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by: Kwan

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

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Kwan
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VaR & ES
COURSE
Managing Financial Risk
PROF.
Nicola Fusari
TYPE
Class Notes
PAGES
5
WORDS
KARMA
25 ?

## Popular in Finance

This 5 page Class Notes was uploaded by Kwan on Wednesday April 13, 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 44 views. For similar materials see Managing Financial Risk in Finance at Johns Hopkins University.

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Date Created: 04/13/16
Risk  IV Wednesday,  April  13,  2016 13:35 •1.  Review  of  the  Homework:  discussion   Data  from  Oxford:  Date,  RV,  Return Q1: 1-­‐month  MOVING  AVERAGE:  R^2;  Average(21  days)*252 1-­‐year  MA RISKMATRIX 2   2 2 Lambda:  ???? 2 =  ƛ*????1+(1-­‐ƛ)*R 1 ???? 1   1) R 12 2) RV 1 3) VAR(R) i GARCH ???? 2  w+????*R +????*????12 12 ML: R t  N(0, t???? ) Log  likelihood:   -­‐0.5*(ln(???? )+R /???? ) 2 1 1 1 Sum  to  max-  -­‐ solver  (non-­‐negatives;  optional  constrain????:  +  ????<1)  [initial  guess:   omega=0.0001,  alpha=0.05,  beta=0.9] 2 Check:  Unconditional  VAR:   ???? =w/(1-­‐????-­‐????)  as  daily-­‐-­‐>  sqrt(252*w/(1-­‐????-­‐????)  )  -­‐-­‐>   similar  to  16% Daily  std=0.01;  Daily  variance=0.0001;  Annual  volatility  =sqrt(0.0001*252)= 16%  (from  data) Two  methods:   1. ^w,  ^????,  ^???? 2. Variance  targeting:  Var(R)=???? , i ^???? &  ^????,  w=???? *  (1-­‐????-­‐????)   HAR RV t+1=a+b *R1 +b *Rt_W+2 *RV_M:   3 OLS:  =linest 1. ^w,  ^????,  ^???? 2. Variance  targeting:  Var(R)=???? , i ^???? &  ^????,  w=???? *  (1-­‐????-­‐????)   HAR RV =t+1 *RV +b1*RV_W+t *R2_M:   3 OLS:  =linest RV_W:  5th  =average RV_M:  21th  =average Q2: ???? 2=RV =a  +  b*????+ℇ t+1 t+1 a=0,  b=1 OLS  of  the  models:  better  models  (>  >  >) Q3: Correlation:  (Price_SP500,  sqrt(RV))  =>  strong  correlated  [longer  interval,  noise   more;  if  5  min  RV,  -­‐-­‐>  -­‐0.9] DateID  -­‐-­‐>  Date:  left,  mid,  right VLOOKUP(A:A,  M:N,  2) P t  ­‐> t  ???? : 1. Corporate  Finance:  A =D + t  Et   t dot   -­‐-­‐> tE =#*P t    -­‐-­‐>  leveragt up  -­‐-­‐>  riskier  -­‐-­‐>  volttility  up  (???? ) 2. Investment:  volatility  up-­‐-­‐>  riskier  -­‐-­‐>  Expected  Return  up  (be   compensated)   -­‐-­‐> t  own   Q4:  use  google  -­‐-­‐ NB.  NASDAQ Log-­‐Ret Log-­‐Ret^2 RV=sum*252 Annual  volatility  =  sqrt  =  70%  [daily:  simple,  intuitive] Assumptions: ????=1 zt   N(0,1) • 2.  Value  at  Risk p:  0.01  (1%);  0.05  (5%) K:  1,  5,  10 V PF  Value  of  portfolio VaR:  a  positive  number   p:  0.01  (1%);  0.05  (5%) K:  1,  5,  10 V PF  Value  of  portfolio VaR:  a  positive  number   Shortcomings:  VaR-­‐  -­‐ the  best  of  the  p  percent,  but  what  about  the   average/the  other  figures? How  to  compute  VaR: 1) Nonparametric:  no  assumptions  (simple) History  repeats  itself. • Historical  Simulation Graph:  to  the  left,  the  best  of  p =percentile(vector,  p) =small(vector,  1),  as  N=100  &    p=0.05  -­‐-­‐>  =small(vector,  5) Eg.  SP500:  Log  returns  &  flip  (change  the  sign)   -­‐-­‐>  the  orange  line Banks/FED  to  report:  conflict  of  interest,  risk  vs.  cash  (FED  up;  banks   down) Orange  line  follows  the  green  line:  1%  not HS  1000:  Risk  -­‐-­‐>  the  same  (bad) -­‐-­‐>  4  limitations:   How  to  choose  the  windows:  250  days/1000  days? Assigning  the  same  possibility:  forward -   different  weights? Negative,  but  what  about  positive  expectations? ????>1: 252:  t,  t+1;  t,  t+2:  126;  t,  t+10:  25 • Weighted  Historical  Simulation Solve  1&2  limitations w  -­‐-­‐>  η: Sum  of  the  weights  =  1 Decreasing  from  now  to  past Pros  &  Cons 2) Parametric:   Three  Assumptions:   R t+1*z t+1 t+1 z t+1   N  (0,1) t  -­‐-t+1 (model  for  volatility) 2) Parametric:   Three  Assumptions:   R t+1*z t+1 t+1 z t+1   N  (0,1) t  -­‐-t+1 (model  for  volatility) ɸ (p)=NORMINV(P) ɸ(p):  Cumulative  probability  distribution ɸ (0.05)=-­‐1.64 ɸ (0.01)=-­‐2.33 If t R ~  N(0,t+1 ???? ), t+1R=  -t+1 *  ɸ (p) 2   2 2 ???? &  risk  &  return:t+1 ????=  ƛ*????t+(1-­‐ƛ)*R t Shortcomings  of  VaR: Big  losses;  aggregate •  3.  Expected  Shortfall ES  >  VaR Compute  VaR  first: • Nonparametric  approach  :  …&  =average • Parametric  approach:  …&  E(z|z<a): φ(−1.65)  :  density  function  =0.1  or  1/sqrt(2*pi)  * ((-­‐1.65/2)^2) Aggregation:  eg.  whether  to  put  B  in  the  portfolio •  4.  Excel  hands  on Norminv:  (lec  1) 0  density 1  cumulative Eg.  Lesson  4_solution.xlsx NEXT  CLASS:  long…  ( ????>1)…

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