Abstract
This study analyzes the rent term premium for leases that can be cancelled by the lessee. We model the lessor’s tradeoff between leasing costs and the cost of cancellation options based on the recognition that many leases are cancellable by lessees, and lease markets involve significant transaction costs. We demonstrate that, regardless of the expected future rents, the rent term structure is upwardsloping when there is no leasing cost but Ushaped when the lessor faces moderate leasing costs. Residential leases in Japan, which are all cancellable by tenants, exhibit the term structure that is consistent with our calibrated model.
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Notes
Source: The Real Estate Roundtable, 2011 Annual Report. Available at http://www.rer.org.
Source: The Equipment Leasing and Finance Foundation, Economic Impacts of the Proposed Changes to Lease Accounting Standards, December 12, 2011. Available at http://www.leasefoundation.org.
This type of lease contract was prevalent before 1941 but eliminated to prevent landlords from evicting incumbent tenants and circumventing rent control during World War II (Survey of New Form of Residence Associated with FixedTerm Lease Contracts, Housing Research and Advancement Foundation of Japan, March 2015).
This requirement is specified by Article 28 of the Tenure Law, which is known as “ShakuchiShakkaHou” in Japan.
Ministry of Land, Infrastructure, Transport, and Tourism, 2013FY Housing Market Survey (Jutaku Shijo Doko Chosa).
The stochastic discount factor is derived from the firstorder condition for the lessor’s utility maximization problem given the lessor’s wealth portfolio and consumption stream.
Ambrose et al. (2002) study the opposite type of leases; in other words, leases with rents that adjust only in the upward direction.
The lessor’s use of alternative lease types does not change our proof because lease values for alternative leases are equalized at any time under the lessor’s consistent pricing condition.
The rent term premium is also affected by the expected net rent gap prior to the final period. We take into account the total rent gap in our numerical exercise.
We use lease contracts that are shorter than or equal to five years because the number of leases longer than five years is small and their tenant characteristics are significantly different from the average characteristics.
In Appendix D, we present the result of additional tests by probit regressions.
In Appendix D, we present the result of additional tests by probit regressions.
This empirical strategy is equivalent to pooling both types of leases and including interaction terms with a fixedlease dummy by treating general leases as a reference group.
The average of the 2003 and 2008 national vacancy rates for rental housing is 19 %.
The estimated term structures exhibit the same shapes based on Models (b), (c), or (d).
The mean values are 16.4 and 15.1 years for building age, 9.5 and 9.8 min for the time to the nearest station in low and highvacancy areas, respectively.
To compute the market rent for the remaining term, we use a homogeneity property of the model. Because the rent risk, renewal costs, and riskadjustments are all multiplicative, the ratio of the \( \left(Tt\right) \) year lease rate to the shortterm rate at time t equals that ratio at time zero. Thus, \( {\hat{R}}_t^{Tt}={\hat{R}}_0^{Tt}\times {R}_t^1/{R}_0^1 \) \( . \)
We implicitly assume that the landlord inelastically supplies an existing rental unit and thus bears all costs associated with market frictions. This assumption simplifies computations because the lessee’s cancellation decisions are not affected by these costs.
The lessor’s risk aversion and the riskiness of shortterm rents represented by a negative covariance with the discount factor alter the probability mass function under measure Q. Specifically, when shortterm lease rates are negatively correlated with the discount factor, a larger probability mass is assigned to the state of a low rent as the risk aversion becomes larger. Then, the lower expected value under measure Q represents the certaintyequivalent value.
Source: Recruit Residential Price Index, January 14, 2013.
Available at http://www.jresearch.net/house/jresearch/rrpi/index.html.
Rotten structures are excluded in this calculation.
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Acknowledgments
We thank Brent Ambrose; Yildiray Yildirim; Ed Coulson; Nai Jia Lee; James Conklin; Masahiro OkunoFujiwara; Hiroyuki Ozaki; Hiroyuki Seshimo; Toshiki Honda; David Geltner, Lynn Fisher; and the participants of the AREUEA International Conference in Korea, the ASSA meeting in Chicago, the Keio University Public Economics Seminar, the 26th ARSC annual conference, the 2013 Japanese Economic Association Autumn Meeting, and MaastrichtNUSMIT symposium for providing valuable comments and suggestions. This research is supported in part by the Keio/Kyoto University Global COE Program of Japan and the Institute for Real Estate Studies at the Pennsylvania State University.
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Appendices
Appendix A: Proofs
Proof of Lemma: To prove the lemma, we define two conditions:

Condition (a)
At least one of the initial leases has not been cancelled until period \( T1 \); i.e., the market rent has not been low enough to induce cancellations of both leases: \( \forall t\le T2:\ {\hat{R}}_t^{Tt}> \min \left\{{\hat{R}}_0^T,{\hat{R}}_0^{T1}\right\} \).

Condition (b)
The market rent for the final period is higher than the preceding rental income under the \( T \) strategy: \( {R}_{T1}^1>{\hat{Y}}_{T2}^T \) .
There are three cases with respect to the rent for the final period. We demonstrate that the rent for the \( T1 \) strategy is strictly higher than the rent for the \( T \) strategy in the first case and is equal to the rent for the \( T \) strategy in the second and third cases.
First Case: Conditions \( \left(\mathrm{a}\right) \) and \( \left(\mathrm{b}\right) \) both hold. If the initial rent for the \( T \) period lease is greater than or equal to the initial rent for the \( T1 \) period lease \( \left(\mathrm{i}.\mathrm{e}.,\ {\hat{R}}_0^T\ge {\hat{R}}_0^{T1}\right) \) , then condition \( \left(\mathrm{a}\right) \) implies that the initial \( T1 \) period lease will never be canceled until maturity. The rent at time \( T2 \) will be \( {\hat{Y}}_{T2}^{T1}={\hat{R}}_0^{T1} \) for the \( T1 \) strategy and \( {\hat{Y}}_{T2}^T= \min \left\{{\hat{R}}_0^T,{\hat{R}}_t^{Tt};t\le T2\right\} \) for the \( T \) strategy. By condition \( \left(\mathrm{b}\right) \), the rent under the \( T \) strategy will be unchanged for the final period \( \left({\hat{Y}}_{T1}^T={\hat{Y}}_{T2}^T\right) \), whereas under the \( T1 \) strategy, the initial lease will expire at time \( T1 \), and the rent during the final period will be adjusted upward to \( {\hat{Y}}_{T1}^{T1}={R}_{T1}^1 \) . Condition \( \left(\mathrm{b}\right) \) also implies that during this period, the rent for the \( T \) strategy will be strictly lower than the rent for the \( T1 \) strategy \( \left({\hat{Y}}_{T1}^T<{\hat{Y}}_{T1}^{T1}\right) \) .
Conversely, if the initial rent is lower for the Tperiod lease than for the \( T1 \) period lease \( \left(\mathrm{i}.\mathrm{e}.,\ {\hat{R}}_0^T<{\hat{R}}_0^{T1}\right) \), then conditions (a) and (b) imply that the initial \( T \) period lease will never be canceled until maturity. Thus, the rent during the final period is the initial rent \( \left({\hat{Y}}_{T1}^T={\hat{R}}_0^T\right) \). In contrast, the \( T1 \) period lease may or may not be cancelled. If the initial lease has expired without a cancellation, the rent during the final period will be \( {\hat{Y}}_{T1}^{T1}={R}_{T1}^1 \). Alternatively, if the initial lease has been cancelled, the rent during the final period will be the historical minimum of market rents: \( {\hat{Y}}_{T1}^{T1}= \min \left\{{\hat{R}}_t^{Tt};t\le T1\right\} \). In either case, conditions (a) and (b) imply that during this period, the rent for the T strategy will be strictly lower than the rent for the \( T1 \) strategy \( \left({\hat{Y}}_{T1}^T<{\hat{Y}}_{T1}^{T1}\right) \).
Second Case: Condition (a) holds but condition (b) does not hold \( \left({R}_{T1}^1\le {\hat{Y}}_{T2}^T\right) \) . The final rent is the same for both strategies \( \left({\hat{Y}}_{T1}^T={\hat{Y}}_{T1}^{T1}={R}_{T1}^1\right) \) because the rent is adjusted to the low level of market rent that exists during the final period regardless of whether the initial T period rent is higher than the \( T1 \) period rent.
Third Case: Condition (a) does not hold. Because both leases will have been cancelled at the same time before time \( T1 \), both strategies will use the same lease during the final period. Thus, the final rent is the same for both strategies: \( {\hat{Y}}_{T1}^T={\hat{Y}}_{T1}^{T1} \).
In summary, the \( \mathrm{T} \) strategy produces a strictly lower rent than the \( T1 \) period strategy \( \left({\hat{Y}}_{T1}^T<{\hat{Y}}_{T1}^{T1}\right) \) if conditions \( (a) \) and \( (b) \) both hold. Otherwise, both strategies give the same rent \( \left({\hat{Y}}_{T1}^T={\hat{Y}}_{T1}^{T1}\right) \) .
Proof of Proposition: Suppose the initial rent for the \( T \) period lease is not higher than the initial rent for the \( T1 \) period lease \( \left({\hat{R}}_0^T\le {\hat{R}}_0^{T1}\right) \). The \( T1 \) strategy will produce a weakly positive rent premium relative to the \( T \) strategy until both leases are cancelled. In addition, the \( T1 \) strategy will generate a strictly higher expected rent than the \( T \) strategy for the final time period that is examined, as demonstrated by the lemma. Thus, the \( T1 \) strategy would provide a strictly larger value to the lessor than the \( T \) strategy; this result would violate the specified consistent pricing condition. Therefore, the initial rent for the \( T \) period lease must be higher than the initial rent for the \( T1 \) period lease \( \left({\hat{R}}_0^T>{\hat{R}}_0^{T1}\right) \). In other words, the term structure of cancellable leases must be upward sloping between \( T1 \) and \( T \). Because we can apply the same argument to any lease term \( u\;\left(u=2,\dots, T\right) \), the term structure for all cancellable leases must be upward sloping.
Appendix B: Detail of Numerical Analysis
We numerically analyze the term structure by parameterizing the riskfree rate, rent volatility, the risk premium on the shortterm rent, the expected rent growth, and most importantly, leasing costs. We construct an annual binomialtree model for an 8 year period and generate 1000 paths of shortterm lease rates. At each node of the tree, the shortterm rate changes by a factor of either \( \exp \left(\sigma \right) \) or \( \exp \left(\sigma \right) \), where σ ∈ [0, ∞) is a rent volatility measure. In the continuoustime limit, an instantaneous rate of rent growth during time period \( \tau \) is normally distributed with the volatility \( \sigma \sqrt{\tau } \). At the beginning of each year, a lessee chooses the rent that is represented by Equation (3).^{Footnote 18} We introduce a proportional leasing cost \( c{\widehat{Y}}_t^T \), which is equivalent to a \( 12c \) month vacancy cost at the time of cancellation. The lost income during vacant period is typically the most significant cost for the lessor.^{Footnote 19} We compute the landlord’s rental income for each rent path because the cancellation option is a pathdependent option. The present value of the Tyear lease is computed as:
where \( {\mu}_t \) is the riskfree discount factor for t time periods, \( {\mathrm{E}}_0^Q\left[{\hat{Y}}_t^T\right] \) is the expected lease rate under the equivalent martingale measure Q, and \( {\mathbb{I}}_{\left\{{\hat{Y}}_t^T\ne {\hat{Y}}_{t1}^T\right\}} \) is an indicator function that takes the value of one if the lease is cancelled and zero otherwise.^{Footnote 20} After computing the present value \( {V}^1 \) for a rollover shortterm strategy, we determine the initial lease rate for a Tperiod lease \( {\hat{R}}_0^T \) such that the consistent pricing condition holds: \( {V}^1 = {\hat{V}}^T \) for T = 2, …, 8.
Appendix C: Parameter Values for Calibration
We determine parameter values as follows. We use 1 % for the riskfree rate because the average endofmonth yields of Japanese Government Bonds are 1.32 % for 10year bonds and 0.65 % for 5year bonds between 2001 and 2012. Regarding rent growth rates and volatility, we use the Recruit qualityadjusted rent index for the Kanto region between 2005 and 2012.^{Footnote 21} In our lease sample, 39 % of general leases and 56 % of fixedterm leases are observed in this region. The average annual growth rate is 0.82 % and standard deviation is 1.97 %. Considering that there are smoothing issues in this aggregate index and that the volatility for an individual property is much larger, we use 1 % for the rent growth and 8 % for the rent volatility. Given that the rent volatility is relatively small, we assume that the risk premium on the shortterm rent is 1 %. Regarding the lessor’s costs, we use the 2008 National Housing and Land Survey and compute the average vacancy rate for rental dwellings to be 19 %.^{Footnote 22} Additional contracting costs are at most a few hundred dollars and ignorable. We use 19 % as the high vacancy rate and 5 % as the low vacancy rate.
Appendix D: The Difference in Property and Tenant Characteristics Between FixedTerm Lease, General Lease, and OwnerOccupied Samples
In this appendix, we present the result of probit regressions regarding the difference between owneroccupied properties and leased properties (Model (a)) and between fixedterm lease properties and general lease properties (Model (b)). Tables 6 and 7 present results for property characteristics and tenant characteristics, respectively. In Model (a), most property and tenant characteristics exhibit statistically significant differences between owneroccupied properties and leased properties. In contrast, in Model (b), differences are not statistically significant for most characteristics. These results are consistent with the descriptive statistics presented in Tables 1 and 2.
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Yoshida, J., Seko, M. & Sumita, K. The Rent Term Premium for Cancellable Leases. J Real Estate Finan Econ 52, 480–511 (2016). https://doi.org/10.1007/s111460159528x
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DOI: https://doi.org/10.1007/s111460159528x
Keywords
 Leasing
 Housing
 Asset pricing
 Cancellation options
 Term structure
 Expectations hypothesis
 Transaction costs
 Hedonic regression
 Japan
JEL Classification
 G12
 G13
 R31