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Managing Financial Risk Week II Notes

by: Kwan

Managing Financial Risk Week II Notes BU.230.730.53.SP16

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About this Document

Excel & AR models
Managing Financial Risk
Nicola Fusari
Class Notes
25 ?




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This 10 page Class Notes was uploaded by Kwan on Wednesday March 30, 2016. The Class Notes belongs to BU.230.730.53.SP16 at Johns Hopkins University taught by Nicola Fusari in Spring 2016. Since its upload, it has received 48 views. For similar materials see Managing Financial Risk in Finance at Johns Hopkins University.


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Date Created: 03/30/16
Risk%II Wednesday,+March+30,+2016 13:32 1.#Joint#Probability#Distribution 3"dimension:+1/36 E(Z)=2*1/36+3*2/36…=7 "+">+UNCONDITIONAL+EXPECTATION CONDITIONAL+ Random+variables:+E(Z|X)=f(X) Linear+relation""properties+2 E(Y|X)+=E(a+bX+ε+|X)=a+bX Y=a+bx +ε,+z=xY=a+bx +ε,+ "">+change+to+be+linear ˆa,ˆb+:+random+variable ε:+N(0,1) Changing+(if+X=0,+0.5,+1,+1.5…,+a=3,+b=2+fixed,+get+y+"">+regressionˆ+a,ˆb) a,+b:+like+normal If+x+known,+better+y+(b+is+not+0):+E(Y|X)=a+++bX+vs.+E(Y) Std+is+small Var(ei)=E(e2) "E(ei)2=1/NˆE2i+ Audio 1 Audio+recording+started:+14:15+Wednesday,+March+30,+2016 Ho:+b=0 ^t:+(^b"0)/st(^b)~N(0,1) 1st+graph:+usually+only+on+textbook Audio+recording+started:+14:15+Wednesday,+March+30,+2016 Ho:+b=0 ^t:+(^b"0)/st(^b)~N(0,1) 1st+graph:+usually+only+on+textbook Move+functions+back+and+forth,+e+of+2nd+graph:+the+linear+model 4th+graph:+bad 2.#Excel Data+" data+analysis+" regression Eg.+Linear+regression.xlsx L|NEST+""array+function+(frequency+function) 1) Select+a+region:+5+rows+*N+columns(parameters) 2) =Linest(C:17C26,+B17:B26,+true,+true)+[y,+x,+constant?,+all+wanted?];+Control+++shift+++enter: ^b;+^a Std(^b);+std(^a) R … 3) ^b/Std(^b):+reject+if+outside"[,2] 3.#AR#models Univariate+Modeling Historical+data+">+model"">+forcast+future+data Correlation:+history+&+future Autocorrelation:+only+one+variable ACF:+(a+shape:+ρτ ) R1 R2 R3 … … RN "">+AR+(Aatoregression) μ+=φ 0(1"φ 1 If+φ =0,+fluctuating+around+0 0 If+φ0=0+[to+simplify] 2 E(R t+2|R t) =+φ R1 t+1++ε t+2=+φ 1 *R t Too+far+in+the+future+ "">+0+(0.9^2000) If+φ0=0+[to+simplify] E(R t+2|R t) =+φ R t+1++ε t+2=+φ 2*R t 1 1 Too+far+in+the+future+ "">+0+(0.9^2000) E(Rt*Rt+τ+): Φ 1:+the+red+curve+(mostly) Φ 1"0.5: If+φ0=0+[to+simplify] E(R t+2|R t) =+φ R t+1++ε t+2=+φ 2*R t 1 1 Too+far+in+the+future+ "">+0+(0.9^2000) E(Rt*Rt+τ+): Φ 1:+the+red+curve+(mostly) Φ 1"0.5: Φ 1"0.5: ARMA=AR+++Moving+average 4.Maximum#Likelihood Max+f(3):+one+point Φ 1"0.5: ARMA=AR+++Moving+average 4.Maximum#Likelihood Max+f(3):+one+point Many+points: Initial+guess+(3,2) =NORM.DIST(A4,3,2,0)… Solver:+product+of+max+changing+mean+&+std Max+f(x)[product:+too+small]=max+ln(f(x)+[the+sum+of+logs] Or+use:++=average: If+εt+1+∼ N+(0,+σε)+known,+rewre+εt+1+and+max+f(εt+1)+ AR(1) AR(2) … AR(P) How+to+choose+P?+from+simple+to+complicated+(if+AR(1)+cannot+reject+0,+AR(2);+if+can+reject,+the+ previous+one…)+[PACF:+partial+auto+correlation+function] st+=+st−1+++εt+ IfΦ 1+1.1,+expect+price+goes+up+in+the+future:+buy+now+until+ Φ 11+(market+is+efficient) IfΦ = 0.9… 1+ Empirical:+PPT+"60+[Lec+2+"solutions] 1.=0:+positiv IfΦ 1+0.9… Empirical:+PPT+"60+[Lec+2+"solutions] 1.=0:+positiv e+or+negative+(No) 2.OLS=max 3.Ret :+big+or+small+(Yes) 4.PPT"46+(run+N+times),+all+different+from+0 As+all+past+data+have+some+help "">+volatility =indirect


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