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