GPIF Working Paper

Analysis for the integrated risk management
between J-REIT and traditional assets
August 24, 2021
Kazuhiro Shimada
Koichi Miyazaki
Tetsuya Oishi

EXECUTIVE SUMMARYGovernment Pension Investment Fund (hereafter referred to as GPIF) invests in three alternative
asset classes: infrastructure, private equity and real estate. As of the end of March 2021, the market
value of those alternative assets was 1.3419 trillion JPY.

GPIF manages alternative assets by classifying them into four traditional asset classes (domestic
bonds, domestic equities, foreign bonds and foreign equities) according to their risk-return
profiles for risk-management purposes.

In this working paper, we regard “J-REIT” as alternative assets for the sake of convenience as afirst step for the integrated risk management between alternative assets and traditional assets, andconsider the degree of necessity to manage separately "J-REIT" as an independent asset class.

1. Introduction
In fiscal 2013, GPIF began managing alternative assets by using a joint investment vehicle withinstitutional investors. In general, alternative assets include a wide variety of assets, including infrastructure,
private equity, real estate, private debt, commodities and hedge funds, while GPIF invests in three assets:
infrastructure, private equity and real estate. GPIF has been deploying capital to alternative assets whilesophisticating investment capabilities, and the total market value of alternative assets as of the end of March
2021 was 1.3419 trillion JPY, representing 0.70% of the total pension reserve. Under the fourth mediumterm management plan, alternative assets are permitted to be invested up to 5% of GPIF's total assets undermanagement. However, needless to say, due attention should be paid to market conditions and investment
risks. Given the increasing value of the alternative assets, we are at the stage of evaluating the way tomanage the risk.This point will be elucidated in this working paper.
The risk-return characteristics of alternative assets differ from those of traditional assets such as
equities or bonds. In “Chapter 8: Alternative Investment”, edited by The Securities Analysts Association ofJapan (2020), Ogishima stated the following characteristics are commonly seen in alternative assets: (1)(NOTE)This working paper summarizes the research results of GPIF staffs, and the content and opinions expressed in the
text do not represent GPIF's official views.

Low liquidity compared with traditional assets; (2) Diversification effects obtained by combining them withtraditional assets; (3) High valuation costs (i.e., complex strategies and schemes, less transparent reporting,etc.); and (4) Difficulty of performance evaluation. Among them, (3) and (4) are the characteristics thatmake it very difficult to manage the risk of alternative assets. It is necessary to overcome these issues
eventually and refine risk management methods. This working paper, as a first step, attempts to examine
the integrated risk management with traditional assets by regarding J-REIT as an alternative asset.
J-REIT is a Japanese version of REIT (Real Estate Investment Trust), and the market was opened in
March 2001. REIT had become an important asset class in the United States and Australia at that time, as afinancial instrument which enables real estate investment while maintaining liquidity. The market value of
J-REIT has increased steadily since it opened, reaching about 17.7 trillion JPY at the end of July 2021, 20
years after its opening.
Ohashi, Kamita and Mori (2003) is one of the earlier preceding studies on J-REIT. They found that JREIT was middle-risk, had low correlations with other assets, generated expected returns on a CAPM
standard, and during its investment horizon, had specific periods to increase the linkage with equities orwith bonds by analyzing J-REIT's risk-return from a variety of perspectives based on weekly data from theopening of the market to March 2003. After their study, numerous studies have been made to analyze JREIT markets. Ishijima, Takano and Taniyama (2006) estimated risk premiums of J-REIT based on Regime
Switching Model for asset pricing. Ito (2013) found that increase of stock prices caused a positive effectand increase of interest rates caused a negative one on J-REIT market by analyzing the impact of stock
prices and interest rates on J-REIT market. Jin (2015) verified the prevailing view that "REIT is a financial
product which is middle-risk and middle-return, in the middle between equities and bonds," by using
monthly data from March 2003 to February 2015 and found that it was high-risk and high-return whenmeasured in the whole period. Jin also showed that there was not much that can be explained by using
market variables for equities, government bonds and real estate, because the returns of J-REIT indicesfluctuated independently. Tsuji (2016) examined the historical trend of dynamic correlation coefficients
between J-REIT indices and equities indices by using DCC-GARCH modelled in Engle (2002) and statedthat both indices showed strong correlations as a whole, but the correlations declined during economic
downturns.
In this way, studies on analysis of J-REIT market have been well accumulated, however, few academic
studies are seen which have approached from the perspective of integrated risk management with traditional
assets, the good characteristics of alternative assets, as stated by Ogishima, "(2) Diversification effects thatobtained by combining them with traditional assets." One of those few studies is Ohashi's presentationmaterial "Analysis of REIT Product Characteristics Using Financing Methods" attached as the referencematerials of Ohashi, Kamita and Mori (2003) that presented the efficient frontier structured by the data ofequities, bonds and J-REIT for only two years. Also, Kawaguchi (2004) described in detail necessity andchallenges of classifying the alternative assets, particularly real estate and real estate securitization products
as a new asset class. Furthermore, as the circumstance after entering Reiwa period, in "Chapter 3: Expanding2

Alternative Asset Investment" under the supervision of Tokyo Marine Asset Management Co., Ltd. (2020),
Hama introduced the opinion of a domestic pension fund that alternative assets had been managed within
the framework of traditional assets, partly due to the small amount of allocation, but according to theincrease of the allocation we started to manage it separately as an independent asset classes after the global
financial crisis.
Accordingly, the purpose of this study is to discuss the necessity of managing alternative assets separately
as an independent asset class when its allocation become greater in the future, by assuming J-REIT as analternative asset, although presently GPIF manages alternative assets by classifying them into bonds orequities according to their risk-return profiles. This paper is structured as follows. In Section 2, we clarified
the risk-return profiles of J-REIT, equities and bonds based on monthly data for about 20 years since theopening of J-REIT market. Section 3 presented the results of empirical analysis on the current approach to
managing J-REIT within the framework of traditional assets such as equities and bonds. In Section 4 wediscussed the necessity of managing J-REIT separately as an independent asset class when the allocation of
J-REIT increased. In Section 5, we verified the efficient frontier consisting of J-REIT, equities and bonds.
In the final Section, we summarized the study and raised future issues.

2. Risk-return profiles of J-REIT, equities and bonds
2.1 The settings of data and analysis
The data used in the empirical analyses are monthly data from April 2003 to June 2021 for the three
indices of Tokyo Stock Exchange REIT Index (incl.dividends, hereafter referred to J-REIT Index), Tokyo
Stock Price Index (incl.dividends, hereafter referred to TOPIX) and Nomura Bond Performance Index(hereafter referred to NOMURA-BPI).
As the settings of analysis, the data period is set into three terms: i) the entire period (April 2003 to June2021), ii) the period [1] (April 2003 to December 2015), and iii) the period [2] (January 2016 to June 2021).
The entire period covered almost 20 years from the opening of J-REIT market to present, the period [1]covered all the period in the preceding study of Jin (2015), and the period [2] covered the corresponding
period of the BOJ's quantitative and qualitative monetary easing policy with a negative interest rate. The
analysis has been made through the following steps: first, we examined how three indices moved over foreach period, second, we calculated the rolling one-year volatility of each index and examined its change,
and third, based on these analyses we understood the returns and volatilities of the three assets over eachperiod.
2.2 The results of the analysis and its implications
Figure 1 shows the historical trends of the three indices, with setting the end of March 2003 as 100. In
June 2021, J-REIT Index, TOPIX and NOMURA-BPI were around 470, 350 and 130, showing that thereturns are high, middle and low, respectively.
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Figure 1: Monthly Cumulative Returns

600

Period[1]（Apr.2003～Dec.2015）

Period[2]（Jan.2016～Jun.2021）

500

400

300

200

100

0

J-REIT Index

TOPIX

NOMURA-BPI(Source: Prepared by the authors from FactSet data)

Regarding risks, Figure 1 shows that NOMURA-BPI barely fluctuates and its risk is low, but it is difficult
to find the magnitude of the risks associated with J-REIT Index and TOPIX. Figure 2 shows the volatilitiesof the indices, and in the period [1] the volatility of J-REIT Index is often extremely higher than that of
TOPIX, which indicates the risk of J-REIT Index is generally higher than that of TOPIX. On the other hand,in the period [2] although the volatility of J-REIT Index is higher than that of TOPIX during the period after
the COVID-19 shock in March 2020, in the period from 2016 up to the COVID-19 shock, the volatility of
J-REIT Index is lower and more stable than that of TOPIX.
Figure 2: Volatility of monthly returns <Annualized>

40%

Period[1]（Apr.2003～Dec.2015）

Period[2]（Jan.2016～Jun.2021）

35%
30%
25%
20%
15%
10%
5%
0%

J-REIT Index

TOPIX

NOMURA-BPI(Source: Prepared by the authors from FactSet data)4

In comparing the returns and volatilities in period [1], period [2] and the entire period in Table 1, thereturns and volatilities of NOMURA-BPI are 0.9% to 1.7% per annum and 1.9% to 2.0% per annum,
respectively, thus the both risk and return are low in all three periods. Comparing J-REIT Index and TOPIX,
both return and volatility of J-REIT Index was about 1%-2% higher than those of TOPIX over the period[1] and the entire period, showing that both risk and return of J-REIT Index was slightly higher. This result
is consistent with the preceding study by Jin (2015). It is interesting to note the results of the analysis forthe period [2], which was not observed in any of the preceding studies. In this period, the volatility of JREIT Index was around 2% lower than that of TOPIX, meanwhile the return of the J-REIT Index wasaround 1% higher than that of TOPIX, showing risk is slightly lower and return is higher. The risk-return
profile of J-REIT Index is considerably more attractive in the period of the BOJ's QQE policy with anegative interest rate, if there are no contingencies such as COVID-19 shock, since the results of the period[2] analysis includes the impact of COVID-19.
Table 1 Risk-Return Characteristic Value
Period [1]Period [2]Whole period

Apr 2003 to Dec 2015

Jan 2016 to Jun 2021

Apr 2003 to Jun 2021

Returns

Returns

Returns

Volatilities

Volatilities

Volatilities

J-REIT Index

10.9%

20.0%

8.6%

13.8%

10.2%

18.3%

TOPIX

8.6%

18.0%

7.7%

15.7%

8.3%

17.3%

NOMURA- BPI

1.7%

1.9%

0.9%

2.0%

1.4%

1.9%

(Source: Prepared by the authors from FactSet data)

3. Approach of managing the risk of J-REIT within the flamework of
the traditional asset
3.1 Method of analysis
To manage risk of J-REIT within the framework of traditional assets, the balances of J-REIT need to beallocated to equities (TOPIX) and bonds (NOMURA-BPI). The balances of J-REIT are allocated to equities
or bonds depending on the risk-return profiles, if the risk-return profiles are close to those of equities it isallocated more to equities, on the other hand if these profiles are close to bonds then it is allocated more tobonds, with making the sum of the allocations equal to the original balance. This method to determine theamount of allocation is shown in pp.121 of Ang, Brandt and Denison (2014). (Constrained estimation
equation that allocates one unit of J-REIT to 𝛽𝛽𝐸𝐸 unit of equity and 𝛽𝛽𝐵𝐵 unit of bond)𝑟𝑟𝑡𝑡𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽 = α + 𝛽𝛽 𝐸𝐸 𝑟𝑟𝑡𝑡𝐸𝐸 + 𝛽𝛽 𝐵𝐵 𝑟𝑟𝑡𝑡𝐵𝐵 + 𝜀𝜀𝑡𝑡
𝛽𝛽𝐸𝐸 + 𝛽𝛽 𝐵𝐵 = 1, 𝛽𝛽𝐸𝐸 ≥ 0, 𝛽𝛽 𝐵𝐵 ≥ 0

(1)
(2)

Here, 𝑟𝑟𝑡𝑡𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽 , 𝑟𝑟𝑡𝑡𝐸𝐸 , 𝑟𝑟𝑡𝑡𝐵𝐵 𝑎𝑎𝑎𝑎𝑎𝑎 𝜀𝜀𝑡𝑡 , each represents the returns of J-REIT Index, TOPIX and NOMURA-BPI,
5

and the regression error at time t. α represents the extent to which J-REIT Index outperforms a portfolioof 𝛽𝛽𝐸𝐸 units of TOPIX Index and 𝛽𝛽𝐵𝐵 units of NOMURA-BPI. The parameters, α, 𝛽𝛽𝐸𝐸 and 𝛽𝛽𝐵𝐵, are estimatedby minimizing the sum of squared errors in the data period under the constraint equation (2).

3.2 The settings of data and analysis
The data used in the empirical analyses are monthly data from April 2003 to June 2021 for Tokyo Stock
Exchange REIT Index (incl.dividends), Tokyo Stock Price Index (incl.dividends), and Nomura Bond
Performance Index (*). In the analysis of individual securities in J-REIT Index, considering that there is asufficient data period and there is no bias in the sectors to which the securities belong to, 28 securities forwhich the data for the last 10 years from July 2011 to June 2021 are included.
The analysis has been made in the following manner: Firstly, we divided the data period into i) the entire
period (April 2003 to June 2021), ii) the period [1] (April 2003 to December 2015) and iii) the period [2](January 2016 to June 2021), and estimated the parameters by using the explanatory variables as TOPIX
and NOMURA-BPI, and the explained variable as J-REIT Index in regression equation (1). Secondly, we
examined whether J-REIT Index have more similar characteristics of equities or bonds in each period to beanalyzed. In addition, the performance of J-REIT Index was compared to the portfolios consisting of 𝛽𝛽𝐸𝐸units of TOPIX and 𝛽𝛽𝐵𝐵 units of NOMURA-BPI, by using the results of the first step, which includes theestimated parameter α, the weights of TOPIX 𝛽𝛽𝐸𝐸 and the weights of the NOMURA-BPI 𝛽𝛽𝐵𝐵 . Thirdly,

through empirical analyses of individual securities in J-REIT Index, we estimated the parameters by using
the explanatory variables as TOPIX and NOMURA-BPI (excluding ABS) and the explained variable as
returns for individual securities in the regression equation (1).

3.3 The results of the analysis and its implications
The result with J-REIT Index being used as the explained variable is shown in Table 2. In the whole
period, the ratio of the weight of TOPIX to the weight of NOMURA-BPI is approximately 6:4. In the period[1], the weight of TOPIX was 0.663 and the weight of NOMURA-BPI was 0.337, which shows that J-REIT
Index had more similar characteristic to equities than bonds. Meanwhile in the period [2], the weight of
TOPIX was 0.343 and the weight of NOMURA-BPI was 0.657, which showed the completely opposite
results.
Table 2: Parameters by Analysis Period
Analysis Period
Period [1]Apr 2003 to Dec 2015

Period [2]

Jan 2016 to Jun 2021

Whole period

Apr 2003 to Jun 2021

α

𝛽𝛽 𝐸𝐸

𝛽𝛽 𝐵𝐵

0.004

0.582

0.418

0.004
0.005

0.663
0.343

0.337
0.657

(Source: Prepared by the authors from FactSet data)

6

The empirical analysis of individual securities of J-REIT Index shown in Figure 3 also shows that theratio of equity to bond varies widely depending on the securities, from 7:3 to 3:7, and the ratio for somesecurities in hotel industry is as much as 90% equity. In this way, the characteristics of J-REIT as equities
or bonds varies widely depending on each period. Therefore, it is difficult to accurately evaluate the total
risk by using the risk management method of allocating J-REIT between equities and bonds at a certain
ratio when the percentage of J-REIT in a portfolio increases.
Figure 3 Results of the parameters for individual securities(Source: Prepared by the authors from FactSet data)(*)
Nomura Bond Performance Index (Nomura-BPI) is used for Domestic bond index data, as in the initial
analyses, to acquire data from April 2003 when data for J-REIT Index began to be available, instead ofusing NOMURA-BPI (excluding ABS) which is GPIF’s evaluation benchmark for domestic bondinvestment. NOMURA-BPI (excluding ABS) is used for individual securities since the analysis period islimited to the past 10 years.

4. Necessity of managing the risk of J-REIT independently
4.1 Issues in managing the risk of J-REIT within the framework of traditional assets
Variance-covariance matrix for the two assets of equities (TOPIX) and bonds (NOMURA-BPI) can beapplied to measure the risk amount associated with J-REIT within the framework of traditional assets, after7

the balance of J-REIT per unit is allocated to 𝛽𝛽𝐸𝐸 units of equity and 𝛽𝛽𝐵𝐵 units of bond. The amount of that

allocation is estimated by the regression equation described in Section 3.1. The first practical problem is thatthe allocation tends to be the same through the investment horizon in many cases. However, as confirmed in
Section 3.3, this allocation varies widely depending on the periods. The second practical problem is that thevariance arising from the error term in the regression equation (1) is ignored. Specifically, the variance ofthe regression error term 𝜎𝜎𝜀𝜀2 is ignored in equation (3), which is obtained by calculating the variance of bothsides of the regression equation (1). The impact of this omission on the portfolio's estimated risk is examinedin the following section.
𝑉𝑉𝑉𝑉𝑉𝑉�𝑟𝑟𝑡𝑡𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽 � = 𝑉𝑉𝑉𝑉𝑉𝑉(α + 𝛽𝛽 𝐸𝐸 𝑟𝑟𝑡𝑡𝐸𝐸 + 𝛽𝛽 𝐵𝐵 𝑟𝑟𝑡𝑡𝐵𝐵 + 𝜀𝜀𝑡𝑡 ) = 𝑉𝑉𝑉𝑉𝑉𝑉(𝛽𝛽 𝐸𝐸 𝑟𝑟𝑡𝑡𝐸𝐸 + 𝛽𝛽 𝐵𝐵 𝑟𝑟𝑡𝑡𝐵𝐵 ) + 𝑉𝑉𝑉𝑉𝑉𝑉(𝜀𝜀𝑡𝑡 )= (𝛽𝛽 𝐸𝐸 )2 (𝜎𝜎𝐸𝐸 )2 + 2𝜌𝜌𝐸𝐸,𝐵𝐵 𝛽𝛽 𝐸𝐸 𝛽𝛽 𝐵𝐵 𝜎𝜎𝐸𝐸 𝜎𝜎𝐵𝐵 + (𝛽𝛽 𝐵𝐵 )2 (𝜎𝜎𝐵𝐵 )2 + 𝜎𝜎𝜀𝜀2

Here

(3)

𝜎𝜎𝐸𝐸 , 𝜌𝜌𝐸𝐸,𝐵𝐵, 𝜎𝜎𝐵𝐵 and 𝜎𝜎𝜀𝜀2 , each represents the volatility of the equity, the correlation coefficient between

the equity and the bond, the volatility of the bond and the variance of the regression error term, respectively.
4.2 The settings of analysis for the necessity of manage J-REIT as independent asset

A total of one unit of portfolio is analyzed with a non-negative weight consisting of J-REIT Index, TOPIX
and NOMURA-BPI. The portfolio risk is measured in three ways, and defined as Risk I, Risk II and Risk
III, respectively.
Risk I: The amount of risk in case that J-REIT is managed independently
This amount of risk is calculated by using a 3×3 variance-covariance matrix for a portfolio consisting of
three assets. The percentages invested in J-REIT Index, TOPIX and NOMURA-BPI are shown as
𝑤𝑤𝑅𝑅 , 𝑤𝑤𝐸𝐸, 𝑎𝑎𝑎𝑎𝑎𝑎 𝑤𝑤𝐵𝐵 , respectively, then Risk I is calculated by the following equation:
RiskⅠ = �(𝑤𝑤𝑅𝑅

𝑤𝑤𝐸𝐸

𝜎𝜎𝑅𝑅2
𝑤𝑤𝐵𝐵 ) �𝜌𝜌𝑅𝑅,𝐸𝐸 𝜎𝜎𝑅𝑅 𝜎𝜎𝐸𝐸𝜌𝜌𝑅𝑅,𝐵𝐵 𝜎𝜎𝑅𝑅 𝜎𝜎𝐵𝐵𝜌𝜌𝑅𝑅,𝐸𝐸 𝜎𝜎𝑅𝑅 𝜎𝜎𝐸𝐸
𝜎𝜎𝐸𝐸2𝜌𝜌𝐸𝐸,𝐵𝐵 𝜎𝜎𝐸𝐸 𝜎𝜎𝐵𝐵𝜌𝜌𝑅𝑅,𝐵𝐵 𝜎𝜎𝑅𝑅 𝜎𝜎𝐵𝐵
𝑤𝑤𝑅𝑅
𝜌𝜌𝐸𝐸,𝐵𝐵 𝜎𝜎𝐸𝐸 𝜎𝜎𝐵𝐵 � �𝑤𝑤𝐸𝐸 �
𝑤𝑤𝐵𝐵
𝜎𝜎𝐵𝐵2

𝜎𝜎𝑅𝑅 , 𝜌𝜌𝑅𝑅,𝐸𝐸 and 𝜌𝜌𝑅𝑅,𝐵𝐵 are newly introduced notations and represent the volatility of J-REIT Index, thecorrelation coefficient between J-REIT Index and TOPIX, and the correlation coefficient between J-REIT
Index and NOMURA-BPI, respectively.

Risk II: The amount of risk in case that J-REIT is managed within the framework of traditional assets
This amount of risk is calculated by allocating the percentage of investment in J-REIT Index 𝑤𝑤𝑅𝑅 between

TOPIX 𝛽𝛽 𝐸𝐸 𝑤𝑤𝑅𝑅 and NOMURA-BPI 𝛽𝛽 𝐵𝐵 𝑤𝑤𝑅𝑅 , and then using a 2×2 variance-covariance matrix for the risk ofthe portfolio consisting of equities and bonds.

8

RiskⅡ = �(𝑤𝑤𝐸𝐸 + 𝛽𝛽 𝐸𝐸 𝑤𝑤𝑅𝑅

𝑤𝑤𝐵𝐵 + 𝛽𝛽 𝐵𝐵 𝑤𝑤𝑅𝑅 ) �𝜎𝜎𝐸𝐸2𝜌𝜌𝐸𝐸,𝐵𝐵 𝜎𝜎𝐸𝐸 𝜎𝜎𝐵𝐵𝜌𝜌𝐸𝐸,𝐵𝐵 𝜎𝜎𝐸𝐸 𝜎𝜎𝐵𝐵 𝑤𝑤𝐸𝐸 + 𝛽𝛽 𝐸𝐸 𝑤𝑤𝑅𝑅���
𝑤𝑤𝐵𝐵 + 𝛽𝛽 𝐵𝐵 𝑤𝑤𝑅𝑅
𝜎𝜎𝐵𝐵2

Risk III: The amount of risk calculated using the same equation to measure the risk as in the Risk II, while
keeping the parameter 𝛽𝛽𝐸𝐸 , 𝛽𝛽𝐵𝐵 the same as it was determined initially
Here it needs to be pointed out that the variance from the error term in the regression equation (1)described in Section 4.1 is equal to the Risk I calculated by substituting(1 −𝛽𝛽𝐸𝐸−𝛽𝛽𝐵𝐵 ).

(𝑤𝑤𝑅𝑅

𝑤𝑤𝐸𝐸

𝑤𝑤𝐵𝐵 ) =In the next section, the analysis has been made in the following manner: Firstly, we measured the magnitudeof the variance arising from the error term in the regression equation (1). Secondly, when calculating the riskof J-REIT within the framework of traditional assets, we measured the risk measurement error arising fromomitting the variance of the error term (hereafter referred to as risk measurement error I), by calculating Risk
I minus Risk II, and also measured the risk measurement error arising from not only omitting the varianceof the error term but also from using the parameter 𝛽𝛽𝐸𝐸, 𝛽𝛽𝐵𝐵 as originally calculated and unchanging thisparameter (hereafter referred to as risk measurement error II), by calculating Risk I minus Risk III.
4.3 The results of the analysis and its implications

Table1 shows volatilities of returns of J-REIT Index, TOPIX and NOMURA-BPI over period [1] and [2],and Table 3 shows the correlation matrices in addition to the volatilities of returns in Table 1. Table 3 showsthat in period [1], the correlation coefficient between J-REIT Index and TOPIX was 0.61, but in period [2]it declined to 0.39. On the other hand, in period [1], the correlation coefficient between J-REIT Index and
NOMURA-BPI was 0.07 but rose to 0.22 in period [2]. In Section 3.3, from the viewpoint of the regression
coefficient 𝛽𝛽𝐸𝐸 𝑎𝑎𝑎𝑎𝑎𝑎 𝛽𝛽 𝐵𝐵 of regression equation (1), we found that J-REIT Index had stronger characteristics

as equities in the period [1] and showed stronger characteristics as bonds in the period [2]. We also foundthat the similar change in characteristics from equities to bonds from the viewpoint of the correlation
coefficient that eliminates the impact of volatility.
The variance-covariance matrix in Risk I, Risk II can be applied by using the parameters in Table 3.
When the weights are set as (𝑤𝑤𝑅𝑅

𝑤𝑤𝐸𝐸

𝑤𝑤𝐵𝐵 ) = (1 −𝛽𝛽 𝐸𝐸−𝛽𝛽 𝐵𝐵 ) to calculate Risk I, it matched thevariance resulting from the error term in the regression equation (1) and was 0.156 and 0.123 for the period[1] and [2], respectively. This indicates that the risk of one unit of J-REIT in long position, and 𝛽𝛽𝐸𝐸 unit of

TOPIX and 𝛽𝛽 𝐵𝐵 unit of NOMURA-BPI in short potion is 15.6% and 12.3% on an annualized basis. The
analysis here, the percentage invested in J-REIT Index is set in 1% increments ranging from 1% to 30%,

and the remainder is equally allocated to TOPIX and the NOMURA-BPI. Figures 4 and 5 show the risk
measurement error I (= Risk I-Risk II) in period [1] and [2], respectively. Figures 4 and 5 take the percentage
of J-REIT Index in the portfolio on the horizontal axis, and the magnitude of the risk measurement error I
on the vertical axis. It indicated that the magnitude of the risk measurement error I relative to J-REIT Index
weight is not as large as the error calculated from the standard deviation of the error term in the regression
9equation (1), and is almost the same in the period [1] and [2]. When the percentage of investment in J-REIT
is 5%, the effects of the error term in the regression equation (1) in the period [1] and [2] are simply
calculated as follows: 15.6% × 0.05 = 0.78%, 12.3% × 0.05 = 0.615%, respectively. However, the actual
risk measurement error I was considerably smaller than the effects of the simple error term, which wasaround 0.1%, as shown in Figures 4 and 5. This was due to the reduction of the impact of the error term inequation (1) through the diversification effect between the investment ratio of the 5% of J-REIT which hasdifference in the risk measurement, 0.05 × (𝑤𝑤𝑅𝑅

𝑤𝑤𝐸𝐸

𝑤𝑤𝐵𝐵 ) = (0.05 −0.05𝛽𝛽 𝐸𝐸−0.05𝛽𝛽𝐵𝐵 ) , and theinvestment ratio of the remaining 95 % which is equally allocated to TOPIX and NOMURA-BPI,
(𝑤𝑤𝑅𝑅

𝑤𝑤𝐸𝐸

𝑤𝑤𝐵𝐵 ) = (0 0.475 0.475). As stated above, the standard deviation of the regression error termin period [1] and period [2], and the volatility of each asset and the correlation coefficient between assets
are interrelated, and the risk measurement error I in period [1] and period [2] turned out to be almost thesame.

Figure 4: Risk Measurement Error I in Period [1]Figure 5: Risk Measurement Error I in Period [2](Source: All figures are compiled by the authors from FactSet data.)
Figure 6 shows that the risk measurement error II in period [2] is negative in the range of 1% to 30%of the investment ratio of J-REIT on the horizontal axis, which indicates that the amount of risk of portfolios
including J-REIT measured within the framework of traditional assets resulted in a larger estimate of theamount of risk than measuring the risk regarding J-REIT as an independent asset. As mentioned in Section
3.3, the weights of TOPIX and NOMURA-BPI were completely inverse in period [1] and [2], so this would
cause a large impact and lead to the miscalculation of the risk in the opposite direction in case the same
weights have been used.

10Figure 6: Risk Measurement Error II in Period [2]Figure 6 Risk Measurement Error II in Period(Source: Prepared by the authors from FactSet data)
Here focusing on the measurement of risk in GPIF. In Chapter 1, it was noted that the total value of GPIF's
alternative assets is 0.70% of the total pension reserve as of the end of March 2021, and GPIF is allowed toinvest up to 5% of its total assets under management in alternative assets. If J-REIT is considered as analternative asset, the impact to the portfolio is nominal as the minimum percentage of investment in J-REIT
is 1% and this is considered as a substitute for the 0.70% at the end of March 2021, shown in Figures 4 and5. However, considering the maximum percentage of alternative assets of 5%, the risk measurement error I
for both period [1] and period [2] would be around 0.1%, and the amount would be 100 billion JPY, whichis calculated by 100 trillion JPY (assuming the amount of domestic assets) x 0.1%. This is the reason why
we stated " Given the increasing value of the alternative assets, we are at the stage of evaluating the way tomanage the risk." in Chapter 1.
Table 3: Risk-Return Characteristics
Period [1]Period [2]Whole period

Apr 2003 to Dec 2015

Jan 2016 to Jun 2021

Apr 2003 to Jun 2021

Returns

Returns

Returns

Volatilities

Volatilities

Volatilities

J-REIT Index

10.9%

20.0%

8.6%

13.8%

10.2%

18.3%

TOPIX

8.6%

18.0%

7.7%

15.7%

8.3%

17.3%

NOMURA- BPI

1.7%

1.9%

0.9%

2.0%

1.4%

1.9%

Period [1] Apr 2003 to Dec 2015
J-REIT Index

TOPIX

NOMURA- BPI

J-REIT Index

1.00

0.61

0.07

TOPIX

0.61

1.00

-0.31

NOMURA- BPI

0.07

-0.31

1.00

11

Period [2] Jan 2016 to Jun 2021
J-REIT Index

TOPIX

NOMURA- BPI

J-REIT Index

1.00

0.39

0.22

TOPIX

0.39

1.00

-0.45

NOMURA- BPI

0.22

-0.45

1.00

(Source: Prepared by the authors from FactSet data)

5. Efficient frontier portfolios consisted of J-REIT, equities and bonds
This Chapter examines the efficient frontier of portfolios consisted of J-REIT, equities and bonds, forwhich preceding studies are scarce. Figure 7 shows the efficient frontier for only two assets, TOPIX andNOMURA-BPI for the period [1] shown in Table 3, based on the returns of J-REIT Index, TOPIX andNOMURA-BPI, the volatility and the correlation matrix, and the efficient frontier when three assets areavailable including J-REIT, with the portfolio's risk on the horizontal axis and the portfolio’s return on thevertical axis. In addition to the two efficient frontiers shown in Figure 7 in period [2], Figure 8 also showsthe efficient frontier when four sub-sector indices of J-REIT Index can be invested as well as the three
assets mentioned earlier. Figure 7 reconfirms that J-REIT has higher risk and higher return than TOPIX in
period [1]. Furthermore, it shows that the portfolio including three types of assets is superior in terms ofrisk-return since the efficient frontier of three assets lies on the upper left-hand side, compared to theportfolio of only two assets, TOPIX and NOMURA-BPI. In particular, focusing on the risk amount of 10%
since the risk (standard deviation) of GPIF’s basic portfolio is 12.32% according to p.36 of FY2020 Annual
Report, the optimized return of the portfolio including only two types of assets of TOPIX and NOMURABPI is 5.7%, while the optimized return of the portfolio including three type of assets with J-REIT Index
added is 6.5%, approximately 80BP higher than the portfolio of two types of assets.

12

Figure 7: Effective Frontier (Period [1]: Apr 2003 to Dec 2015)(Source: Prepared by the authors from FactSet data)
Furthermore Figure 8 shows that J-REIT has lower-risk and higher-return than TOPIX in period [2].
Therefore, in period [2], the move of the efficient frontier to the upper left is larger by adding J-REIT to thetwo assets of TOPIX and the NOMURA-BPI than in period [1]. Focusing on the risk amount of 10% similarly
to period [1], the optimized return of the portfolio including only two types of assets of TOPIX andNOMURA-BPI is 5.4%, whereas the optimized return of the portfolio including three types of assets with JREIT Index added is 7.0%, and the portfolio's return is improved as much as approximately 160BP. In
addition, the appropriate selection of funds within J-REIT Index that invest in high-performance sectors willraise the optimized return to 11.5 %, an approximate 450BP improvement in portfolio returns. Thus, the riskreturn efficiency of the portfolio could increase to a considerable degree by adding J-REIT to the portfolio.
Figure 8: Effective Frontier (Period [2]: Jan 2016 to Jun 2021)(Source: Prepared by the authors from FactSet data)

13

6. Summary and future challenges
This study firstly analyzed the risk-return profiles of J-REIT, equities and bonds based on monthly data
for about 20 years since the opening of J-REIT market and found that J-REIT has characteristics of highrisk and high-return, or low-risk and high-return compared to equities. Secondly, the risk measurement error
would arise when J-REIT is allocated between equities and bonds at a certain fixed ratio since the degreeof equity and bond characteristics inherent in J-REIT varies significantly depending on the period. Thirdly,
the risk measurement error will be too large to be overlooked when the percentage of J-REIT in the portfolio
increases. Finally, if the efficient frontier is figured with accurately measured risk level, the efficient frontierwith J-REIT added to the portfolio will move to the upper left, showing that the portfolio's performance
improves in terms of risk-return profiles.
As the risk-return profile of traditional assets moves toward low-risk and low-return in the long-term
trend, J-REIT's returns are attractive as mentioned earlier, and alternative assets that has less liquidity than
J-REIT are expected to have even higher returns. On the other hand, it is difficult to measure the risk ofalternative assets compared to traditional assets, and it takes longer time to realize the return on alternative
assets than traditional assets. Moreover, when investing in alternative assets, it is necessary to thoroughly
examine whether it is desirable compared to the risk-return profile of traditional assets and how risk-return
profiles improve when the portfolio is structured in combination with traditional assets and alternative assets.
As the first step, this working paper elucidated the necessity of managing the J-REIT separately as anindependent asset class, considering J-REIT as an alternative asset. The future challenges are to establish
more sophisticated and advanced risk-management methods for private REIT which have relatively highfrequency of price updates among alternative assets, and for private equity, infrastructure, real estate, andother funds that have less liquidity.

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