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by: Kwan

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# Managing Financial Risk Week II Notes BU.230.730.53.SP16

Marketplace > Johns Hopkins University > Finance > BU.230.730.53.SP16 > Managing Financial Risk Week II Notes
Kwan
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Excel & AR models
COURSE
Managing Financial Risk
PROF.
Nicola Fusari
TYPE
Class Notes
PAGES
10
WORDS
KARMA
25 ?

## Popular in Finance

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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