80024622 1996

Science for Open and Environmental Systems 80024622 KIKUCHI, Atsushi Optimal Asset Allocation with Real Estate The institutional investors such as life insurance companies, trust banks, and pension funds, have to allocate their funds to several assets in order to obtain the higher but stable rate of return. Real estate is viewed as a portfolio diversifier, or risk reducer. Historically, real estate has been defined as only investments in private real estate equity and private real estate debt. The investors, who wanted to invest real estate, needed to buy and hold individual buildings directly. There were no secondary and securitized markets for private real estate debt or private real estate equity. Today, however, with the advent of securitization, the definition of real estate for institutional investors has broadened to cover many structures. We examine the relationship among the real estate index, stock index, and bond. index. We can find the difference among them. We examine that optimal asset allocation problem with real estate using mean-variance approach with the available data sets. We use the Sumitomo Life Research Index(SLRI), TOPIX, and Nikko Bond Performance Index. The results show that real estate can reduce risk on the asset mix. In our future research, we need to examine the model using additional data.

Optimal Asset Allocation with Real Estate 2001 80024622

A Study of Funds Allocation on Decentralized Organization 2001

1 1... 2 1-1... 3 2... 4 2-1... 5 2-2... 6 2-2-1... 6 2-2-2... 7 2-2-3... 8 2-2-4... 9 2-2-5... 11 3... 13 3-1... 14 3-1-1... 14 3-1-2... 16 3-2... 18 3-2-1... 18 3-2-2... 18 3-2-3... 18 3-2-4... 19 4... 20 4-1... 21 4-2 -(I)... 22 4-2-1 -(I)... 22 4-2-2 -(I)... 28 4-2-3 MV... 28 4-2-4 MLPM... 35 4-3 -(II)... 42 4-3-1 -(II)... 42 4-3-2 -(II)... 44 4-3-3 MV... 44 4-3-4 MLPM... 46 5... 49 5-1... 50... 51... 52 1

1 2

1 2000 5 11 2001 9 J-REIT: J-REIT 1991 1996 3

4

1 2-1 optimal asset allocation optimal portfolio 2 4 2-1 1 2 3 5

86 3 1990 2-2 2-2 4 3 4 3 9 223 2 3 100 6

7 2-1 2-1 2-1

11. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 2-3 2-3 8

2-4 ( ) ( ) : SPV : special purpose vehicle 2-4 2-2 9

2-2 5 2-5 5 debt CP equity 10

2-5 6 Topix National Council of Real Estate Investment Fiduciaries NCREIF 1996 10 :SLRI 6 SPC J-REIT 11

SLRI NOI 4 12

13

rp re Var(R) Minimize subject to n n Var( R) σ x x ( 3.1 ) P E j= 1 k = 1 jk j k r r ( 3.2 ) n j= 1 x j = 1 ( 3.3 ) x 0 ( j = 1,..., n) ( 3.4 ) j x X ( 3.5 ) σ jk : j k : j x = (x 1,, x n ) T x j r E r j rp : : j n : r = r x p j j= 1 (3.3) (3.4) (3.5) X (3.2)(3.4) x j 7 R 1, R n r 1t,, r nt, t = 1,, T r jt t j T p t p t = Pr{( R1,..., Rn ) = ( r1 t,..., rnt )} ( 3.6 ) p t 1/T 7 t t 14

jk r jt T 1 σ = ( r r )( r r ) ( 3.7 ) jk T t= 1 jt jk Var(R) n n j= 1 k = 1 j kt k Var( R) σ x x ( 3.8 ) jk j k (3.8) (3.7) (3.8) n n T 1 Var (R) = ( rjt rj )( rkt rk ) x jx j= k = T 1 1 t= 1 n 1 = T n n ( rjt rj ) x j ( rkt rk ) xk = j= k = T t 1 1 1 1 = T n ( r r ) x k T jt j j T t= 1 j= 1 t= 1 j= 1 y = r x r t j= 1 jt j p 2 = 1 T n 2 r jtx j rp T 1 2 Var( R) = y t ( 3.9 ) T t= 1 Minimize 1 T T t= 1 2 y t ( 3.10 ) subject to n j= 1 r x y = r jt j t p ( t = 1,..., T ) ( 3.11 ) rp r E ( 3.12 ) n j= 1 x = 1 ( 3.13 ) j x 0 ( 3.14 ) j x X ( 3.15 ) 15

Bawa and Lindenberg Mean-Lower Partial Moments model : MLPM lower partial moments 3-1 r G rg rt 3-1 k LPM ( R ; r G ) (3.16) k T 1 k LPM k ( R ; rg ) rt rg ( 3.16 ) 8 T t= 1 d + d = r r ( 3.17 ) t t t G + d t d t 0 (3.17) (1) r r 0 t G d t = + t 0, d = r r ( 3.18 ) t G 8 a = max ( a, 0 ) 16

(2) r r 0 t G t + t d = ( r r ), d = 0 ( 3.19 ) d d + 0 t t t G t = rt rg d ( 3.20 ) + d t d t + t d t d 0, 0 ( 3.21 ) + (3.17) d t d t 0 + + + + d = 5 t d d t t = 0 dt = 5 d t = 2 d t = 7 + 0 + t d t d = 0 ( 3.22 ) (3.21) + d t (3.22) d t d t 0 + (3.17) d d D + t d t d = r r + d 0 ( 3.23 ) t G d t t t { r + d r, d 0 ; t = 1 T } D = t t G t,..., ( 3.24 ) { d t dt D} = rt rg t min ( 3.25 ) k LPM ( R ; r G ) d t Minimize 1 T T t= 1 ( d t ) k ( 3.26 ) subject to n j=1 r jt x j + d t r G ( t = 1,..., T ) ( 3.27 ) d 0 ( 3.28 ) t (3.2)(3.5) k = 1 k = 2 2 k 3 k=2 17

NH FH OH F S 0 F 1+ rf = ( 3.29 ) 0 S 1 + r D r F r D : : (3.29) F t t+1 t t+1 t t+1 t t 9 (3.29) 9 :5 t t+1 t+1 18

j j NH j FH j NH j FH 1 2 njp NH 1NH 2NH nnh H 1FH 2FH nfh jnh : j jfh : j 3-2 19

20

-(I) -(II) 4-1 4-2 NUOPT 10 4-1 -(I) 4-2 -(II) 10 NUOPT 21

-(I) { }7 { }5 4-1 4-1 4-2 4-2 19921999 4-3 22

4-3 1992-1999 SLRI 90 NCREIF 92 93 4-3 4-4 4-3 1992-1999 4-4 1992-1999 4-3 7 SLRI NCREIF 23

4-4 SLRI NikkoBPI GSBI NCREIF NikkoBPI GSBI SLRI NCREIF 4-4 NH FH 4-4 1992-1999 4-5 4-6 4-5 1992-1999 24

4-6 1992-1999 4-5 NH FH FH NH FH NikkoBPI SP500_NH NCREIF_NH SP500_NH 4-6 SLRI NCREIF_NH NikkoBPI NCREIF_NH SP500_NH TOPIX SLRI NCREIF_FH NikkoBPI NCREIF_FH SLRI NikkoBPI 25

4-5 SP500_NH NikkoCBPI NikkoBPI NCREIF_NH GSBI TOPIX SLRI 4-5 1992-1999 NH 7 NikkoBPI NikkoCBPI SP500_NH 1 4-5 26

4-6 SP500_FH NikkoCBPI NikkoBPI NCREIF_FH GSBI_FH TOPIX SLRI 4-6 1992-1999 FH 7 NCREIF_FH NikkoBPI NikkoCBPI SP500_FH 1 4-6 27

MV 2 MLPM MLPM 6.22%15.94%NH0.02% 5.22%13.84%FH0.02% 5.22%15.94%OH0.02% 4-7 4-7 NHMV 4-7 28

4-8 4-8 FHMV 4-8 29

4-9 4-9 OHMV 4-9 NH FH OH 4-10 4-15 30

31 4-10 NHMV 4-11 NHMV

32 4-12 FHMV 4-13 FHMV

33 4-14 OHMV 4-15 OHMV

34 4-10 4-11 6.22%8.00% 4-8 11.00% 4-12 4-13 5.22%10.66% NCREIF_NH 4-9 TOPIX GSBI_FH 4-14 4-15 5.22%10.66% NCREIF_NH 4-10 TOPIX GSBI_FH

4-16 4-16 NHMLPM 4-16 LPM 35

4-17 4-17 FHMLPM 4-17 36

4-18 4-18 OHMLPM 4-18 NH FH OH 4-19 4-24 37

38 4-19 NHMLPM 4-20 NHMLPM

39 4-21 FHMLPM 4-22 FHMLPM

40 4-23 OHMLPM 4-24 OHMLPM

41 4-19 4-20 6.22%8.78% NCREIF_NH 4-8 NikkoBPI 11.00% NikkoCBPI SP500_NH 4-21 4-22 5.22%10.78% NCREIF_FH 4-9 TOPIX GSBI_FH NikkoBPI SP500_FH NCREIF_FH 4-23 4-24 5.22%10.78% NCREIF_NH 4-10 TOPIX GSBI_FH NikkoBPI SP500_FH NCREIF_FH

-(II) { }4 { }3 4-1 19851999 4-25 1985-1999 4-7 4-8 4-7 1985-1999 42

4-8 1985-1999 4-7 NikkoBPI NikkoBPI 4-8 SLRI TOPIX NikkoBPI NikkoBPI NikkoCBPI SLRI TOPIX 4-26 1985-1999 43

MV 2 MLPM MLPM 6.36%8.56% 0.02% 4-27 4-27 MV -(II) 4-27 44

45 4-28 4-29

4-28 4-29 6.36%7.38% SLRI 4-27 NikkoBPI NikkoBPI 4-16 4-30 MLPM -(II) 4-30 46

47 4-31 MLPM 4-32 MLPM

4-31 4-32 6.36%8.54% SLRI 4-30 48

49

1996 50

[1] J.L.Pagliari Jr., J.R.Webb, J.J.Del Casino1995 Applying MPT to Institutional Real Estate Portfolios : The Good, The Bad and Uncertain, Journal of Real Estate Portfolio Management, Vol.1, No.1, p.88-97 [2] 1998,, Vol.36, No.12, p.29-40 [3] 1999 1999 7, [4] 2001, [5] 1999, [6] 2001 2001, [7] 1998SPC, BP [8], /NTT 1991, 51

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