Value-at-Risk (VaR)

Value-at-Risk (VaR)

Active Risk Management Framework Jul-00 Bank of Israel Foreign Currency Dept. Major risks managed by the department Measurable Hardly Measurable currency risk operational risk

interest rate risk liquidity risk some credit risk some credit risk Zvi Wiener Bank of Israel slide 2 Currently used methods

benchmark as a starting point limits on position limits on counterparty other limits Zvi Wiener Bank of Israel slide 3 Proposed Scheme Three layers: 1. Global (yearly) stop loss

2. Dynamic VaR bounds 3. Limits to non-measurable risk components (credit, liquidity, etc.) Zvi Wiener Bank of Israel slide 4 Global (yearly) stop loss In order to avoid a big loss we should introduce a global stop loss (like 30-40bp). As soon as the portfolio approaches the stop loss, we should decrease VaR limits for each desk, so that they become zero as soon as the stop loss is reached. Zvi Wiener Bank of Israel slide 5 Dynamic VaR bounds

Each desk will receive its weekly VaR that can be used for risk taking (like 3-5 bp initially). This VaR can be used by each desk (or temporarily borrowed from another desk). If at some time moment VaR limit is exceeded, the manager must return to the permitted VaR during one day (or get a special permission). See example below. Zvi Wiener Bank of Israel slide 6 Reporting and responsibility Zvi Wiener investment committee

desk managers risk manager Bank of Israel slide 7 Investment committee is responsible for setting the yearly stop loss limit setting VaR limits for each desk weekly supervising the desk managers

(but not interfering their decisions too much) supervising stress test results (?) Zvi Wiener Bank of Israel slide 8 Desk manager is responsible for keeping the risk under his VaR limit returning to the limit if exceeded reporting to the investment committee on his current VaR and its components

cases of overexposure and how it was handled reasons for the current exposure (?) Zvi Wiener Bank of Israel slide 9 Risk manager is responsible for supporting and developing the VaR program measuring and reporting VaR of the whole portfolio communicating to desk managers and investment committee on diversification among desks

backtesting, stress test Zvi Wiener Bank of Israel slide 10 VaR and stop-loss take-profits VaR can NOT replace the technique of setting stop loss and take profit limits. However VaR can answer the following questions: what is the current probability that the stop loss (take profit) order will be met during some time interval, or to give the probability distribution over a specified time horizon. Setting stop loss orders can reduce VaR. Zvi Wiener Bank of Israel slide 11

VaR and stop-loss take-profits 1 day 1 week P&L Zvi Wiener Bank of Israel slide 12 Advantages This language of risk is used worldwide Uniformity of different risks

More freedom to desk managers in risk allocation More transparency on current risks and potential losses Cross time and cross asset comparison Zvi Wiener Bank of Israel slide 13 Example (Tal, Zvi) Assume that the short dollar benchmark has neutral duration of T=6 months. Manager has VaR limit of 3 bp. and he has to make two decisions: a % of assets kept in spread products q duration mismatch

we assume that all instruments (both treasuries and spread) have the same duration T+q months. Zvi Wiener Bank of Israel slide 14 Contour Levels of VaR (static) 6 4 2 q - duration 0 mismatch -2 -4 -6 0

0.2 0.4 0.6 0.8 1 a (% of spread) Zvi Wiener Bank of Israel slide 15 6 VaR=3 bp 4 2

q - duration mismatch 0 position -2 VaR=2 bp -4 -6 0 0.2 0.4 0.6 0.8

1 a (% of spread) Zvi Wiener Bank of Israel slide 16 6 In order to reduce risk one can increase duration (in this case). 4 2 0 -2

-4 -6 0 q - duration mismatch Zvi Wiener 0.2 0.4 0.6 0.8 1 a (% of spread) Bank of Israel slide 17

What we can do using limits 6 4 2 0 -2 -4 VaR = 6 bp -6 0 Zvi Wiener 0.2 0.4

0.6 Bank of Israel 0.8 1 slide 18 duration mismatch (yr) Current position 2M, 10% spread 5% weekly VaR=2.2 bp 0.2 0.1 0 -0.1 weekly VaR limit 3 bp

-0.2 spread % 0 Zvi Wiener 0.2 0.4 0.6 Bank of Israel 0.8 1 slide 19 What should be done

a simple VaR measuring tool at trading desks professional software (RMG or other) reporting in terms of VaR to get used to this new language to build a historical data set backtest stress test library Zvi Wiener

Bank of Israel slide 20 Proposed Scheme Three layers: 1. Global (yearly) stop loss (30-40 bp.) 2. Dynamic VaR bounds (initially 3-5 bp.) 3. Old limits to non-measurable components (credit, liquidity, etc.) Zvi Wiener Bank of Israel slide 21

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