PORT VaR SeminarRobert CramptonSeries 1 02/27/2015

Agenda

• What is VaR• How is VaR computed on PORT<go>• Different VaR Methodologies used on PORT<go>• Analyzing VaR on PORT<go>• Settings• VaR Comparison• VaR Terminology

• Factor Breakdown• Monte Carlo/Historical VaR Simulation

• VaR on the Optimizer• Generating a VaR report

What is VaR• VaR measures the maximum dollar loss projected given inputs

for the time horizon and confidence level. • VaR can be measured on the portfolio, benchmark, or

active/difference portfolio.• Based on a distribution of returns, whether historical or

derived via a simulation, we can find the specified dollar value ranges.• PORT calculates VaR based on three different percentile ranges:

• “I am 95% confident that I can lose at most $VaR in a given horizon period”

95% 97.5% 99%

VaR Methodologies on PORT• Five types of VaR are provided on the PORT<go> system in

Bloomberg, each model utilizes the Bloomberg Multi-Factor Risk Model in order to keep VaR consistent with Tracking Error data• You can choose which Factor Model to use while calculating VaR

through your PORT settings

Parametric VaR

Historical 1y VaR

Historical 2y VaR

Historical 3y VaR

Monte Carlo VaR

Parametric VaR• Assumes factor returns and non-factor returns are normally

distributed • We first model each factor, and assume each of these has returns

are normally distributed.• We next look at our exposures to each of these factors. Each

factor will have different exposures calculations. • HINT!: To see the exposures to each of the factors, we can look in the

Tracking Error tab on PORT. The factors sub tab is going to show us our portfolios exposure to the said factor model.

• Using the selected factor model we can model a normal distribution of portfolio returns and a standard deviation value.• 95%: -1.645*SD• 97.5%: : 1.96*SD• 99%: 2.33*SD

Parametric VaR

• Simplest of all three of the methodologies.

• Underestimates VaR since returns are usuallyfat tailed

• Used for linear securitiessince we assume normaldistribution we are fully dependent on linearfactor model

Benefits / Drawbacks with Parametric VaR

Historical VaR• Historical VaR builds on Parametric VaR, as it does not assume a

normal distribution for all of the factor returns. • We build a distribution of factor returns based on the historical

performance of those factors. • Given historical factor returns and current portfolio exposures,

(again, seen on the Tracking Error tab) we can model the corresponding returns for all securities in a portfolio and aggregate these returns on the portfolio level.

• Given the aggregated portfolio returns we create a historical distribution of said returns and compute the desired percentile of the distribution for VaR

• PM’s currently have the choice to use 1-3 years of factor return history on PORT<go> for historical VaR.

• Thus, we allow for flexibility on how to construct the distribution of historical factor returns.

Monte Carlo VaR• Rather than using historical factor returns to predict future

portfolio movements, we are creating a forward looking distribution of returns by generating possible simulations• Due to the use of 10,000 different simulations used (compared to

1, 2, 3 years of daily history) Monte Carlo has a higher statistical accuracy than historical

• Bloomberg pulls simulations from a joint distribution of factor and non factor returns

• Bloomberg runs 10, 000 different simulations• We can find these on the VaR simulations subtab

VaR for Nonlinear Securities• Unlike parametric VaR, historical and monte carlo models allow

computation for non-linear securities since both models use actual simulations rather than assuming normal distribution

• Currently we use 3 pricing models to capture security non-linearity:• Delta/Gamma approximation

• Use delta/gamma and duration/convexity factors based on selected model• Full Valuation

• Used for securities with highly non-linear pricing• Use actual realized prices for each simulation• This is computationally demanding and cannot be realistically implemented for a

multi-asset risk system that updates daily. To expedite the computation while faithfully representing the risk profiles of nonlinear instruments, many methods have been developed such as stress matrix pricing below.

• SMP• The basic idea of stress matrix pricing (SMP) is to compute full valuation on a low

dimensional grid. The scenario P&L is then approximated by interpolating on the grid during simulation.

VaR Methodology

VaR-Main View

VaR-Main View – Customization

VaR-Settings

• Settings effect your Distribution and Factor Breakdown sub tabs

• Remember that your VaR value is effected by the risk model you have loaded

VaR-Main View

• VaR as a percent of Market Value• (135,666.75/4,547,135.50)*100=2.98%VaR %

• Measures the change in VaR if that security or grouping was removed from the portfolio

• This will sum to overall VaR

Component VaR

VaR-Main View

• Measures the percent contribution to the portfolios total VaR

• =component VaR/Total VaR 2359.28/49,193.3=4.8%

VaR % Contribution

• Ratio of Portfolio VaR to Benchmark VaR, a ratio of 2 would show that the loss of your portfolio is twice as large as that of the benchmark

• 49,193.3/176,852.1=.28VaR Ratio

VaR Comparison

VaR Comparison

• Based on your units, the impact on portfolio VaR given a 1% increase or $100 increase in the position of the security or group

• Ex: Given a portfolio VaR of 226666.95 and a position of 300,000 in FHR 3423 PB. My Marginal VaR is 1.76. When I increase my position to 300,100 my portfolio VaR becomes 226668.7=226666.95+1.76

Marginal VaR

• Measures your change in portfolio VaR if you completely remove your exposure to a security or grouping. Again this is based on your default units

• Ex: Given a portfolio VaR of 226666.95 and a position of 300,000 in FHR 3423 PB. My Partial VaR is -6,692.69. When I remove my position my portfolio VaR becomes 219974.26=226666.95-6692.69

Partial VaR

• Also known as “Expected Shortfall”, Measures the expected loss in the underlying currency of the portfolio when the confidence level is surpassed. Per market convention this is the average of P&L generated for the tail beyond the confidence interval

• The higher the confidence level, the higher the average of the tail and therefore the greater the conditional VaR

Conditional VaR

VaR Distribution

VaR Simulations

VaR Factor Breakdown

Optimizing Using VaR

My exposure to EUR 10Y

KRR is contributing

23.96% to my VaR

BEFORE I Decrease my

Exposure

Optimizing Using VaR

My Optimization

AFTER I Decrease my Exposure

Optimize Using VaR

Custom Reporting• ActionsCreate/Edit TemplatesVaR• Choose PDF or Excel• Choose the Subtabs you are interested in • Create charts based on Main View subtab

Custom Reporting

Custom Reporting

THANK YOU!