PRE-ASYMPTOTIC MEASURE OF FAT TAILEDNESS Nassim Nicholas Taleb - - PowerPoint PPT Presentation

PRE-ASYMPTOTIC MEASURE OF FAT TAILEDNESS

Nassim Nicholas Taleb Tandon School of Engineering, NYU

Speed of statistical inference (number of summands) and diversification effects are same.

kappa and Portfolio ÒRiskÓ

!"#$%&'($)%!*+,%-.+/*/0/" 1234235

6"#+0("+%'7%8#/%9#*$")."++

!"#$

: ;<;=>!?9>;%@A>BB%C8*.*/"%6'D"./+EF%%G0(/'+*+ : =>!?9>;%@A>BBF%9#*$%"HI'."./

%&'()F%

: J-;-2K'.K"./(#/*'.%D"#+0("+ : L0#./*$"%K'./(*M0/*'. : </N"(

Preasymptotics for Summands

There is no such thing as infinite summands in the real world n ÒlargeÓ but not asymptotic is not necessarily in the perceived distributional class

!"#$%&'()'*)+,-+)!"#$%"&.#")/&-&.)

B/#M$"%O*+/ ?P0*Q

1"2"($/&3"4) 5"2.($/)6&-&.

77

8#9):;<)2'.)=><

7?

: 8")$(")&2."("+."4)&2)@/$++)'*)*&2&.")-"$2)2'.) 2"@"++$(&/9)*&2&.")%$(&$2@"A : :;<)-'(")B2$.,($/C : :;<)-'(")B"**&@&"2.C)"D@"E.)*'()2'2)1$,++&$2 : :;<)'2/9)B"**&@&"2.C)$+9-E.'.&@$//9 #"2@")2'.)*'()!"#"$% B+-$//C)!

='-")F&+.'(9)'*)=><

: ;2'.#"()G$9).') B-"$+,("C)H'.#) 56> I)+E""4)'*) 66J

K"+,/.+

=('M$"D+%*.%$*/"(#/0("

: 9".)".KR%/'%/("#/%#$$%/#*$%"HI'."./+%ST%#+%J#0++*#.

: ;)/'L2'(-$/)G&.#)#&L#))M)+.$9+)/'L2'(-$/),24"() +,--$.&'2 : ;)/'L2'(-$/)G&.#)/'G))M)H"#$%"+)/&N")2'(-$/

?O

6'L2'(-$/)!',24+

Infinity Shminfinity

¥ For a Lognormal, ÒX large but not infinityÓ is even

more ambiguous.

¥ For a lognormal, Ò! low is ambiguousÓ

??

;)2&@")"P,$/&.9

5,-,/$2.+

: =&-E/9Q)+&2@") "#$#%&!'()*+,-+).)/!)(#$$&!,(0)1)!)2#$#%&!'()*+,-+).)/304 : 8")-$.@#)@,-,/$2.+)'*)R"$(+'2).').#'+")'*)2S+,--"4)6'L2'(-$/ : R$($-".(&3$.&'2)4"."(-&2"+).#")R"$(+'2)B@/$++C)T#"(")R"$(+'2)UVW

X&2$/-"2."

?Y

5,H&@)$/E#$

Z-E&(&@$/)[$EE$)=RYOO

!"#$%&' ()*)$ +",&$)-" ."$/ 012)$)-" &#3 +",&$)-" ."$/ 4 544 644 744 844 944 :44 ! 5/;9 5/<4 5/<9 5/=4 5/=9 6/44 !