GPIF Working Papers

Real estate fund returns and debt ratio (leverage)

June 21, 2024
Amane Saito

EXECUTIVE SUMMARY

Koichi MiyazakiWhen a real estate fund acquires real estate, it is financed by debt portion (e.g., by bank loans)and equity portion (e.g., invested from investors). Normally, when institutional investors invest in areal estate fund, they are investing in the equity portion. If there are two real estate funds that
acquire the same property but have different capital structures, institutional investors may earndifferent returns depending on which real estate fund they invest in.

This study takes the debt ratio (leverage) as an indicator of capital structure and examines theimpact of capital structure on the returns of real estate funds. This will allow institutional investors
to build models to monitor the extent to which real estate funds are operating with an optimal
debt ratio. In addition, it will pave the way for a relative value analysis of investments in real estate
funds as alternative assets versus investments in corporate bonds as traditional assets.

（Note: This working paper is a compilation of research results by GPIF staff, and the contents and opinions expressed in the text do not
represent the official views of the GPIF.

1. Introduction
When a real estate fund acquires real estate, it is financed by debt portion (e.g., by bank loans) and equity
portion (e.g., invested from investors). Normally, when institutional investors invest in a real estate fund, they
are investing in the equity portion (see Figure 1 in Section 2). Therefore, if there are two real estate fundswith different capital structures that acquire the same real estate, the returns earned by institutional investors
may differ depending on which real estate fund they invest in, even if they are investing in the same realestate.
This study takes the debt ratio (leverage) as an indicator of capital structure to examine the impact of
capital structure on real estate fund returns. The positive impact of an increase in the debt ratio (leverage)(i.e., a reduction in the equity portion) on the return of a real estate fund is that it increases the return of thefund by allocating more of the rents earned from real estate to the smaller equity portion. Conversely, thenegative impact of an increase in the debt ratio (leverage) (i.e., a reduction in the equity portion) is that, in
addition to an increase in interest expense due to an increase in the amount of debt, the increase in the debt
ratio increases credit risk, and the interest rate on the debt itself also increases.
I would like to contrast the impact of such a capital structure on the returns of real estate funds with theargument that "if the strict assumptions of the MM theory (Miller and Modigliani (1961)), which assume aperfect capital market, are relaxed to bring it closer to reality, the discussion of the optimal capital structurep. 1will be a trade-off between increased tax savings due to an increased debt ratio (leverage) and increased
bankruptcy risk (increased interest expense). First, the disadvantage of increasing the debt ratio (leverage)is the same for both MM theory and real estate funds (increased bankruptcy risk (increased interest
payments)). On the other hand, the advantages of an increase in the debt ratio (leverage) differ between MM
theory and real estate funds: MM theory offers tax savings, while investments in real estate funds offer
almost no tax savings due to an increase in the debt ratio (leverage). For example, assuming a J-REIT, aspecial exception under the tax law (Article 67-15 of the Act on Special Measures Concerning Taxation) is
applied, which virtually exempts investment corporations of real estate investment trusts from corporate
taxation. Under this special exception, if an investment corporation that meets certain conditions pays out anamount equivalent to more than 90% of its income before income taxes (income under the tax law) as
distributions to unitholders, the amount equivalent to such distributions can be recorded as "expenses" under
the Corporate Tax Law. In other words, real estate funds are virtually exempt from corporate tax in the firstplace, and the benefit of tax reduction does not depend on the debt ratio (leverage). In light of the above
contrast, we can utilize prior research on optimal capital structure based on MM theory by adjusting theanalytical framework so that the benefit of increasing the debt ratio (leverage) can be treated as an
improvement in return rather than a tax saving effect. There are two frameworks for such prior research:
the financial engineering approach and the corporate finance approach.
Brennan and Schwartz (1978), Leland (1994), and Leland and Toft (1996) are among the major previous
studies of the financial engineering approach. Brennan and Schwartz (1978) was the first paper to attempt
a quantitative analysis of optimal debt ratios. There, they determined the optimal debt ratio based on numericalanalysis techniques, assuming that the debt-free firm value process follows a diffusion process of constantvolatility. Although an important first step, the study does not provide analytical solutions for the value ofrisky debt or the optimal debt ratio, and thus does not provide a general comparative statics argument either.
To overcome this, Leland (1994) examined the value of corporate debt and optimal capital structure in a
unified analytical framework. Assuming that the value of corporate assets follows a diffusion process ofconstant volatility, they derived analytical results on the relationship between the value of long-term corporate
debt and optimal capital structure with respect to parameters such as corporate risk, taxes, bankruptcy costs,
etc. Leland and Toft (1996) extended the model of Leland (1994) to deal not only with the amount of debt
(debt ratio) but also with the maturity structure of debt, and obtained analytical results that allow discussionof optimality in terms of both the debt ratio and the maturity structure. Thus, the financial engineering
approach is superior in capturing the mechanism of the effect of parameters representing corporatecharacteristics on the value of corporate debt under the optimal capital structure through comparative statics.
On the other hand, since credit spreads are determined endogenously, it is not flexible enough to set the realcredit spreads observed from the corporate bond market, which is a hurdle for its use in practice.
The corporate finance approach is an approach that examines the optimal capital structure based on theso-called corporate valuation model. The corporate valuation model is explained in detail in Damodaran (2001),
and Kokubo and Miyazaki (2005) extend this model to include not only the amount of debt (debt ratio) but
also the maturity structure of debt. The corporate valuation model regards the discounted present value of
future free cash flows generated by a company based on its weighted average cost of capital (WACC) as

p. 2

its current corporate value. Since corporate value increases as the WACC decreases, the optimal capital
structure is the debt ratio that minimizes the WACC, given the cost of equity and the cost of debt as priced
in the financial markets. Both Damodaran (2001) and Kokubo and Miyazaki (2005) use a rating matrix (which
represents credit spreads according to credit ratings) to describe the cost of debt priced in financial markets.
Tsuchiya (2017) is another reference that gives some indication of the use of such an approach in practice.
To quote the main points of Tsuchiya (2017), “(1) Given the fact that, in reality, the amount of debt funding
and interest costs depend on ratings, how rating strategies are considered in the optimal capital structure
approach is of paramount importance. (2) Ratings are often thought to be determined by the level of capital
adequacy ratios and D/E ratios, but what is considered important in assigning a rating varies depending on
the characteristics of the industry to which the company in question belongs. (3) The methodologies of theratings are not disclosed in detail. Therefore, we would also like to add that in order to clarify the methodology,
it is necessary to analyze the rating based on the status of other companies in the same industry that haveobtained the rating.”
Therefore, in this study, in a framework corresponding to citation (1), we take corporate bond yields as a
substitute for the debt interest rates of real estate funds and examine the debt interest rates according tocredit ratings. With regard to citations (2) and (3), we first refer to Niimi (1998) to confirm the relationshipbetween credit ratings and financial indicators. Next, based on the ordered logit/probit model (Kobayashi(2001) and Kitamura (2009)), in which financial indicators including debt ratios are explanatory variables andthe level of the quantified rating is the explained variable, we discuss the impact of debt ratios on the latentvariables that determine the level of ratings. Linking these two analyses together, we finally discuss theimpact of debt ratios on debt interest rates and returns of real estate fund. This will allow institutional
investors to build models to monitor the extent to which real estate funds are operating with an optimal debt
ratio. In addition, it will pave the way for a relative value analysis of investments in real estate funds asalternative assets versus investments in corporate bonds as traditional assets.
This paper is organized as follows. In section 2, we describe the scope and framework of the analysis andthe rating data. In section 3, the relationship between ratings and financial indicators is clarified using anordered logit/probit model. In section 4, we review the impact of debt ratios on debt interest rates andreturns of real estate fund through numerical examples based on historical data. The final section will beaccompanied by a summary and future issues.

2. Scope, framework and rating data
2.1 Scope and Framework of Analysis
This study will focus on the returns of institutional investors that invest in real estate funds. Figure 1
shows an image of the balance sheet of a real estate fund. As pointed out in section 1, when the ratio ofdebt increases (decreases) in fundraising by a real estate fund, the investment from investors (equity portion)
decreases (increases) accordingly. Such changes in the debt ratio affect the investment returns ofinstitutional investors through the proportion of the returns earned by the real estate fund allocated to thedebt and equity portions. The impact of the debt ratio on institutional investors' returns (𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 ) can bep. 3

expressed by equations (1) to (3).

𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 = 𝑛𝑛𝑛𝑛𝑛𝑛_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑛𝑛𝑡𝑡 /(1 − 𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡𝑡𝑡 )(1)

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑_𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡 = 𝑟𝑟𝑡𝑡 × 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡(3)𝑛𝑛𝑛𝑛𝑛𝑛_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 = 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 − 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑_𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡(2)

The return on investment ( 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 ) is calculated as the net return on real estate investment(𝑛𝑛𝑛𝑛𝑛𝑛_𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 ) divided by the investment ratio (1 − 𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡𝑡𝑡 ). 𝑛𝑛𝑛𝑛𝑛𝑛_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 is calculated

as the return on real estate investment (𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 ) less the cost of debt (𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑_𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡𝑡𝑡 ). In this study,

only the income return, which is the rental income from real estate at the present time 𝑡𝑡, is considered as
the return of the real estate fund (𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 ), and factors such as the growth of rental income

and the capital gain on the property it generates are not considered. As the debt ratio of the real estate fundincreases (decreases), 𝑛𝑛𝑛𝑛𝑛𝑛_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 will decrease (increase) and 1 − 𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡𝑡𝑡 will decrease(increase). Even if the same 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡 is obtained, we can confirm the relationship that 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡

depends on the debt ratio. The debt interest rate (𝑟𝑟𝑡𝑡 ) may rise or fall depending on the creditworthiness ofthe borrowing entity. This study focuses on the fact that 𝑟𝑟𝑡𝑡 varies with the debt ratio.
ASSETS

Liabilities
and Equity

Debt
Asset
Equity(Source: Prepared by the authors)

Figure 1: Real Estate Fund Balance Sheet Image
Explained variable

Debt
interest
rate

Estimation

Investment
grade←High Yield

Explanatory variables

S&P / Fitch

Moody's

Indicator

AAA

Aaa

AA

Aa

A

A

BBB

Baa

BB

Ba

Profitability

Ratio of after-tax operating income to net sales

B

B

Efficiency

Capital turnover

GrowthFive-year average growth rate of net sales

Size
Ordered
Logit/Probit Stability
Model
Debt ratio←

Financial resilience

Variable
Total capital
Ratio of equity and capital reserves to total capital
Ratio of total liabilities to total equity
Ratio of EBIT to interest payment(Source: Prepared by the authors)

Figure 2: Analytical Frameworkp. 4

Figure 2 illustrates the framework of the analysis. Based on Niimi (1998), seven financial indicators areused to explain ratings. Namely, the firm's (1) size, (2) stability, (3) debt ratio, (4) financial resilience, (5)profitability, (6) efficiency, and (7) growth indicators, each of which is used in an ordered logit/probit modelwith the rating as the explained variable. The rating is an ordinal number indicating the creditworthiness ofthe company. In the ordered logit/probit model analysis, the latent variable, which is the cardinal number
corresponding to the explained variable, is calculated, and the coefficients of the explanatory variables are
estimated. Next, the level of the credit spread is matched to each notch of the rating. This makes it possible
to consider the amount of change in the level of the credit spread through the rating when the value of the
explanatory variable changes, reflecting the coefficient of that variable. Specifically, the change in the latentvariable is calculated when the debt ratio changes, and the level of the credit spread rises or falls accordingly,
allowing the calculation of the change in the credit spread corresponding to the change in the latent variable,
even if the change in the debt ratio does not result in a change in rating. In this study, investment returns areanalyzed using the cost of debt with the credit spread calculated by this method.
2.2 Rating Data
The analysis covers companies in the S&P 500, as of August 31, 2023. We use Moody's ratings data forcompanies that are rated by at least two of the major rating agencies. We review the ratings of the sample,
which are represented by notches (rating tiers) from Aaa to C in Moody's ratings. Each notch is assigned anumber from 1 to 3, with 1 indicating a relatively high rank within the notch, 2 indicating a medium rank, and3 indicating a relatively low rank. In this analysis, 16 notches from Aaa to B3 are included.
Table 1 shows the distribution of ratings for the 157 companies included in this analysis. No firms are
Table 1 Distribution of Ratings for Analysis

Table 2 Distribution of ratings for analysis(after aggregation)

Number ofcompanies
Aaa

3

Aa1

0

Aa2

4

Number ofcompanies

Aa3

7

Aaa

3

A1

13

A2

17

Aa

11

A3

18

A

48

Baa1

25

Baa1

25

Baa2

40

Baa3

9

Baa2

40

Ba1

5

Baa3

9

Ba2

6

Ba

14

Ba3

3

B1

4

B

7

B2

3

合計

157

B3

0

合計

157

(Source: Authors' compilation from FactSet)(Source: Authors' compilation from FactSet)p. 5

assigned a rating of Aa1, and the same is true for rating of B3. Most of the companies assigned a rating are
distributed between Baa1 and Baa3, while the number of companies assigned a rating from Aa2 to Aa3 (highrating) or from Ba1 to B2 (low rating) is relatively small. It is possible that the parameters of the orderedlogit/probit model cannot be estimated due to this small number of companies in some notches. Therefore, inthis analysis, we aggregate all notches other than Baa1 through Baa3 into a single notch by eliminating thedistinction based on relative ratings within a notch. Table 2 shows the distribution of ratings after aggregation.
Aggregation ensures enough samples above A and below Ba ratings.

3. Relationship between ratings and financial indicators
3.1 Model
In this section, based on Kitamura (2009), we provide a brief explanation of the ordered logit/probit model
used in the empirical analysis that follows in the next section. The explained variables in the orderedlogit/probit model are represented by the following ordinal numbers.

𝑦𝑦𝑖𝑖 = 1, 2, 3, … , 𝐽𝐽 (1 < 2 < 3 < ⋯ < 𝐽𝐽)
When such explained variables are estimated by the ordinary least squares, a problem arises because theexplained variable is treated as a cardinal number. Therefore, in the ordered logit/probit model, we considera regression model for the continuous latent variable corresponding to the explained variable (𝑦𝑦𝑖𝑖∗ ). 𝑥𝑥𝑖𝑖′

represents the explanatory variables (seven financial indicators). 𝛽𝛽 is the parameter for each explanatory
variable, and 𝑢𝑢𝑖𝑖 is the error term. 𝑥𝑥𝑖𝑖′ and 𝛽𝛽 are vectors.

𝑦𝑦𝑖𝑖∗ = 𝑥𝑥𝑖𝑖′ 𝛽𝛽 + 𝑢𝑢𝑖𝑖 𝑖𝑖 = 1, 2, … , 𝑛𝑛
The observed data, the explained variable (𝑦𝑦𝑖𝑖 ) and the latent variable are defined as followings. The real

number is divided into 𝐽𝐽 intervals, corresponding to 𝐽𝐽 choices.

𝑦𝑦𝑖𝑖 = 𝑗𝑗 ⟺ 𝑘𝑘𝑗𝑗−1 < 𝑦𝑦𝑖𝑖∗ < 𝑘𝑘𝑗𝑗 𝑗𝑗 = 1, 2, … , 𝐽𝐽

𝑦𝑦1 = 1 ⟺ 𝑘𝑘0 < 𝑦𝑦𝑖𝑖∗ < 𝑘𝑘1 ⟺ 𝑘𝑘0 − 𝑥𝑥𝑖𝑖′ 𝛽𝛽 < 𝑢𝑢𝑖𝑖 < 𝑘𝑘1 − 𝑥𝑥𝑖𝑖′ 𝛽𝛽𝑦𝑦2 = 2 ⟺ 𝑘𝑘1 < 𝑦𝑦𝑖𝑖∗ < 𝑘𝑘2 ⟺ 𝑘𝑘1 − 𝑥𝑥𝑖𝑖′ 𝛽𝛽 < 𝑢𝑢𝑖𝑖 < 𝑘𝑘2 − 𝑥𝑥𝑖𝑖′ 𝛽𝛽…

𝑦𝑦𝑖𝑖 = 𝐽𝐽 ⟺ 𝑘𝑘𝐽𝐽−1 < 𝑦𝑦𝑖𝑖∗ < 𝑘𝑘𝐽𝐽 ⟺ 𝑘𝑘𝐽𝐽−1 − 𝑥𝑥𝑖𝑖′ 𝛽𝛽 < 𝑢𝑢𝑖𝑖 < 𝑘𝑘𝐽𝐽 − 𝑥𝑥𝑖𝑖′ 𝛽𝛽
𝑘𝑘0 = −∞, 𝑘𝑘𝐽𝐽 = ∞Considering the cumulative density function 𝑓𝑓(𝑢𝑢𝑖𝑖 |𝑥𝑥𝑖𝑖 ) = 𝑑𝑑𝑑𝑑(𝑢𝑢𝑖𝑖 |𝑥𝑥𝑖𝑖 )/𝑑𝑑𝑑𝑑 of the density function 𝑓𝑓(𝑢𝑢𝑖𝑖 |𝑥𝑥𝑖𝑖 ) of

p. 6

the error term 𝑢𝑢𝑖𝑖 , we denote the case where 𝑦𝑦𝑖𝑖 takes a certain value as follows.
𝜋𝜋𝑖𝑖𝑖𝑖 = 𝑃𝑃(𝑦𝑦𝑖𝑖 = 𝑗𝑗|𝑥𝑥𝑖𝑖 ) = 𝐹𝐹�𝑘𝑘𝑗𝑗 − 𝑥𝑥𝑖𝑖′ 𝛽𝛽� − 𝐹𝐹�𝑘𝑘𝑗𝑗−1 − 𝑥𝑥𝑖𝑖′ 𝛽𝛽�
If Gaussian distribution is used as the probability distribution function, the model is an ordered probit model,
and if the logistic distribution is used, the model is an ordered logit model. The ordered logit/probit probability
function multiplied by the above probabilities is as follows.

𝐽𝐽
𝑑𝑑𝑖𝑖𝑖𝑖
𝑑𝑑𝑖𝑖𝑖𝑖𝑑𝑑
𝑑𝑑
𝑓𝑓�𝑦𝑦𝑖𝑖 �𝑥𝑥𝑖𝑖 ; 𝛽𝛽, 𝑘𝑘1 , 𝑘𝑘2 , … , 𝑘𝑘𝐽𝐽−1� = (𝜋𝜋𝑖𝑖1 ) 𝑖𝑖1 (𝜋𝜋𝑖𝑖2 ) 𝑖𝑖2 … �𝜋𝜋𝑖𝑖𝑖𝑖 � = ��𝜋𝜋𝑖𝑖𝑖𝑖 �
𝑗𝑗=1

𝑑𝑑𝑖𝑖𝑖𝑖 �1 If 𝑗𝑗 is chosen（𝑦𝑦𝑖𝑖 = 𝑗𝑗）
0 otherwise
The log-likelihood function is defined as follows and is estimated using the maximum likelihood method to
obtain an unbiased estimator of the parameters.

𝑛𝑛

𝐽𝐽

log𝐿𝐿�𝛽𝛽, 𝑘𝑘1 , 𝑘𝑘2 , … , 𝑘𝑘𝐽𝐽−1 ; 𝑦𝑦, 𝑥𝑥� = � � 𝑑𝑑𝑖𝑖𝑖𝑖 log 𝜋𝜋𝑖𝑖𝑖𝑖
𝑖𝑖=1 𝑗𝑗=1

3.2 Relationship between ratings and financial indicators
Table 3 shows the distribution of ratings, the explained variable, and summary statistics for the explanatory
variables. The rating distribution shows a concentration of companies in the A to Baa3 ratings. In terms of
the explanatory variables, the debt ratio, ratio of total liabilities to total equity, which is the focus of thisanalysis, averages 67.99% for the sample companies, with a minimum value of 2.02% and a maximum valueof 251.83%. Cases where the debt ratio exceeds 100% indicate that the company is insolvent. Next, the size
indicator, total capital, averages $0.05 trillion for the sample companies, with a minimum value of $0.00 trillion
and a maximum value of $0.37 trillion. The stability indicator, ratio of equity and capital reserves to total
capital, averages 26.87%, with a minimum of 0.00% and a maximum of 729.46%. The average ratio of EBIT
to interest payment for the financial resilience indicator is 20.03%, with a minimum of -15.62% and a maximumof 209.64%. The minimum value is negative, indicating that the company has a loss before interest and taxes.
The profitability indicator, ratio of the after-tax operating income to net sales, averaged 15.11%; theefficiency indicator, the capital turnover, averaged 0.84%; and the growth indicator, the five-year average
growth rate of net sales, averaged 8.32%.
Table 4 shows the estimation results of the ordered logit/probit model. The size, debt ratio, and profitability
indicators are each significant. Thus, we confirm that firms with larger size, lower debt ratios, and higher

p. 7

Table 3 Summary statistics
Stability

Size

Debt ratio

Ratio ofRatio ofequity andtotal
capital
Total capital
liabilities toreserves tototal equity
total capital

Financialresilience

Profitability Efficiency

Ratio of
EBIT tointerest
payment

Ratio ofafter-tax
operatingincome tonet sales

Capitalturnover

GrowthFive-year
average
growth rateof net sales

Number of samples

157

157

157

157

157

157

157

Mean

0.05

26.87

67.99

20.03

15.11

0.84

8.32

Variance

0.07

59.42

28.35

29.88

11.80

0.89

8.38

Min

0.00

0.00

2.02

-15.62-38.98

0.04

-8.92

25%

0.01

7.91

51.53

6.08

8.08

0.44

3.54

Median

0.03

17.99

64.30

9.99

14.14

0.65

7.09

75%

0.05

32.18

77.33

21.49

22.11

0.96

10.95

Max

0.37

729.46251.83209.64

52.75

8.89

48.85

(Source: Authors' compilation from FactSet)

Table 4 Estimation results
Moody's (n=157)
Logit
Coefficient

ProbitSD

CoefficientSD

Total capital

15.95 **

3.46

8.85 **

1.78

Ratio of equity and capital reserves to total capital

0.00

0.00

0.00

0.00

Ratio of total liabilities to total equity-0.02 **

0.01

-0.01 **

0.00

Ratio of EBIT to interest payment

0.01

0.01

0.01

0.00

Ratio of after-tax operating income to net sales

0.07 **

0.02

0.04 **

0.01

Capital turnover

0.47

0.29

0.18

0.10

Five-year average growth rate of net sales

-0.03

0.02

-0.02

0.01

**p<0.01, *p<0.05(Source: Prepared by the authors)corporate profitability tend to have higher ratings. Therefore, a lower debt ratio, which is the explanatory
variable focused on in this analysis, is likely to increase the latent variable of the rating and lead to a higher
rating, suggesting that the debt interest rate is suppressed. In the next section, we will estimate the impact
of debt ratio on the debt interest rate using the values of the coefficients of the logit model obtained in theestimation. The results of the estimation will also be used to discuss the optimal debt ratio for real estate
investment.

4. Numerical example
4.1 Data and Analysis Setup
In this section, we use the values of the coefficients obtained from the estimation in section 3.2 to estimate
the impact of changes in the debt ratio on the debt interest rate. The results of the estimation also be used
to discuss the optimal debt ratio for real estate investment. It is difficult to obtain enough data to conduct astatistical analysis of the debt ratio of a real estate fund and the fund's debt interest rate. Therefore, we
use as proxy variables the debt ratios of U.S. listed companies, including those in the real estate sector, andthe level of credit spread (Option Adjusted Spread, OAS) corresponding to the rating level of the company inquestion.
Figure 3 shows the OAS for U.S. corporate bonds by rating level, and the trend of the OAS since 1999shows that the higher the rating, the lower the OAS level, and the lower the rating, the higher the OAS level.

p. 8

(%)
25
20

AAA/Aaa
A
BB/Ba

AA/Aa
BBB/Baa
B

15
10

0

1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024

5

(Source: Authors' compilation from FRED ECONOMIC DATA)

Figure 3: Trend of OAS
In addition, the OAS has expanded and contracted in response to business cycles and financial market shocks.
For example, the OAS has expanded during the U.S. recession since 2001, the global financial crisis through2009, and the European crisis triggered by Greece around 2012. OAS also expanded during the 2016referendum on Britain's exit from the European Union (Brexit), the U.S. presidential election in 2016, and theglobal spread of the COVID-19 in 2020. Since OAS is the interest rate added to the treasury yield based on
the credit quality of the company, we used the U.S. 10-year government bond yield plus OAS as the debt
interest rates in our estimations.
Next, the MSCI/PREA U.S. ACOE Quarterly Property Fund Index (hereinafter referred to as "MSCI U.S.
Property Fund Index") is used as the real estate fund return data. The MSCI U.S. Property Fund Index shows
the income returns of core strategy and diversified real estate funds in the U.S. 1. Figure 4 shows the trendsof the MSCI U.S. Property Fund Index and the U.S. 10-year government bond yield since 1999.
The MSCI U.S. Property Fund Index rose to about 9% in 2003, then declined until 2009, after which thelevel has been gradually declining, although it temporarily recovered to around 7%. The U.S. 10-year
government bond yield declined from over 6% in 2000 to below 1% in 2020, and then rose to over 5% after2022.
The income return on real estate reflects the economic and financial environment up to that point in time,and is a so-called "backward-looking" value. On the other hand, the U.S. 10-year government bond yield isa "forward-looking" value that reflects forecasts for the future economic and financial environment, and1

The MSCI U.S. Real Estate Fund Index was used in this analysis due to data availability. However, the concept of improving
returns through aggressive use of leverage is more appropriate for real estate investments in real estate funds that aim forhigh returns by giving managers more discretion (opportunity funds) than in core strategy and diversified real estate funds(core funds), which are covered by the MSCI U.S. Real Estate Fund Index. Opportunity funds are more likely than core funds tohave higher returns than core funds. Opportunity funds are expected to generate somewhat higher returns than core funds,
so the nature of real estate funds should also be considered when examining the relationship between debt ratios and realestate fund returns in the future.

p. 9

(%)

10

MSCI U.S. Property Fund Index

9

U.S. 10-year government bond yield

8
7
6
5
4
3
2

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

0

1999

1

(Source: Authors' compilation from Factset and MSCI)

Figure 4: MSCI U.S. Property Fund Index and U.S. 10-Year Government Bond Yield
caution should be exercised when making comparisons with the MSCI U.S. Property Fund Index at the same
point in time. In fact, the figure shows that the U.S. 10-year government bond yield tends to move ahead of
the MSCI U.S. Property Fund Index.
Using the above data, we make two estimates. Section 4.2 checks how the level of OAS changes when
the debt ratio changes. We identify differences in changes by rating and at three points in time that reflect
the expansion and contraction phases of the OAS. In section 4.3, we assume that the return on a real estate
fund is the return on the MSCI U.S. Property Fund Index, and use time series data to check to what extent
the investment return received by institutional investors changes when the debt ratio of that real estate fundchanges.
4.2 Debt ratio and level of OAS
This section examines the extent to which the increase in the debt ratio affects the OAS level. We estimate
the impact of the OAS level on the rating that can be obtained as of August 31, 2023, when compared to
the OAS level as of August 31, 2023. In addition, we utilized the OAS level as of March 1, 2024, whichreflects recent market trends, and March 23, 2020, when the financial markets are disrupted by the COVID19 pandemic.
Table 5 shows the level of OAS for each rating according to the debt ratio of the companies. (a) is the
OAS as of August 31, 2023, (b) is the OAS as of March 1, 2024, and (c) is the OAS as of March 23, 2020.
First, we confirm that according to the estimation results in (a), the relationship between the estimated OAS
increases by 1 bps for every 10% increase in the debt ratio for Aa- and A-rated companies. For example, if
the debt ratio of an Aa-rated company increases from 35% to 40%, the OAS increases from 0.58% to 0.59%.
The OAS expansion for a 10% increase in debt ratio is 1-2 bps for a Baa1 rating, 4-5 bps for a Baa2 rating,and 5 bps for a Baa3 rating, confirming that the lower the rating, the larger the OAS expansion.
Next, in (b) as of March 1, 2024, which reflects recent market trends, the range of change in OAS forp. 10

Aa- to Baa2-rated companies is generally the same as in (a). On the other hand, the range of change for
the Baa3 rating is 3 bps, which is smaller than in (a). it is plausible to consider that, although the lower the
rating, the greater the fluctuation of the OAS level itself, during economic periods when the OAS declines
overall, as in (b), the change in the OAS in relation to the debt ratio is also suppressed.
As of March 23, 2020 (c), when the overall level of OAS was expanding, the change in OAS expanded foreach of the ratings. For a 10% increase in the debt ratio, the OAS expanded by 1-2 bps for the Aa rating, 4
bps for the A rating, 5-6 bps for the Baa1 rating, 6-7 bps for the Baa2 rating, and 56 bps for the Baa3
rating. As in (b), in (c), the lower the rating during the OAS expansion phase, the greater the sensitivity of
the OAS increase to the debt ratio increase.
As described above, we confirm that the range of change in OAS as a function of debt ratio varies fromrating to rating, and is also affected by the business cycles.
Table 5: OAS according to debt ratio levels
Ratings

Estimated OAS by debt ratios
30%

Aa

0.57

35%

40%

0.58

45%

50%

55%

Averagedebt ratio

0.59

0.60

0.61

0.62

55.62

A

0.94

0.95

0.96

0.97

0.99

1.00

62.30

Baa1

1.14

1.16

1.17

1.19

1.21

1.23

69.62

Baa2

1.14

1.18

1.23

1.28

1.33

1.38

63.35

Baa3

1.68

1.73

1.78

1.82

1.87

1.92

62.58

(a) OAS as of August 31, 2023

Ratings

Estimated OAS by debt ratios
30%

35%

40%

45%

50%

55%

Averagedebt ratio

Aa

0.50

0.51

0.52

0.52

0.53

0.54

55.62

A

0.77

0.78

0.79

0.80

0.81

0.82

62.30

Baa1

0.94

0.96

0.97

0.98

1.00

1.01

69.62

Baa2

0.96

1.00

1.03

1.07

1.11

1.15

63.35

Baa3

1.39

1.42

1.46

1.49

1.53

1.57

62.58

(b) OAS as of March 1, 2024

Ratings

Estimated OAS by debt ratios
30%

35%

40%

45%

50%

55%

Averagedebt ratio

Aa

2.61

2.63

2.64

2.66

2.67

2.69

55.62

A

3.01

3.05

3.09

3.13

3.17

3.21

62.30

Baa1

3.67

3.72

3.78

3.84

3.89

3.95

69.62

Baa2

3.64

3.80

3.96

4.13

4.29

4.45

63.35

Baa3

5.46

5.61

5.77

5.92

6.07

6.23

62.58

(c) OAS as of March 23, 2020
(Source: Prepared by the authors)

p. 11

4.3

Debt Ratios and Real Estate Fund Returns

In this section, we use time series data to identify changes in the return on investment in a real estate fundreceived by institutional investors when the debt ratio of the real estate fund changes, even for the same
real estate fund return. This allows institutional investors to build models to monitor the extent to which realestate funds are operating with an optimal debt ratio in mind. As pointed out in section 4.1, the MSCI U.S. Real
Property Fund Index returns differ from the U.S. 10-year government bond yield in terms of whether the
information reflected is “backward-looking” or “forward-looking”. However, for the sake of simplicity in thisanalysis, the debt interest rate corresponding to the MSCI U.S. Property Fund Index return in period t is the
U.S. 10-year government bond yield plus the OAS in period t.
Figure 5-1(a)-(c) shows the investment returns from real estate funds received by institutional investors,
by rating, for real estate acquisitions with debt ratios between 20% and 50% from the first quarter of 1999
to the fourth quarter of 2023. Each figure represents the level of investment returns. In (a), which covers
Aa ratings, investment returns are 10.0% for a 20% debt ratio and 12.7% for a 50% debt ratio in the second
quarter of 2002, followed by a 5.2% return for a 20% debt ratio and a 5.5% return for a 50% debt ratio in
the third quarter of 2008. After rising to 7.5% to 9.8% over the second quarter of 2010, investment returns
have gradually declined.
Since 1999, real estate fund returns have generally exceeded the debt interest rate, so that the higher
the debt ratio, the higher the investment return. The trend in (b) for A-rated assets is generally similar tothat for Aa-rated assets. In (c), the investment returns for all debt ratios are lower than in (a) and (b) for
Baa-rated loans.
We can also confirm this trend in Figure 5-2, which shows the excess return on leveraged fund versus noleverage fund. In (a), which shows the excess return from Aa-rated leveraged fund, is about 1% for a 20%
debt ratio in 2002 and about 4% for a 50% debt ratio. In the same time, in A-rated (b), the excess return isabout the same for a 20% debt ratio with (a) and 3.5% for a 50% debt ratio, which is lower than that of (a).
On the other hand, during the same period when the Baa rating (c) is assigned, the excess return is less than
1% when the debt ratio is 20% and less than 3% when the debt ratio is 50%, confirming that the cost of thedebt interest rates increases with a lower rating compared to (a) and (b), pushing down the excess return.
From 2006 to 2008, the negative excess return is about -1% larger for (b) than for (a) when the debt ratio
is 50%, and even more than -1% for (c). Subsequently, even after 2009, the higher the rating, the greater
the upside of the excess return and the smaller the downside is shown.
Figure 6-1 shows real estate investment returns by rating for each debt ratio level. In (a) through (c), thehigher the debt ratio, the greater the boost to earnings from leverage. Figure 6-2 shows excess returns
from leverage by rating for each debt ratio level. In (a) through (c), the volatility of the excess return fromleverage of real estate funds is greater as the debt ratio increases. Figures 6 show that the higher the rating,the greater the upside, and the more restrained the downside.
The above analysis indicates that leverage to increase the debt ratio can increase the range of excess
return compared to the case where no leverage. In addition, higher credit ratings suppress the debt interest
rate, thereby increasing the return for institutional investors. Through the estimation process, we develop amodel for institutional investors to monitor the extent to which real estate funds are managing their

p. 12

14%

14%

14%

12%

12%

12%

10%

10%

10%

8%

8%

8%

6%

6%

6%

4%

4%
2%

20% debt ratio

30% debt ratio

40% debt ratio

50% debt ratio0%1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023

2%

4%
20% debt ratio

30% debt ratio

40% debt ratio

50% debt ratio

2%0%1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023(a)Aa Rating

20% debt ratio

30% debt ratio

40% debt ratio

50% debt ratio0%1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023(b) A Rating(c)Baa Rating(Source: Compiled by the authors from Factset, FRED ECONOMIC DATA, and MSCI)

Figure 5-1 Debt Ratio and Real Estate Fund Returns (Level)
5%

5%

5%

4%

4%

4%

3%

3%

3%

2%

2%

2%

1%

1%

1%

0%

0%

0%

-1%

-1%

-1%

-2%

-2%

-2%

-3%
-4%

20% debt ratio
40% debt ratio

30% debt ratio
50% debt ratio-5%
1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023(a)Aa Rating

-3%
-4%

20% debt ratio
40% debt ratio-3%

30% debt ratio-4%

50% debt ratio-5%
1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023(b) A Rating

20% debt ratio

30% debt ratio

40% debt ratio

50% debt ratio-5%
1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023(c)Baa Rating(Source: Compiled by the authors from Factset, FRED ECONOMIC DATA, and MSCI)

Figure 5-2 Debt ratios and real estate fund returns (excess return due to leverage)

p. 13

14%

14%

14%
AA/Aa

AA/Aa
A

12%

BBB/BaaA

12%

BBB/Baa

AA/Aa
A

12%

BBB/Baa

10%

10%

10%

8%

8%

8%

6%

6%

6%

4%

4%

4%

2%

2%

2%

0%
1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023

0%1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023

0%1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023

(a) 30% debt ratio(b) Debt ratio 40%(c) Debt ratio 50%(Source: Compiled by the authors from Factset, FRED ECONOMIC DATA, and MSCI)

Figure 6-1 Debt Ratios and Real Estate Fund Returns (Levels)
5%

5%
AA/Aa

4%

A
BBB/Baa

3%

5%
AA/Aa

4%

A
BBB/Baa

3%

AA/Aa

4%

A

3%

BBB/Baa

2%

2%

2%

1%

1%

1%

0%

0%

0%

-1%

-1%

-1%

-2%

-2%

-2%

-3%

-3%

-3%

-4%

-4%

-4%

-5%
1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023

-5%1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023

-5%1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023

(a) 30% debt ratio(b) Debt ratio 40%(c) Debt ratio 50%(Source: Compiled by the authors from Factset, FRED ECONOMIC DATA, and MSCI)

Figure 6-2 Debt ratios and real estate fund returns (excess return due to leverage)

p. 14

investments with an awareness of optimal debt ratios. In this analysis, the MSCI U.S. Property Fund Index isused as a proxy variable for real estate fund returns, which originally differed by portfolio property. We thenestimate how the investment returns received by institutional investors would change if the ratings and debt
ratios of the real estate fund are changed. Therefore, a strong assumption is made that real estate fundreturns are the same for all ratings and debt ratios, and actual investments require analysis that reflects theindividual characteristics of the real estate properties in which they invest.

5．Summary and future issues
Based on an ordered logit/probit model with financial indicators including debt ratios as explanatory
variables and quantified rating levels as explained variables, this study discussed the impact of debt ratios onlatent variables that determine rating levels. Next, we estimated the impact of debt ratios on real estate funddebt interest rates and real estate fund returns.
The results of the estimation using the ordered logit/probit model indicated that in addition to the size andprofitability indicators, the debt ratio indicator focused on in this analysis significantly affects the level of therating. The results confirmed that the degree of influence of the level of debt ratio on the OAS is greater
the lower the rating. It was also shown that the impact of the debt ratio on the OAS differs depending onwhether the corporate bond market as a whole has a wide or tight OAS depending on the economic andfinancial environment. Next, an estimation of the effect of the debt ratio on the investment returns ofinstitutional investors in real estate funds showed that since 1999, real estate fund returns have generally
exceeded the debt interest rates, indicating that returns increase as the debt ratio increases. However, whenmonetary policy is tightened, borrowing costs increase, pushing down investment returns when debt ratios
are high. The increase in the debt interest rates is large when the credit rating is low, confirming that the
downward effect of higher borrowing costs on investment returns during the tightening phase is as large as
the upward effect on the excess return obtained through leverage.
Based on the above results, when institutional investors invest in real estate funds, an increase in the debt
ratio of the fund can be expected to boost returns. On the other hand, if the real estate fund has a low credit
rating, the increase in borrowing costs due to a higher debt ratio should be taken into account to have acommensurately large downward effect on investment returns. In addition to the rating and debt ratio of theborrower, the debt interest rates are also affected by the monetary policy cycle, so it is advisable to time
one's entry into the market.
We discuss future issues for this analysis. In this analysis, debt ratios of listed companies, including thosein the real estate sector, and OAS were used as proxy variables for debt interest rates based on the credit
quality of real estate funds. In addition, the MSCI U.S. Property Fund Index, which captures income returns
from portfolio properties in core funds, was used as the return on real estate funds. Therefore, it does not
capture the effect of capital gains from rising real estate property prices, nor does it take into account thelevel of yield of opportunity funds that seek to increase returns through borrowing (leverage). Furthermore,
the analysis neglects the individual nature of the properties in which they are invested. In addition, this analysis
uses data from the same time period to estimate the income return of real estate funds, which is ap. 15

"backward-looking" measure, and the yield on U.S. 10-year government bonds and OAS, which are "forward
looking" measures of the debt interest rates. Therefore, for a more practical analysis, it is preferable to use
return data that includes actual real estate fund debt ratios and debt interest rates, as well as capital returns.
It will also be necessary to consider in the future how to handle the difference in nature between real estate
fund returns (“backward-looking”) and debt interest rates (“forward-looking”).
In addition to the above, one of the objectives of this analysis is to enable a causal analysis of the relativevalue between the return on real estate funds and the return on U.S. corporate bond investments. For example,
when comparing investment opportunities in corporate bonds and real estate funds, in a phase of widening
credit spreads, the yield obtained by investing in corporate bonds increases, while the return from leveragein real estate funds decreases due to higher borrowing rates. When institutional investors consider investingin real estate funds, they will need to conduct relative value analysis based on the impact on investment
returns through such debt interest rates. Through efforts to make these analyses practical, it is hoped that
real estate investments, which are considered alternative assets, will be subject to active discussion basedon quantitative analysis in the same way as traditional assets such as stocks and bonds.

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