Risk Statistics - standard deviation σ = σ 2 1/2(3...

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Risk Statistics and Historical Data Statistics Let p i = probability of outcome i, where p i = 1. X i = outcome i of some variable X. Y i = outcome i of some variable Y. Projections Historical Data Set (sample, not the population) (1) Expected value (EV) n n n EV(X) = p i X i EV(X) = ( X i )/ n = ( 1/n )X i i=1 i=1 i=1 (2) Variance ( σ 2 ) n n σ X 2 = p i [ X i - EV(X) ] 2 s X 2 = { [ X i - EV(X) ] 2 }/ (n-1) i=1 i=1 standard deviation ( σ ) = ( σ 2 ) 1/2
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Unformatted text preview: standard deviation ( σ ) = ( σ 2 ) 1/2 (3) Covariance ( σ XY ) n n σ XY = ∑ p i [ X i- EV(X) ][ Y i- EV(Y) ] s XY = { ∑ [ X i- EV(X) ][ Y i- EV(Y) ] }/ (n-1) i=1 i=1 (4) Correlation ( ρ XY ) ρ XY = ρ YX for all i, j. ρ XY = σ XY ÷ [ σ X σ Y ] ρ XY = s XY ÷ [s X s Y ]-1 ≤ ρ YX ≤ 1 for all i, j....
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