PRE-ASYMPTOTIC MEASURE OF FAT

TAILEDNESSNassim Nicholas Taleb

Tandon School of Engineering, NYU

Speed of statistical inference (number of

summands) and diversification effects are same.

kappa and Portfolio “Risk”

!"#$%&'($)%!*+,%-.+/*/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 “large” but not asymptotic is not necessarily in

the perceived distributional class

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

0

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, “X large but not infinity” is even

more ambiguous.

• For a lognormal, “σ low is ambiguous”

??

;)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!