents in the Stockholm CBD for seven out of 15 years between 1977 and 1991, with an upward-sloping structure in the bullish real estate markets of the 1980s shifting to a downward slope in 1990 at the start of the bearish years for real estate markets. Further evidence is provided by the lease-valuation model of Stanton and Wallace (2002) estimated on data for suburban malls in 14 U.S. metropolitan areas. They find significant differences in the slope of the term structure across markets.

There is a number of other empirical studies of commercial leases where lease length is one of the rent explaining variables. The evidence on the impact of lease length varies. Early studies on U.S.

data by Brennan, Cannaday and Colwell (1984) as well as Benjamin, Sa-Aadu and Shilling (1992) report statistically insignificant term effects, whereas Benjamin, Boyle and Sirmans (1990) find a negative and significant relationship between rents and term. Wheaton and Torto (1994) in a comprehensive study of over 50 U.S. metropolitan markets found a consistently positive term effect. Fisher and Webb (1997) found a significant positive term parameter for Chicago suburbs, but insignificant effects in a similar analysis for the Chicago CBD (Webb and Fisher, 1996).² None of these hedonic studies, however, allows for possible variation in the term structure of lease rates over time.

Most studies have made use of U.S. data. Here, we study the term structure of rents using a rich database of office rental agreements for the three largest Swedish cities (Stockholm, Gothenburg, and Malmö). The Swedish market differs from the U.S. market in at least two important ways.

First, the duration of a typical Swedish lease (3 years) is shorter than that of a typical U.S. lease.

Second, Swedish lease contracts are “purer”, i.e. have fewer option clauses than their U.S.

counterparts. This feature makes them well suited for testing whether implicit forward rents are good predictors of future spot rents. A total of 4,387 leases for the period 1998—2002 are available for analysis. This period is characterized by sharp rent increases with rents growing by 50 to 90 percent in the Stockholm region, and by 40 to 50 percent in Gothenburg and Malmö. The data

1 See Clapham and Gunnelin (2002).

2 For further reviews of hedonic rent studies, see Dunse and Jones (1998) and Gunnelin and Söderberg (2003).

includes information about the maturity of leases, which ranges from a few months to over ten years. Apart from age the dataset is limited on information about the property, but unique property identifiers make it possible to control for location and other property characteristics.

We use regression analysis to estimate the term structure of rents. Given the role of term structure effects, we proceed to investigating the sensitivity of rental indices to the method used for constructing such indices. Three types of indices are considered: indices computed from rent averages, indices that control for the structural and locational characteristics of properties, and indices which control both for the characteristics of properties and the lease maturities. Controlling for the characteristics of properties appears to be very important, but controlling for the maturity of leases also has a sizeable impact on the estimated indices.

Based on these estimates of the term structure, we extract implicit forward rents and test for the ability of current forward rents to predict future spot rents. To the best of our knowledge, this is the first formal test of the expectations hypothesis for commercial leases. We find a positive (and significant) relationship in Stockholm, but implicit forward rents underestimate actual increases in rent levels and we can reject the hypothesis that forward rates are unbiased predictors of future spot rents. This conclusion holds true even when transaction costs are taken into consideration.

The current paper differs in several ways from that of Gunnelin and Söderberg (2003), henceforth GS. First, we use a larger and more detailed dataset covering several markets and a more recent time period. Second, GS estimate a parametric term structure, whereas the current study uses a non-parametric approach thereby putting less restriction on the term structure curve. Third, they discuss the relationship between term structure and rental expectations only informally. They note that the variation in term structure by and large seems to be consistent with the evolution of market rents during the examined period, but they do not formally test if the term structures predict future rents. The key contribution of this paper is to test such a relationship statistically. Finally, GS restrict the sample to leases signed during a four-month period each year, thus discarding a significant number of observations. This paper employs an interpolation scheme in order to use leases signed throughout the year to infer the January term structure.

The structure of the paper is as follows. Section 2 provides a brief theoretical background on the term structure of rents. We then go on to giving an empirical overview of the main features of Swedish office markets in recent years in section 3, followed by a presentation of the data set used in this study in section 4. Our estimates of term structures are presented in section 5, followed in

section 6 by an analysis of the importance of considering the term structure of rents when constructing rental indices. Section 7 reports the results of our tests of the predictive power of implicit forward rents. Finally, section 8 contains some concluding remarks.

2. A Theoretical Background

The main objective of this paper is to study whether forward rents can predict future spot rents.

This is similar in spirit to studies of the expectations hypothesis of interest rates; see Macaulay (1938) for an early statement and Campbell, Lo and MacKinlay (1997), section 10.2 for a textbook exposition. The most straightforward way to test the expectations hypothesis of rents would be to compare spot rents with rents in forward contracts for the same period. However, lack of data on actual forward leases prevents us from doing so. Forward leases further than 6-9 months into the future are normally only found in larger office properties and in development projects. Even in these cases, tenants rarely commit to leasing more than two years ahead. In view of these data limitations, we use implicit forward rents derived from spot rents for different contract lengths instead of actual forward rents.

The use of implicit forward rents instead of actual forward rents can be motivated by equilibrium arguments as in the literature on leasing, see e.g. Miller and Upton (1976), McConnell and Schallheim (1983), Schallheim and McConnell (1985), Grenadier (1995, 2002), and Stanton and Wallace (2002). Viewing leasing as a purchase of the use of an asset over a specified period of time, the equilibrium value of a lease must equal the present value of the service flow provided from the lease object. Therefore, two different strategies for leasing a unit for a given period of time, providing the same service flow, must have the same value. For example, the present value of the service flow from a five-year lease must equal the present value of the service flow from a three-year lease plus a two-year forward lease starting three years ahead. Hence, if the rental market is efficient in the sense that a given service flow is priced the same irrespective of contract structure, then implicit forward rents should equate forward rents if such a market existed.

The pure form of the expectations hypothesis of rents holds true only under very special conditions.

It is well known from the interest rate literature that forward rates are unbiased estimates of future spot rates only in the extreme case that the interest rate is deterministic. Theoretical work by Clapham and Gunnelin (2002) shows that similar restrictions are required for rents. More specifically, they show that (abstracting from transaction costs) forward rents are unbiased

estimates of future spot rents only if the market is risk-neutral towards variations in rent and the short interest rate is uncorrelated with the short rent level under the risk neutral measure. The latter will hold true if stochastic increments of the two processes as well as drifts, if stochastic, are uncorrelated. They also show that the slope of the rental term structure curve is related to risk- neutral rent expectations rather than to objective expectations. The lower the risk-neutral expectation, the less upward-sloping is the term structure. Since risk-neutral expectations normally are lower than objective expectations, these results suggest that implicit forward rents generally are downward biased estimates of future spot rents.

The downward bias may further be increased by landlord transaction costs of entering and terminating a lease relation, e.g. search costs of finding a new tenant. To reduce transaction costs, landlords are induced to offer lower rents on longer leases (more steeply downward sloping term structure curve) to attract and reward long-term tenants. Miceli and Sirmans (1999) construct a model that explicitly takes into account transaction costs (including search costs and the costs of reconditioning a unit). The rent reductions for longer term rental agreements lead to self-selection between low- and high-mobility tenants. However, by considering transaction costs when calculating implicit forward rents this type of bias can be mitigated. In other words, when transaction costs are accounted for, in should be possible to test for the true effect of market anticipations with respect to rental levels.

To summarize, we do not expect the expectations hypothesis in its pure form to hold. However, in the same way as the expectations hypothesis for interest rates, though biased, is considered useful for the purpose of studying market expectations, we believe that forward rents may contain useful information of rent expectations in the property market.

3. Office Markets in Stockholm, Gothenburg, and Malmö

We study the office rental markets in the three largest metropolitan areas of Sweden: Stockholm, Gothenburg, and Malmö. For the Stockholm region, we identify three submarkets: the CBD, the city outside of the CBD, and the suburban areas in the metropolitan region outside of the city of Stockholm. Our data for Gothenburg and Malmö pertain to the two cities proper, i.e. excluding suburbs. All three cities show a classic monocentric urban structure, with a relatively well defined CBD area. Properties in the CBD areas house mainly retail and office premises. In the inner city outside of the CBD, office and multi-family residential uses dominate. The metropolitan areas

include a number of smaller cities and municipalities, giving them a somewhat polycentric character. The number of inhabitants in the three cities were 755,000, 471,000 and 262,000, respectively, in 2001.

In broad terms, the Swedish rental market resembles those of other European countries. Rents are determined by market forces, although the office market in Sweden was subject to rent control until 1972. Swedish law restricts rents by giving tenants the right of possession at the end of a lease period, i.e. the landlord has to agree to a renewal of the contract at a “fair market rent”, or else pay damages. Negotiations over renewals are therefore likely to be a bargaining game with incomplete information about the other player’s preferences and opportunities. Consequently, it may be important to control for possible effects of renegotiations compared to new contracts when analyzing the determinants of the rent structure.

The official Swedish Land Registry records property transaction prices, but – as in most other countries – information concerning commercial leases is generally not publicly available. In particular, no rental indices exist. The limited market information available is provided by property consultant companies, generally based on a limited number of observations and undocumented statistical analysis. Table 1 reports key indicators for the office markets covered in our study taken from the Swedish Property Indicator (Svensk Fastighetsindikator), an annual report published since 1990 for the major markets based on a variety of information sources. It is regarded as a reliable source of information about the state of the market.

Table 1 shows that price and rent levels differ sharply across the three markets, with Stockholm rents and price levels being more than twice as high as those of Gothenburg and Malmö. All three markets experienced a significant upswing with respect to both rents and values in the late 1990s, with yields remaining fairly constant. Rents and property prices have increased by about the same magnitude as during the property boom of the late 1980s. During that boom, in contrast, yields fell and prices increased approximately twice as much as rents, suggesting elements of speculative behavior. During the time period examined in this paper, there is little to contradict the hypothesis that the market has been driven by fundamentals alone.

Other market indicators are displayed in Figure 1. Vacancy rates were still high in the mid 1990s, but have been gradually falling in all three regions. In Stockholm, vacancy rates were remarkably low in 1998—2000, but have been slowly increasing during the last couple of years. In the other

markets, particularly in Malmö, recovery from the real estate crisis has been slower, and vacancies never reached such low levels as in Stockholm.

Data on new office supply in Stockholm over the time period 1985—2001 are also displayed in Figure 1. No reliable long time series are available for Gothenburg and Malmö. In Stockholm, construction activity has been fluctuating considerably with a pronounced peak in the late 1980s, almost no building in the mid-1990s, and increased activity in recent years. The average annual rate of construction was 1.4 percent of the total stock (corresponding to 126,000 square meters).

For the years 2000 and 2001, the rate of office construction was 2.2 percent in Stockholm, 1.4 percent in Gothenburg, and 4.7 percent in Malmö. The high activity in Malmö reflects expected demand in the region following the completion of the bridge to Copenhagen.

4. Data

Since lease units are not perfect substitutes for one another, it is not possible to observe directly the term structure of lease rates. Rather the term structure has to be estimated, controlling for variation in location, physical attributes, and various clauses that affect the rent of individual units. This study uses information on office leases from the database of the SFI/IPD Swedish Property Index.

This index has been produced since 1997 drawing on information about the holdings of 14 major Swedish property owners, including insurance companies, pension funds, and specialized property holding companies.³ These companies annually supply data pertaining to their portfolio of income- producing properties. The SFI/IPD dataset contains data for approximately 2,400 properties, predominantly office properties. Geographically, the dataset represents the whole country, but the capital Stockholm dominates, with a share of some 70 percent (based on market values).

Table 2 contains summary statistics and definitions of the variables included in our dataset. We use data on new office leases signed from 1998 to 2002 in the following submarkets: (1) Stockholm CBD, (2) the remaining part of the inner city of Stockholm, referred to as Stockholm city, (3) the remaining part of greater Stockholm, referred to as Stockholm suburbs, (4) the inner city of Gothenburg, and (5) the inner city of Malmö. Contracts that concern internal transactions within a company are excluded. Furthermore, we exclude leases of units whose area is below 15 m². Finally, a few leases with exceptionally high or low base rents are excluded. This leaves us with a total of 4,387 leases.

Rent is measured by the base rent on a net basis. We can distinguish three categories of leases: (1) standardized leases with a CPI clause, (2) leases with graduated rents, and (3) “other leases”. The latter category contains mostly leases with flat unindexed rents, but also some leases with various, for us unknown, clauses. There is no information about tenant improvements, the amount and timing of lease discounts or to what percentage leases with CPI clauses are indexed. Hence, it is not possible to fully control for all cash-flow consequences associated with a particular lease.⁴ We do not believe, however, that this distorts our results to any large extent. First, commercial leases in Sweden tend to be standardized. Various options and clauses that are common in the U.S. and other countries seldom appear in Swedish rental contracts. With few exceptions property owners use a standard contract provided by the Swedish Property Federation. Second, the fraction of leases with graduated rents in our dataset is less than one percent (see averages of the Lease_2 dummy variable in Table 2). Third, tenant improvements (paid for by the landlord) tend to be more common in soft markets with high vacancy rates, and all property markets considered in our study have performed strongly during the period under review. Finally, the fact that we do not know the index clause for each lease does not constitute a serious issue as inflation was low during this period (1-2 percent per year only on average).

Not surprisingly, and consistent with table 1, rents in our sample are highest in the Stockholm CBD, where the average rent is approximately 63 percent higher than in Stockholm City and almost three times as high as in Stockholm Suburbs, Gothenburg, and Malmö. The variable Age, captures the effective age of the building.⁵ In our dataset the average age is about twice as high in the Stockholm CBD as in the suburbs. This is a consequence of how Stockholm (like other cities) has expanded, with a higher proportion of older buildings in the center, than in the more recently developed suburbs.

The average lease term is very similar across areas and quite close to three years. The distribution of leases by lease length and year is given in Appendix I. In fact two thirds of all observations are three-year leases, which is the default alternative on the Swedish market. Remaining contracts are divided rather evenly between shorter and longer contract lengths. We note that there is very little

3 SFI/IPD are about to publish an historical index going back to 1984.

4 As discussed by Webb and Fisher (1996), Fisher and Webb (1997), and Stanton and Wallace (2002), a unified way of comparing leases with variable cash flow is to use the level annual rental payment that has the same present value as the actual cash flows from the lease.

5 This variable, which is collected from the Property Assessment Register, is set by the tax authorities and coincides with the actual age of the building until a major renovation is being made. At each major renovation a modified year of construction (värdeår) is determined reflecting the estimated economic age of the building after the renovation.

variation in lease-lengths across time and markets.⁶ We can also identify when a lease is the result of renegotiations with the current tenant. As the rent level following renegotiations might be different from that of new lease contracts, we use a dummy variable for renegotiation, Reneg. The proportion of renegotiated leases is higher in Stockholm than in the other markets; apparently due to a higher tenant turnover in the Gothenburg and Malmö markets.

Three dummy variables are used to control for the type of heating clause in the contract. In the default case (two thirds of all contracts), heating is included in the base rent. In two percent of the contracts, the tenant provides and pays for the heating (Heat_1). In one contract out of five, the landlord provides for heating, but the base rent is net of heating expenses (Heat_2). Finally, there is a number of cases with unknown heating clauses (Heat_3).

Two dummy variables control for different lease clauses. The default contract (90% of all contracts) has inflation compensation only. A small number of leases (around one percent) have graduated rents (Lease_1), and in six to ten percent of all cases there is no information about escalation clauses (Lease_ 2). Most of these contracts have flat rents with no inflation compensation, but this category also includes a limited number of contracts with special clauses and options, perhaps 1-2 percent. We believe this is a much smaller fraction than in the U.S.

Finally, the database includes 871 building dummy variables, making it possible to control for the influence of location and other building characteristics, and for property owner. The average number of contracts per property is 5.0.

5. The Term Structure of Rents

As our main purpose is to study the predictive power of implicit forward lease rates, we need to estimate the term structure in a way that allows us to extract forward rents at different maturities, without contaminating these estimates with parametric assumptions. Stanton and Wallace (2002) model the term structure as an exponential function assumed to be constant over time, whereas Gunnelin and Söderberg (2003) model the term structure as a quadratic function allowed to shift from year to year.

6 An interesting topic for further research would be to examine whether shifts in the preferred maturity are related to volatility in the future term structure. Obviously, and as suggested by an anonymous referee, when longer time series of

We use a non-parametric approach when estimating the term structure. For each of the years 1998- 2002, dummy variables referring to seven different lease lengths from 12 to 72 months are defined.

We estimate the following equation by OLS:

( )

( )

( ) ( ) ( )

(

_iⁱ

)

_i,02^{i i}_{i i} ^{i,00 i i,01}

i i i

i i

i i

i i

i i

e Year

Year Year

Year

Year 2

Lease a Lease_1 a

Heat_3 a

Heat_2 a

Heat_1 a

Reneg a

Age a Age a a Rent

′ +

⋅

′ +

⋅

′ +

⋅

′ +

⋅

′ +

⋅

′ +

⋅ + +

+ +

+ +

+ +

+ +

=

g Buildin g

h Lengt f

h Lengt e

h Lengt d

h Lengt c

h Lengt b

99 ,

98 8 ,

7 6

5 4

3 2 2

1 0

_ ln

(1)

where b=

[

b₂,...,b₆

]

, c=

[

c₁,...,c₆

]

, d=

[

d₁,...,d₆

]

, e=

[

e₁,...,e₆

]

, f =

[

f₁,...,f₆

]

1 0,a ,..., a

and

are vectors of parameters to be estimated, as have to be the parameters . Length

[

g₁,...,g₈₇₁

]

= g

( )

a8 i = [12, 24, 36, 48, 60, 72] is a vector of dummy variables representing the lease length in months. Year dummies apply to the month of January for each year. We interpolate linearly for intermediate months in the following way. For lease i, signed in month j of year Y, Year_i,Y = 13− j 12, and

(

1

)

12

1 = −

+ j

Year_i,Y . We employ an analogous interpolation scheme for the length dummies when the lease length is not an integer number of years.

We perform these regressions separately for the five geographical markets: Three submarkets within the Stockholm metropolitan region, Gothenburg, and Malmö. The results presented in Table 3 demonstrate that the regressions are successful in accounting for the rent variation, with adjusted R-squares varying from a low .58 in Malmö to a high .78 in Gothenburg. Much of the explanatory power is due to the property dummies not presented in the table. They capture location and other characteristics of the property, as well as the various rent setting strategies used by landlords. The only property characteristic included is age, which is generally insignificant given the property dummies.⁷ Among the dummy variables representing contract features, two stand out as consistently significant. Contracts that are renegotiated with the incumbent tenant tend to have rents between 4 and 10 percent below those for new tenants. Further, rents that do not include heating costs are 5 to 10 percent higher than those where heating is included. This appears counter- intuitive. However, based on discussions with Swedish real estate professionals we interpret the variable as an indicator of unmeasured quality characteristics, since contracts for higher priced offices typically do not include heating.⁸

rental agreements become available, it will be possible to test the predictability of the volatility in the term structure.

7 Size was found to be insignificant in all regressions and was deleted from the regressions.

8 In our sample the average (median) rent for offices with heating included is 1,595 (1,555) compared to an average of 1,717 (1,661) when heating is not included.

The term structure is represented by a set of dummy variables as described above. A first question is whether accounting for contract length matters at all. We have tested for that against the null hypothesis of all contract length coefficients being restricted to the same value. As we see from Table 4, this restriction is rejected by standard F-tests (at the 10 percent level or lower) in about half the cases. Given that we expect the term structure to matter in some market situations but not in others, this is an expected outcome. The implied term structure curves are presented in Figures 2a- e. These are constructed by evaluating the estimated equations at the mean values for the explanatory variables, except lease length, and taking anti-logs. It is clear from the corresponding coefficient estimates in Table 3 that the individual lease-length coefficients are estimated rather imprecisely, with typical standard errors around 0.2. Given that no structure is put on the term structure curves, the irregular shape of some of them should come as no surprise. Nevertheless some patterns emerge upon closer inspection.

Due to transaction costs in renewing contracts one would expect a premium on short-term contracts (Miceli and Sirmans, 1999). If there is such a pattern, it should primarily be seen at the short end of the term structure curves, whereas rent expectations and risk considerations should be relatively more important in explaining the slope at longer contract lengths. In our term structure curves we do not see any consistent pattern at the short end, however. Averaging across years for different markets, we see that the average difference between 12 and 24 month rents is positive in Stockholm CBD and suburbs and in Malmö, but negative in Stockholm city and Gothenburg.

To illustrate the general tendency of the term structure curves at the most frequent contract lengths, we have taken the difference between the average of the 48 and 60 month rents on the one hand and the 24 and 36 month rents on the other hand, thus disregarding the 12 and 72 month rents that tend to be estimated with less precision. These differences are positive – i.e. the term structure curve tends to be upward sloping – for all years in Stockholm CBD, which is the strongest market, and in Stockholm city (except in 1998). They are also positive for all years in Gothenburg, whereas the pattern is more mixed for Stockholm suburbs and Malmö.⁹

Looking across markets for different years, the average slope is slightly negative for 1998 and increasingly positive for later years. If we interpret the slope as an indicator of rent expectations, this suggests strongest expectations of rent growth in Stockholm CBD, and generally stronger

9 The impression of a mostly positively sloped rent structure is confirmed by regressions where rent is parameterized as a linear function of contract length.

growth expectations toward the end of the period. The former result is consistent with the relative performance of the various markets during this period. The latter pattern may be more surprising, since 2002 is widely regarded as a turning point for Swedish office markets, in particular in Stockholm, and one would have expected this to be reflected in relatively lower rents for longer term contracts.

6. Rental Indices

Estimated rent differences across contract lengths are sometimes quite large, and the tests reported above indicate that the contract length is a statistically significant factor in explaining rents in many cases. This suggests that it should be important to account for contract length in describing the general evolution of the rent level. To address this issue, we have computed rent indices based on three different methods: A naïve index that measures the average rent per square meter in the sample; an hedonic index based on a regression equation like (1) but not including contract length;

and an hedonic index including contract length based on equation (1). The two hedonic indices express the change in rent level for an “average” lease, with all independent variables (including the composition of lease lengths) held constant at their average values, taken across all years and regions in the sample.

The rates of change of the indices are displayed in figure 4. This confirms that rents increased faster in Stockholm CBD and Stockholm city than in other areas during this period, in particular in 1999 and 2000. Despite differences in amplitude, the pattern of rental development is quite similar in all three Stockholm submarkets, with the highest rates of rent growth in 1999 and 2000, and a pronounced reduction in 2001. This similarity is not surprising since they are part of the same metropolitan region. Gothenburg has a smoother development with little change in growth rates from year to year, whereas the graph for Malmö shows a distinct peak in 2000, probably related to the construction of the bridge between Sweden and Denmark, bringing Malmö “closer” to Copenhagen.

Comparing the three indices, we see that the two hedonic indices follow each other rather closely year by year, while there are several examples of large differences between the two hedonic indices on the one hand and the mean-rent index on the other hand. The importance of controlling for attributes is in line with the findings of Webb and Fisher (1996) who find that although the sample average follows their estimated hedonic index rather closely in most years, there are instances when

they differ strongly. Likewise in our data there are years where the change in averages differs by more than 10 percentage points from the change of the hedonic indices. Accumulating over all five years, there remain substantial differences for some markets; for Stockholm city the rate of rent change is 67 percent according to the hedonic index accounting for term, but only 44 percent looking at the average rent. Differences are not consistent across regions, however, not even with respect to the sign. Comparing the two hedonic indices, differences are smaller. There is no example of differences from year to year being larger than 5 percent and the largest difference over the whole period is for Stockholm CBD, where the index not accounting for term records an increase of 98 percent compared with 83 percent for the index that accounts for term.

If an index is measured with error that should presumably add to the variance of it. Of course five years of data is too short to get a reliable estimate of variance. Still it may be worth noting that there is some tendency for the average rent to exhibit more variance than the hedonic indexes, in particular for Stockholm city and Stockholm suburbs. There is not much difference in variance, however, between the two hedonic indices.

7. Forward Rents and Future Spot Rents

In order to study how well forward rents predict future rents, we need to calculate implicit forward rents. Based on the discussion in section 2, we posit that the present value of leasing a unit for T-t years at time t, PV

(

RT₋t_,t

)

, equals the present value of leasing a unit for S-t years at time t,

(

RS t_,t

)

PV ₋ , plus the present value of signing a forward lease of the unit for T-S years at time t, starting at time S, PV

(

RT^F₋S_,t

)

. Formally:

(

RT t_,t

)

PV

(

RS t_,t

)

PV

(

RT^FS_,t

)

PV ₋ = ₋ + ₋ . (2)

To calculate PV

(

R_T−t,t

)

and PV

(

R_S−t,t

)

in equation (2), we use the estimated rents, at time t, for leases of length T-t and S-t, respectively, from rental equation (1). We then solve for PV

(

RT^F₋S_,t

)

, from which the implicit forward rent is extracted. The present value calculations are made assuming that the leases are fully adjusted for an inflation rate of 2 percent

F t S, T−

R

10, and with a nominal

10 Two percent coincides with the inflation target of the Riksbank (the Swedish Central Bank). Actual inflation rates (12-month moving CPI changes) during this period fluctuated between –0.4 and +3.2 percent.

discount rate of 8 percent. Using a wide range of discount rates, we found that the calculations are insensitive to the choice of the discount rate.¹¹ The same insensitivity is noted by Webb and Fisher (1996) when they transform rental streams to present values to calculate “effective” rents.

For each of the five property markets under study, a total of 40 implicit forward rents are calculated for different values of t, S, and T: 14 based on the term structure for 1998, 12 based on 1999, and 9 and 5 based on 2000 and 2001, respectively. Appendix II provides details on how these figures are derived. We run regressions to test whether the forward rate at t, , bears any relation to the corresponding spot rate subsequently realized at S, R

F t S

RT_{− ,}

T-S,S. In the regression analysis, we normalize

these rates by dividing both by the spot rate at time t. This yields:

t S T

F t S T

R R

, , 1

−

= −

λ ,

t S T

S S T

R R

, , 2

−

= −

λ

where is the spot rent at time t for a T-S year lease calculated from the estimated term structure at time t, and is the spot rent at time S for a T-S year lease calculated from the estimated term structure at time S.

t S

RT_{− ,}

S S

RT_{− ,}

In Figures 3a-e, the two λ ratios are plotted against each other for each of the five areas. It is obvious that there are some extreme outliers, in particular for λ1. For this reason, we perform two sets of regressions, one based on all observations and one excluding λ values below 0 and above 2.5. It is also worth noting that we are dealing with a regression equation with measurement errors, since both term rents and forward rents are estimated with error. It is well known that a measurement error in an independent variable leads to inconsistent parameter estimates with a bias towards zero.

We test for the predictive power of forward rents by regressing (for each property market separately) the λ2 ratio on the λ1 ratio using OLS.¹² If the forward rent has any predictive power, then the slope of the equation should be different from zero. If the intercept is zero and the slope equals unity, then the forward rent is an unbiased predictor of the future spot rent. The results of these regressions are displayed in Table 5a. Clearly, the hypothesis that implicit forward rents are unbiased predictors of future spot rents is overwhelmingly rejected; the intercept is significantly

11 For example, the average value of the forward rents in the Stockholm CBD calculated with a 4 percent discount rate is 2,325 SEK, while the corresponding figure is 2,344 SEK using a 12 percent discount rate.

greater than zero and the slope coefficients are significantly less than unity in all cases. The results for the three Stockholm markets are fairly similar and indicate that there is some predictive power in the term structure. The slope coefficients are all between 0.2 and 0.3, with t-values safely above 2, except for the CBD when outliers are excluded. A 10 percent increase in the forward rent predicts an increase in future spot rent by between 2 and 3 percent. For Gothenburg and Malmö, on the other hand, the regressions explain none of the variation in rents and forward rents do not appear to predict future spot rents.

As discussed above, the term structure may be affected by transaction costs. In equilibrium, rents will adjust such that landlords are indifferent between signing a long lease, thereby avoiding the risk of having to search for a new tenant, and signing a short lease and expecting to face extra costs for another short lease as the first lease expires. To account for this, we have also performed regressions where we deduct a transaction cost from the first and last year of each lease when calculating implicit forward rates according to expression (2). We set the transaction cost equal to 30 percent of the average yearly rent in the data set for 3-year leases contracted in 1998. The results from these regressions are presented in Table 5b. We can see that results are fairly similar to those where we do not adjust for transaction costs. If anything, the model now performs slightly better with the slope coefficients for Stockholm CBD without outliers and for Gothenburg now being significant at the 10 percent level.

Overall, we conclude that there is evidence that the term structure of rents contains information that could be used for forecasting future rents.

8. Concluding Remarks

Do rents vary with contract length? And, if so, do forward rents contain information about future spot rents? We believe we have answered the first question in the affirmative. Based on a rich database of more than 4,000 office rental agreements in the three largest cities of Sweden, we have shown that adding contract length to a hedonic rent equation – controlling for other contract features and physical and locational building characteristics – and allowing for these effects to be time-varying frequently adds significantly to the explanatory power of the equation. As a way of demonstrating the importance of accounting for the term of rental contracts in a proper manner, we have compared rental indices based on hedonic equations with and without contract length among

12 This is in analogy with a huge literature on interest rates and exchange rates; see e.g. Fama (1976).

the variables. Our results show that the indices can be substantially distorted if the term of the leases is not taken into account.

We have attempted to go beyond merely demonstrating that “term structure matters”. The simplest theory holds that the term structure of rents – in analogy with the term structure of interest rates or that of forward currency contracts – is determined by expectations about future spot rents.

Assuming rational expectations, this translates into the hypothesis that the forward rents implicit in the current term structure are unbiased predictors of future spot rents. The hypothesis of unbiasedness is resoundingly rejected for all markets, but for the Stockholm markets forward rents have significant predictive power for future spot rents, although they are strongly downward biased.

Perhaps the strong underprediction should not come as a surprise. With rent increases in excess of 100 percent over the time period examined, it may not be that surprising that only 20 to 30 percent of this was anticipated in Stockholm, and almost nothing in Gothenburg and Malmö. The difference between regions might indicate that the Stockholm office market is more sophisticated than the other two markets, possibly because of the greater role of institutional investors.

Our findings that forward rents have only a relatively weak predictive power need to be put in perspective. It is well known that analogous tests for currencies and bonds tend to yield similar results. With regard to exchange rates, Froot and Thaler (1990) counted 75 published studies with regressions of the rate of depreciation against the forward premium. The average coefficient estimate in these studies was -0.88, not even positive. The foreign exchange literature has responded to this apparent anomaly in two ways. One has been to model time-varying risk premia, the other to dig into various data problems, e.g. the big and infrequent jumps associated with devaluations (the “peso problem”).

Likewise, the real estate literature needs to deepen the theoretical understanding of the pricing of risk in rental contracts, and develop databases that will allow us to describe the term structure with greater precision. In particular, there is a strong need for data for more regions and longer time periods. This would allow the expectations hypothesis to be tested in various phases of the real estate cycle, and more generally to investigate what macro-economic factors impact when long term rents are formed on the market. It would also make it possible to account for differences across markets, e.g. the relative importance of domestic and international institutional investors. Last but not least, longer time series would permit tests of the predictability of the volatility as well as of the level of future rents.

References

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Table 1. Selected property market indicators for prime location office properties in Stockholm, Gothenburg, and Malmö (Rents and prices in SEK/m²)

Year 1996-1997 1997-1998 1998-1999 1999-2000 2000-2001 Stockholm

Rent 2,400—3,000 2,500—3,400 2,800—3,800 3,500—4,500 4,500—5,500

Yield 5—6% 5—5.75% 4.8—5.5% 4.8—5.5% 5.5—6%

Price 35,000—45,000 40,000—48,000 45,000—55,000 50,000—60,000 55,000—65,000 Gothenburg

Rent 1,000—1,300 1,000—1,500 1,100—1,600 1,300—1,800 1,400—2,000

Yield 7—8% 6.5—7.5% 5.5—6.5% 5.5—6.5% 6—6.75%

Price 9,000—13,500 10,000—17,000 12,000—20,000 14,000—23,000 16,000—24,000 Malmö

Rent 800—1,100 850—1,400 900—1,600 1,000—1,600 1,100—1,800

Yield 6.5—8% 6—7% 5.5—6.5% 5.5—6.5% 6—6.75%

Price 6,500—12,000 8,000—16,000 9,000—18,000 10,000—18,000 11,000—19,000 Note: The average exchange rate during this period was 9 SEK/USD.

Source: The Swedish Property Indicator.

Table 2. Sample means (standard deviations in parentheses) Variable Stockholm

CBD Stockholm

City Stockholm

Suburbs Gothenburg Malmö

Log_rent 8.107 7.620 7.110 7.102 7.076

(0.301) (0.349) (0.394) (0.329) (0.298)

Age 38.592 31.803 19.457 29.016 37.848

(23.792) (20.277) (11.793) (19.631) (21.223)

Term 39.066 37.989 37.060 38.168 37.139

(11.135) (11.718) (13.851) (11.524) (12.441)

Reneg 0.483 0.512 0.455 0.382 0.390

Heat_1 0.022 0.021 0.017 0.017 0.017

Heat_2 0.186 0.246 0.238 0.213 0.194

Heat_3 0.091 0.037 0.090 0.036 0.124

Lease_ 1 0.009 0.005 0.007 0.021 0.030

Lease_ 2 0.072 0.072 0.098 0.068 0.063

No. of

observations 671 1206 1225 811 474

Variable definitions:

Rent Annual base rent per square meter.

Age Effective age of the building (in years), taking renovations into account as estimated by the tax assessment authority.

Term Length of the rental contract (in months).

Reneg Renegotiation dummy; Reneg=1 when the rent is a result of renegotiation.

Heat_1 Heating clause dummy; Heat_1=1 when heating is provided and paid for by the tenant.

Heat_2 Heating clause dummy; Heat_2=1 when base rent it net of heating.

Heat_3 Heating clause dummy; Heat_3=1 when type of heating clause is unknown.

Lease_1 Lease type dummy; Lease_ 1=1 when a contract includes rent escalation clauses.

Lease_2 Lease type dummy; Lease_ 2=1 when a contract deviates from a standard CPI-indexed contract. This includes contracts with flat rents as well as contracts with various option clauses.

Table 3. Hedonic regression results.

Variable Stockholm CBD Stockholm City Stockholm Suburbs Gothenburg Malmö

Intercept 7.275 (0.233) *** 6.713 (0.383) *** 6.847 (0.209) *** 6.593 (0.295) *** 7.327 (0.670) ***

Age 0.012 (0.009) -0.036 (0.014) ** -0.011 (0.015) -0.022 (0.011) ** -0.040 (0.036)

(Age)² 0.000 (0.000) 0.001 (0.000) ** 0.000 (0.000) 0.000 (0.000) 0.000 (0.000)

Reneg -0.060 (0.022) *** -0.099 (0.019) *** -0.099 (0.023) *** -0.035 (0.017) ** -0.050 (0.030) *

Heat_1 -0.020 (0.048) 0.034 (0.067) -0.042 (0.094) -0.019 (0.050) 0.092 (0.079)

Heat_2 0.083 (0.039) *** 0.047 (0.027) * 0.064 (0.028) ** 0.081 (0.020) *** 0.100 (0.035) ***

Heat_3 -0.060 (0.042) -0.123 (0.048) *** -0.118 (0.066) * -0.028 (0.053) 0.012 (0.074)

Lease_ 1 0.001 (0.082) -0.015 (0.072) 0.049 (0.073) -0.089 (0.041) ** -0.032 (0.144)

Lease_ 2 0.032 (0.040) 0.031 (0.034) 0.051 (0.036) 0.036 (0.032) -0.034 (0.072)

D_24_1998 0.044 (0.146) 0.597 (0.356) -0.131 (0.152) 0.191 (0.225) 0.120 (0.227)

D_36_1998 0.074 (0.166) 0.135 (0.228) -0.466 (0.130) 0.217 (0.214) -0.023 (0.213)

D_48_1998 -0.096 (0.198) 0.254 (0.230) -0.563 (0.205) 0.234 (0.233) -0.188 (0.240)

D_60_1998 0.330 (0.145) 0.426 (0.244) -0.233 (0.158) 0.223 (0.228) 0.180 (0.233)

D_72_1998 -0.443 (0.229) 0.178 (0.360) -0.224 (0.169) 0.011 (0.227) -0.727 (0.874)

D_12_1999 0.247 (0.295) 0.367 (0.277) -0.247 (0.169) 0.169 (0.273) 0.182 (0.259)

D_24_1999 0.164 (0.197) 0.052 (0.217) -0.352 (0.130) 0.292 (0.222) 0.133 (0.241)

D_36_1999 0.173 (0.162) 0.247 (0.220) -0.290 (0.127) 0.347 (0.212) 0.148 (0.202)

D_48_1999 0.269 (0.167) 0.215 (0.228) -0.292 (0.147) 0.286 (0.217) 0.073 (0.237)

D_60_1999 0.151 (0.172) 0.252 (0.225) -0.184 (0.146) 0.376 (0.221) 0.172 (0.218)

D_72_1999 0.322 (0.193) 0.119 (0.271) -0.149 (0.165) 0.047 (0.247) 1.875 (0.984)

D_12_2000 0.903 (0.298) 0.282 (0.240) -0.156 (0.143) 0.339 (0.240) 0.089 (0.200)

D_24_2000 0.195 (0.176) 0.541 (0.239) -0.187 (0.138) 0.275 (0.228) 0.153 (0.232)

D_36_2000 0.377 (0.164) 0.444 (0.219) -0.143 (0.128) 0.393 (0.212) 0.133 (0.205)

D_48_2000 0.435 (0.188) 0.602 (0.226) -0.162 (0.148) 0.458 (0.216) 0.151 (0.224)

D_60_2000 0.373 (0.171) 0.449 (0.223) -0.091 (0.133) 0.463 (0.220) 0.132 (0.246)

D_72_2000 0.432 (0.232) 0.272 (0.437) -0.016 (0.178) 0.795 (0.332) 0.187 (0.223)

D_12_2001 0.609 (0.200) 0.595 (0.241) 0.041 (0.146) 0.338 (0.237) 0.427 (0.264)

D_24_2001 0.678 (0.195) 0.549 (0.230) -0.106 (0.139) 0.609 (0.224) 0.303 (0.230)

D_36_2001 0.647 (0.163) 0.666 (0.220) -0.015 (0.129) 0.515 (0.212) 0.317 (0.207)

D_48_2001 0.791 (0.173) 0.701 (0.228) -0.185 (0.161) 0.519 (0.230) 0.425 (0.212)

D_60_2001 0.703 (0.169) 0.791 (0.225) 0.046 (0.134) 0.672 (0.219) 0.503 (0.220)

D_72_2001 0.366 (0.431) 0.906 (0.327) -0.406 (0.249) 0.657 (0.304) -1.311 (1.080)

D_12_2002 0.699 (0.220) 0.774 (0.232) -0.037 (0.145) 0.474 (0.239) 0.517 (0.275)

D_24_2002 0.160 (0.258) 0.538 (0.241) -0.039 (0.156) 0.272 (0.367) 0.367 (0.233)

D_36_2002 0.823 (0.166) 0.775 (0.222) -0.015 (0.133) 0.566 (0.214) 0.384 (0.208)

D_48_2002 0.560 (0.194) 0.646 (0.318) 0.256 (0.194) 0.699 (0.230) 0.387 (0.230)

D_60_2002 0.758 (0.181) 0.823 (0.225) -0.038 (0.160) 0.573 (0.219) 0.404 (0.231)

D_72_2002 0.936 (0.219) 0.679 (0.985) 1.301 (0.265) 1.059 (0.342) 0.653 (0.222)

Adjusted R² 0.712 0.627 0.732 0.776 0.583

The table reports results of estimating eq. (1) by OLS.

Dependent variable = log rent per square meter.

White adjusted standard errors are in parenthesis.

*** .01 level of statistical significance, ** .05 level of statistical significance, * .10 level of statistical significance.

No significance level is indicated for the year and term dummy variables.