This project is a continuation of Problem Set I in computing increasingly refined
risk measures and evaluating their Out-Of-Sample performance. Let IS and OOS
be the In-Sample and Out-Of-Sample periods, respectively.
1. For the best IS specifications 1-3, 4-6 and 7-9 of Problem Set I produce OOS
1-period-ahead forecasts of the 5%, 1% and 0.1% VaRs using:
i. Extreme Value Theory
ii. Filtered Historical Simulations
iii. Filtered Weighted Historical Simulations
2. Produce OOS 1-period-ahead forecasts of the 5%, 1% and 0.1% VaRs using:
iv. Historical Simulations
v. Weighted Historical Simulations
3. Backtest your VaR forecasts i.-v. performing Unconditional Coverage Testing
and Independence Hypothesis Testing.
1. Produce OOS 20-, 60- and 120-periods-ahead forecasts of the 5%, 1% and
0.1% VaRs for i.-v. and the Gaussian case of Problem Set I.
2. Backtest the 20-, 60- and 120-periods-ahead VaR forecasts.
1. Produce OOS 1-period-ahead forecasts of the Expected Shortfall for i.-v.
2. Backtest the Expected Shortfall forecasts.
Once you have completed the empirical analysis prepare a technical report discussing and interpreting your findings. You should comment, among others, on:
• the performance of the various approaches to VaR
• the performance of the various approaches to Expected Shortfall
• the sensitivity of the two risk measures to the specification/modeling of the
Include Tables and Figures to either help better support your analysis or to use as
counter-examples. Do not include irrelevant material such as lines of code, etc.
You are to perform your investigations on the Fama-French returns of the portfolio
assigned to you in Problem Set I. The IS and OOS periods are those defined in
Problem Set I:
• IS: 20080102-20131231
• OOS: 20140102-20160129
This project counts toward 50% of the final mark. You are encouraged to have
discussion sessions among yourselves but you must submit individual reports. Submissions must be in pdf format and uploaded to Loop by midnight of May 18th.
Make sure you read and understand the referencing guidelines found at:
EF5123 Problem Set I
The goal is to compute increasingly refined Value-at-Risk measures and evaluate
their Out-Of-Sample performance. Let IS and OOS be the In-Sample and OutOf-Sample periods, respectively. Consider the location-scale representation of the
rt = µt + σt · zt with COV(zt, zt−j) = 0, ∀j 6= 0
Use the IS period data to estimate the following specifications:
1. µt = 0; σt 2 = σ2; zt ∼ N(0, 1)
2. µt = µ; σt 2 = σ2; zt ∼ N(0, 1)
3. µt : ARMA(p, q); σt 2 = σ2; zt ∼ N(0, 1)
4. µt = 0; σt 2 : RiskMetrics; zt ∼ N(0, 1)
5. µt = µ; σt 2 : RiskMetrics; zt ∼ N(0, 1)
6. µt : ARMA(p, q); σt 2 : RiskMetrics; zt ∼ N(0, 1)
7. µt = 0; σt 2 : GARCH∗(p, q); zt ∼ N(0, 1)
8. µt = µ; σt 2 : GARCH∗(p, q); zt ∼ N(0, 1)
9. µt : ARMA(p, q); σt 2 : GARCH∗(p, q); zt ∼ N(0, 1)GARCH∗ indicates the best IS specification amongst the asymmetric EGARCHand GJR-GARCH (Hint: rank the various models and their parametrizations usingInformation Criteria). For all the above specifications (1-9):1. Produce OOS 1-period-ahead forecasts of µt.2. Produce OOS 1-period-ahead forecasts of σt 2.3. Calculate OOS 1-period-ahead 5%, 1% and 0.1% VaRs.4. Backtest your VaR forecasts: test whether the observed number of VaR violations is statistically different from the promised 5%, 1% and 0.1%. Define:• N: number of OOS observations• N1: number of OOS VaR violations• π b = N1/N: observed fraction of violations• p: promised fraction of violationsThe Likelihood-Ratio-Test (LRT) for the Unconditional Coverage (UC) of theVaR should be performed using the following test statistic:LRTUC = 2 · N1 ln π b p + (N − N1) ln 1 1 − − π b p ∼ χ2 (1)EF5123 Problem Set IAnalysisDiscuss:• the performance of the various approaches to VaR• the performance of RiskMetrics vs GARCH: expected or unexpected?• the sensitivity of variance and VaR estimates and forecasts to the specification/modeling of the conditional meanDataYou are to perform your investigations on the returns of the assigned Fama-French25 portfolio. The data 25 Portfolios 5×5 Daily is posted on the course webpage. Make sure to read the data description contained in the file. Your IS andOOS periods are defined as follows:• IS: 20080102-20131231• OOS: 20140102-20160129Here you may find your assigned portfolio:Duaa Maad Small-LowAnthony Small-3Ang Small-HighTao 2-2Manasa 2-4Elisa 3-LowMichael 3-3Kanika 3-HighAmodu-Rufai Big-LowLin Big-3Yunjing Big-High