人工知能学会
経営課題にAIを！ビジネスインフォマティクス研究会 (第7回)
JSAI Special Interest Group on Business Informatics (SIG-BI #7)

ISGH>N?Xpd=O@NBK  ,`3mWFSD2+*/\x,b:<;]
Why portfolio reconstruction algorithm OLMAR gets excessive revenue?
ļƣ ° 1 źÐ ±Ĵ 1 Î őŞ 1 èŊ ƪĀ 2âƣƪƭ 1

Kazunori Umino1, Takamasa Kikuchi1, Masaaki Kunigami1, Takashi Yanada2 and Takao Terano1
11ĥéĬÚÝ
Tokyo Institute of Technology2
è¼ÚÝ
2
Yamaguchi University

Abstract: ģœŝB, Ƹ"qrXucRŕ0=-P;"O OLMAR ĺRãƎ@, ƔƜºŎRýMPOƁÊRªĦ., ?3ƥĢ@Q68;¤ĂR9,='<(;"OA&RīƇ.6. ćB, tlrX|Y¨ĮŢT}_|dw<!O OLMAR ĺ', óšÌ?ĩöìÕ<ƥĢ@Q68;ıŸ0O6I@B, ĩA×µ@%";, ƥĢ@čū., ×µAęŻAėÃĂ'®ŉ½Ÿ?, łßA×µłĂ'ÜÏ0O=Ŷ

$6. 4.;, tlrX|Y¨ĮĆT}_|dwB, łßA×µłĂRŜĭō@®ŉ0OÿƁ'!OB1<!O. ģœŝB, 4AL#?ßRJ=@, kgeil@Ļŏ.6ªĦRż86. ģƍĕ<B, Ė6@
ŉĄ.6ĘţAƥĢĩökg@%";, 1) OLMAR ĺ<ƔƜºŎ'ýMPO,=. 2) OLMAR ĺ'Óģ=0OŗµñÑƮŅRŉ";ĘţAƥĢĩökg@%";łßA×µłĂ'ÜÏ0O,=. 3)łßA×
µłĂRŀ´¶.6kg<B, OLMAR ĺ@L8;ƔƜºŎ'ýMP?",=RŔƊ.6.

4-82ģœŝAŏōB, Ĕ·òAàƬAĩkgeil@%";, »÷^clRŶą.;JVki[cRTWlqrXw.;"O OLMAR (On-LineMoving Average Revrsion)ĺ@Ļŏ., ?3ƔƜºŎRýMPOA&RªĦ0O,=<!O[1]. OLMAR
ĺB, ŗµñÑ&MĜō@Ú() Ż(Ʈ).6ĩö', ŗµñÑ@Ƙ:)ņƎ@LNƔƜºŎRýOtlrX|Y¨ĮĆĈĺ<!O[2][3].
ģśAªĦ§áB, 1) OLMAR ĺ'ŉ";"OĈĺRĪĜť¬kg@ƞŉ0O,=@LN, àƬAĩkgeil@%";M&AĩA×µł
Ă'ī©½Ÿ&?, 2) M&AĩA×µłĂ@LNƔƜºŎ'ýMPOA<!PC, 4AłĂR<(OƩNä-)0O,=< OLMAR AqrXucB>#×¶0OA&? A 2 Ŀ<!O.
Ù)Aœŝŷ@LNīƇ'żQP, Ƹ"qrXuc'ýMPO,='ÔÅ-P;"O[3][4][5][6][7].
.&.?'M, ĸIMP6kgeil@ã.;,Ġƞ¶Rż"qrXucR+O,=@Ļ².
;%N, kgeil4AJA@ã0OªĦBżQP;"?"[3][6][7][8]. ĩ×µ'{hw@Ƙ*PC, ƔƜºŎRƥĢ@Q6NTWlqrXw0O,=BËƯ<!N, OLMAR ĺ'M&Aĩ×µAłĂR®ŉ.;"O=0PC, G<@!(M&@-P;,?&86ĩ×µAłĂ=,4PR®
ŉ0Oj[oi['ÜÏ0OB1<!O.
 OLMAR B ¤ Ŗ ? T } _ | d w < ! N ? ' M ,“ ?3, ƔƜºŎ'ýMPOA&? ” @9";Bœ
ŝ-P;"?". ģœŝ<B, ĩ×µAłĂRªĦ., OLMAR ĺ'Þßō@ƔƜºŎR+OxZ
odwAƃĚRƈHO.
ģƍĕAƁ?ƐńBĳA=%N<!O.
 Ė6?kgeilŉĄ., OLMAR AT}_|dw'ġ´<!O,=Rŕ., kgeil'
ƥĢ@čū0Oĩ×µłĂRč9,=RĚM
&@0O.
 OLMAR ĺ'®ŉ0OłßA×µłĂRŀ´¶0OėĺRŕ0.
 OLMAR @LOƔƜºŎ', ģœŝ<ĚŔ@.
6ĩ×µłĂ@Ü.;"O,=Rŕ0.
ģƍĕ<B, OLMAR ĺAÓģ=?8;"OŗµñÑƮŅRƞŉ.6ÕÀAĩ×µłĂ@9";1

人工知能学会
経営課題にAIを！ビジネスインフォマティクス研究会 (第7回)
JSAI Special Interest Group on Business Informatics (SIG-BI #7)

AªĦRż", ƔƜºŎ'ŌŇ0OxZodwRªĦ0O.
ƾŞ<Bģƍĕ<ŉ"OĎİ%LD OLMAR ĺ@ƨ0OƋĚRż", 3 Ş<ģƍĕAªĦĈĺRƋĚ., 4 Ş<Ė6@ŉĄ.6ƀĔAkgeilAīƇũħRŕ., 5 Ş@%";G=I=0O.

2.

!! =!!
,!!!!

ģƍĕ<ŉ"OĎİ@9"ƋĚ0O!% %"%#! "# zZa^Tv!"#$%&'(!! =1!

 ! !"# =!!!!!! ,!!!

$(#$" !
(!!!)ģīƇ<ŉ0OƆ¾=ĄÆR@ßŴ0O

iĩö i(i=1,…,N)tĜĿ tƺt=1,…,Sƻ67.¦ĢƧAkg'ÜÏ.?"ÕÀBkg'ÜÏ0OĜĿAHRƙ0!!,! ĜĿ  @%*Oĩö  A|gMAD!"!,! ĢƧ  ĘRŉ"6ĜĿ  @%*Oĩö AŗµñÑƮŅMDD!"! (!1: !2)ĜĿ t1 &M t2 G<Aĩö  AĠÚmhW!

!"#!! = 100 !! − !"#$%&'(!! / !! ,

3. oisNtlrX|YRĮĆ0OTeilĔy{

2R1 jh0Vw.;fqĜ¯  @%*OƑňAĪR  =0O=,AƑňRĜ¯  &MĜ¯  G<č.6ĜA|g BĳAL#@?OĪA Żð'Ú(", 2ƵŰ@Ƒň¥Pğ$'Ɠ
,N»÷^clA£&?Ö³<|g'Úð@
Ľå0O,=<!O[2].

!!
!
!!! !
!!!

,

!" = ! !"# !"! , '$"&!& !! = max !! ,
!∈ !,!

!! = !! – !! ,!""! = max !! ,!∈ !,!

2R2 ISGH>N?Xpdes G<ñÑ=ªēR^l}0O,=&M,LNŜĭō@Ī×µAłĂRŇ&.6T}_|dw'ƦŌ-P6. 4A<ĠJƸ"qrXucRŕ.6Ĉĺ' Follow-the-Loser ="#Zj_|@ç0OĈĺ<!N,4AžōĈĺ' OLMAR ĺ<!O=ÔÅ-P;"O[3][9].
Follow-the-Loser =B,Ə*Ũ(Ī' Ż.;"O)ĩöųRï@ƟĊ.;,Ī' Ż&Mę@ƕ/;ñÑÉî0O,=RĢú0OĈĺ<!O.
OLMAR ĺB,ŗµñÑƮŅ(MAD)AƸ"ĩöųRï@ƟĊ0OĈĺ<!N,¦;Akgeil<
ĠJ|gAƸ"Ĉĺ<!O=ƄQP;"O.6
7.,ĲĿ=.;B,
1) MDD(ĠÚmhW)'Ú(),Ĝō?Ƒň

3R1 mW_Ztc3Yk
ģœŝ<B,OLMAR ĺ<ŉ"MP;"OŗµñÑƮŅ@Ó:)ĩöArU}g|\Aġ´Ă=,4,&MƔƜºŎ'ýMPOĩ×µłĂRªĦ0O AĈƳ=?O
<1>ĩkgeilA¦ĩöA MADŗµñÑ  ƮŅ=|gRķIO<2>MAD Aä-?Ƴ@fl.6<Ƙ¡)  ĿAñÑRķI4AR|gAñÑ=.|gĝŭRýO<3> kg¦A  L=[0.25,0.5,1,3,5]qe  lAñÑR|gĝŭLNķIO
3R2 mW_Ztc63FSD~rgUģœŝ<BMAD @LNƔƜ|gAýMPOłĂ'ī©<(PC4AłĂRĽåG6Bưï@ä-)0O,=< OLMAR ĺ@LNƔƜºŎ'Ľå
G6BýMP?",=RīƇ0Oģœŝ<BŗµñÑƮŅ@LN|gĝŭ@ÑŽ'!OÕÀ
@|gĝŭ@ü"kgRſĴ0OĢƧ k AMAD!!,! RķI6<|gĝŭRķ  Ięĩöų= ŻĩöųAĵHR Aö  @Ó:(kgARĞ(Đ$OÑŽA!
  O L=1.0(%) ARR  A|gAkg dU =4PØA dD @ª*4P5P
Aİľ ëRķI dU = dD Aİľ ë'ş.
)?OL#@kgRđ., modify_dU R dU
@Ų(Đ$O(1,2). kgRđ@LN, |  gAŬÇ@ë'ŇGP6ÕÀB, 4Aë<  !O add_mean R MAD < 0 A¦kg2

人工知能学会
経営課題にAIを！ビジネスインフォマティクス研究会 (第7回)
JSAI Special Interest Group on Business Informatics (SIG-BI #7)@Ñş@ơª0O(3).!"#$% =!"##$%(!")!"##$%(!")

(1)

,(2)(!"#(!")!!"#(!"#$%&_!"))

 ,  (3)modify_dU=1.0+ratio(dU-1.0)!""_!"#$ =ž  ®ŉkgeil!"#!! A¦kgĔ Ɔ@ŕ.6ſĴkgAđRĢƧ kǆ[20,40,80]AƳ<űNƙ.đRż"ƀĔAŗµñÑ@ã0O  1%AĵHę Ż  kgAİľ ëAëRůä-2O¦Ĵ ÿƁ@ā/;ĵHRĴĶŅ  @ā/;Ĵ0O,=J½Ÿ<!OƠĴ¦ĴAÕÀB a=1.0 =?NƠĴAÕÀB 0<a<1.0=?O(4)
 modify_dU=1.0+(1-a(1-ratio))(dU-1.0) ,(4)3R3  OLMAR_random s
{hw@ĩöRƟĊ.tlrX|YRĮĆ0OñÑĩöĔ%LDĩöAñÑčĢƧ'  ĺ@ş."Ĉĺ<!N»÷ÉĔJÁ/<!
O  ĺ@LOqrXucAĶƖãƎ=0O
3R3 oisģœŝ<B,  AīƇRż#.
(1) ŗµñÑƮŅ(MAD)Rŉ", MAD 'uVnc
A ŻæƱ@Ļŏ., łĂ(|gAÑŽ:|gĝŭAĵHK¢Ã)RªĦ0O. OLMAR
ĺB, Ż.;"OĩöAHRĉ#T}_|dw7&M<!O[3].
(2) |gAÑŽ'!PC, 4P@ã.;ſĴ
đRż"ę ŻAİľ ëAƝ"RĴ
0O. ,PR, ƀĔAžō?ŗµñÑ@ã.
;ż#.
(3) OLMAR ĺ%LD OLMAR_random ĺ@LN,Y|bn}ĩkg%LDſĴđRż86kg@ã.;avy~azRż", 4AƝ"RªĦ0O.

4. o|l4R1 FSDCEG ģīƇ<ŉ"OkgeilBY|bn}ĩkgeil ŚƷ=  Š<ŕ0kgAſĴđ
Rż86JAAƅ
ŚƷ<!O¿kgeilAłþR @ŕ0ž   ĎĔAñÑAƝ"RƂO= kg@ã0OſĴđ<BñÑÉ
î&Ml~m¢Ã@×¶.;O' kg<B
F=S>×¶'Ɠ,8;"?"

ſĴđ@LNY|bn}&MłĂ'Ú()×¶.;"O <BƑňŅ'Ú()ę.6ĩö@LN|gAñÑ''8;%N  <Bŋ?O×¶'Ɠ,NÚ()

Ż0OƤĨ'ŇĆ-P;"Oû4A

L#?kgAŌŇıô@ƨ0OªĦ'ÿƁ<!OkgÂkg`Vd

4AAłþ

SP:S&P500

1999.1~2016.4|g4359 Ę,391 ƤĨ(ñÑ)= 8.86(Û)=4.60

Hurst ĎĔ(ñÑ)=ƑňŅ=0.460.06~434.4
ñÑ MDD= 71.6

NK:Nikkei225

1999.1~2016.4|g4254 Ę,183 ƤĨ(ñÑ)= 2.62(Û)=1.62

Hurst ĎĔ(ñÑ)=ƑňŅ=0.480.14~56.6
ñÑ MDD= 78.7

SP_mod:1999.1~2016.4|g

SP @ſĴđR4359 Ę,391 ƤĨ(ñÑ)= 44.4

ż"łßA×µ*4.2 Š¹Ł(Û)= 11.0

łĂRŀ´¶.

ƑňŅ=
Hurst ĎĔ(ñÑ)=

0.024~6098.9

0.54

ñÑ MDD= 70.7

NK_mod:1999.1~2016.4|g

NK @ ſ Ĵ đ 4254 Ę,183 ƤĨ(ñÑ)= 1.95

Rż"łßA×*4.2 Š¹Ł(Û)=1.216kgµłĂRŀ´¶.6kgƑňŅ=Hurst ĎĔ(ñÑ)=

5.6×10-6~27.90.49

ñÑ MDD= 79.4


4R2 Wn_Ztc
SP ¦ĩökg(N=1688338)R,MAD =4AŵĘ
A|gRsil.,ČÚ.6JARÍ 1 @ŕ.,
SP %LD NK A MAD =|gR(ž 2,3)@ŕ0
SP kg<B, MAD '   <!PCŪƅō@ġĄ?Ƹ"|g'ýMPO,='Q&86Ɯ¸  ò&9  ƤĨAkg<!Nø­@ß.6ƥĢ@Q6Oĩ×µłĂ'ŔƊ<(6NK kg<J, ƞ«@ŗµñÑRƟĊ0PC, MAD ' 1% <Ƹ"|gRýMPO,='ŕ-P
6.

3

人工知能学会
経営課題にAIを！ビジネスインフォマティクス研究会 (第7回)
JSAI Special Interest Group on Business Informatics (SIG-BI #7)

¦ĩökg(N=1688338)R,MAD =4AŵĘA
|gRsilAĵHR 3.2 Š<ŕ.6ĈƳ@
LN  1%A×µAłĂRĽå-26ũħRÍ 2@ŕ0. MAD @ã0O|gAę¢Ã'ěĴP;"O. ģ]cA 40 ĘƧA MAD=[-40,-45]B¦
A 0.1 %LD 0.025%@Őø0O.

Í 1 SP A¦kgRŉ"6ŗµñÑƮŅ(40 ĘAMOD)=ŵĘA|gAªí.  1.0% <B,ęŻAÑŽ'Ɠ,N, MAD A'ä-"F>,ŵĘA|gBƸ)?8;"O. ?%, ¿ŮŭBêLNŗµñÑƮŅ  0.5,1,3,5%Rŕ.;"O.
ž 2 SP kg@%*O 40 Ę MAD =ŵĘA|g:|g' MAD AuVncðAČÚ@LNŵĘAñÑ|g'Ö³.;"O.
ƹŗµñÑƮŅøĘŧ&MŵĘŧ(MAD)G<A|g0.25-32.0

0.5-27.3

1.0-22.0

3.0-14.3

5.0-11.2

1.00551.00441.00331.00251.0014Í 2 SP kg@%*OđĢƧ k=[20,40,80]AſĴũħÍ  =Á/Ĥ<!O'MAD @ā/;|g'
ę0O¢Ã'ſĴ-P;"O?%, MAD B, 3.2<2>@%";,ƿ9AĢƧ@%*OđR%,?8;"O',žō?ĢƧAſĴR
ż#,=<, đØAĢƧ($C 60,100 Ę)?>AŗµñÑ@ƨ.;Jġ´<!86(Í 3).

ž 3 NK kg@%*O 40 Ę MAD =ŵĘA|g:|g' MAD AuVncðAČÚ@LNŵĘAñÑ|g'Ö³.;"O.
ƹŗµñÑƮŅøĘŧ&MŵĘŧ(MAD)G<A|g0.25-26.7

0.5-23.6

1.0-20.3

3.0-15.1

5.0-12.6

1.00581.00371.00401.00141.0009 MAD @LNĪ×µłĂRċ©½Ÿ<!N, 1%§AØP=Ƃ?-POƴÒ<čūō@Ƹ"|g'ŌŇ.;%N, OLMAR ĺAƔƜºŎ@ƨ.;"O½ŸĂ'ŕ-P6.Ř?ŃĹ(MAD AuVncðAÚ(-AH@ƢĿRŲ(Ŝĭō@|c[R»O,=<ƔƜºŎRýMPO½ŸĂ'!O,='ŕ-P6
4R3 Wn_Z3FSD~rgUÍ 3 SP kg@%*OđĢƧ k=[20,40,80]ØA]cJÄI; 0.5A|gRĶƖ0O  ĘØB
AkgA|gAƸ-'ſĴ-P;"OG6ſĴAãƎ=.6   ØAkgJſĴ-P;"OƁ?ŗµñÑ@Ó:(ę ŻAªí@%*OÑŽ'ſĴ-P6,=<AĢƧ@%*OÑŽJſĴ-P;"O67.,Œ"ĢƧ(20 Ę)AſĴBŤõ'ă),ûĒŹ0OÿƁ'!O.
4R4 OLMAR s+95 OLMAR_random s29;   AJLPSAMQ

4人工知能学会
経営課題にAIを！ビジネスインフォマティクス研究会 (第7回)
JSAI Special Interest Group on Business Informatics (SIG-BI #7)< īƇ 1 > qrXucAīƇkgeil@%"; OLMAR ĺ%LD
OLMAR_random ĺ@LNƔƜ|g'ýMPO&RīƇ.6. »÷^clR 0.15%=.6]c<A SP %LD SP_mod Rŉ"6avy~azũħRÍ 4,5 @ŕ0.

Í 4 SP kg@%";,»÷^cl 0.3%< 40 ĘAŗµñÑŉ"6]cAũħ<!O. OLMAR ĺB, Vki[cRTWlqrXw.,ƑňŅB 170 řõ=?8;"O', OLMAR_random B»÷^clJ&&O6I, Vki[cRThqrXw.;"O.

ĳ@, kg SP @ſĴđRż86kg<!O
SP_mod Rŉ"6avy~azũħ(Í 5)<B,
Vki[cB 40 @Ƒň'ę.;"OA@, OLMAR ĺAƑňBÚ() Ż.;"O. 4.1 Š<JƚE6 Hurst ĎĔAñÑ', ñÑÉî¢Ã(H<0.5)&M, l~m¢Ã(H > 0.5)@×¶.6,=<,Ż0OĩöB-M@ Ż0O¢Ã'ùƲ.6½ŸĂ'!O. G6, |gAłĂ(Ú(-)AQ
1&?Ɲ"', ƑňĪ@ã.;ĎĔƨĔō?ùƲ
R$O6I, qrXuc@Ú(?×¶R$
O[10][11].
ÁįAīƇR, kg NK %LD NK_mod @LOũħRÍ 6,7 @ŕ0. KBN, OLMAR ĺB®ŉ.;"6łĂ'?)?O6I, Vki[cBLNÚ(?
|gRŕ.;"O@J&&QM1, ƑňĪB
1/10 řõ@G< Ż.;O. SP_mod %LD NK_modkgRŉ"6ÕÀB, OLMAR_random ĺ<B, »÷^cl@LOqrXucA 'ƂMPO',
Vki[cAµ(@ƛƫ.;"O,='ŔƊ<(6.

Í 4 AũħLN, OLMAR ĺB 18 òƧAkg@%";Vki[cAòñÑ|gB 13.4%<!OA@ã., OLMAR ĺB 34.5%=?8;"O. 67.,ĠÚmhW(MDD)B 49.5%&M 98.28ƹ@ČÚ.;%N, Ĝō@ƑňĪB 1/50  @?8;"O. ,P@LN, ƍĕ[2]<ƆƗ-P;"OƸ"mhWAÈƶ'¨ŔƊ-P6.

Í 6

NK_mod kg@%";, »÷^cl 0.3%< 110ĘAŗµñÑŉ"6]cAũħ<!O. NK kg@%";J, SP kg=Áį@, OLMAR ĺBVki[cRTWlqrXw.;"O', 4AëBä-".

Í 5 SP_mod kg@%";, »÷^cl 0.3%< 40 ĘAŗµñÑŉ"6]cAũħ<!O. OLMAR ĺB,V
ki[c'ę.;"O@J&&QM1 Ż.;"O.
OLMAR ĺAL#@, ĩA×µłĂAƠR®ŉ.6Ĉ
ĺ<B, Vki[cA×¶=ƨ?)¤ĂAH'qrXuc@ùƲ0O,='ĚM&@?86. L8;,
OLMAR ĺ@ƞ.6×µłĂRč9ĩöRƟĊ0OÿƁ'!O.

Í 7

NK_mod kg@%";, »÷^cl 0.3%< 110ĘAŗµñÑŉ"6]cAũħ<!O. NK_mod kg5

人工知能学会
経営課題にAIを！ビジネスインフォマティクス研究会 (第7回)
JSAI Special Interest Group on Business Informatics (SIG-BI #7)@%";J, SP_mod kg=Áį@, OLMAR ĺBĠJŻ.;%N, Vki[cRÚ()ThqrXw[}hu.;"O.

[ƽ] Li, Bin, and Steven CH Hoi. "On-line portfolio selection

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withmovingaveragereversion." arXiv

preprint

arXiv:1206.4626 (2012).
[ƾ] Li, Bin, et al. "Moving average reversion strategy foron-line portfolio selection." Artificial Intelligence 222(2015): 104-123.
[ƿ] Li, Bin, and Steven CH Hoi. "Online portfolio selection:A survey." ACM Computing Surveys (CSUR) 46.3 (2014):35.
[ǀ] Li, Bin, Doyen Sahoo, and Steven CH Hoi. "OLPS: atoolbox for on-line portfolio selection." Journal of
Machine Learning Research 17.35 (2016): 1-5.
[ǁ] Nyikosa, Favour M., Michael A. Osborne, and Stephen J.
Roberts. "Adaptive Bayesian Optimisation for Online
Portfolio Selection." Workshop on Bayesian Optimization
at NIPS. Vol. 2015. 2015.
[ǂ] Ha,Youngmin.

"Onlineportfolio

selection

withtransaction costs including market impact costs." Browser
Download This Paper (2016).
[ǃ] Gao, Li, and Weiguo Zhang. "Weighted Moving Average
Passive Aggressive Algorithm for Online Portfolio
Selection." Intelligent

Human-Machine

SystemsandCybernetics (IHMSC), 2013 5th International Conference
on. Vol. 1. IEEE, 2013.
[Ǆ] Lin, Xiao, et al. "Boosting Moving Average Reversion
Strategy for Online Portfolio Selection: A Meta-learning
Approach." International

Conferenceon

Database

Systems for Advanced Applications. Springer, Cham,2017.
[ǅ] Kroll, Yoram, Haim Levy, and Harry M. Markowitz.
"Meanvariance versus direct utility maximization." The
Journal of Finance 39.1 (1984): 47-61.
[ƽƼ]Rasheed, Bo Qian Khaled, and B. Qian. "Hurstexponent and financial market predictability." IASTED
conference on Financial Engineering and Applications(FEA 2004). 2004.
[ƽƽ]

Carbone, Anna, Giuliano Castelli, and H. Eugene

Stanley. "Time-dependent Hurst exponent in financial
time series." Physica A: Statistical Mechanics and its
Applications 344.1 (2004): 267-271.

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