FRM Zvi Wiener Following P. Jorion, Financial Risk Manager Handbook Financial Risk Management

FRM Chapter 11 Introduction to Market Risk Management Following P. Jorion 2001 Financial Risk Manager Handbook

Ch. 11, HandbookZvi Wiener slide 3 Old ways to measure risk notional amounts sensitivity measures (duration, Greeks) scenarios ALM, DFA assume linearity do not describe probability

Ch. 11, HandbookZvi Wiener slide Bonds duration 1952Markowitz mean-variance 1963Sharpe’s CAPM 1966Multiple risk-factors 1973Black-Scholes option pricing 1983RAROC, risk adjusted return 1986Limits on exposure by duration 1988Risk-weighted assets for banks; exposure limits by Greeks 1993VaR endorsed by G Risk Metrics 1997CreditMetrics, CreditRisk+

Ch. 11, HandbookZvi Wiener slide 5 How much can we lose? Everything correct, but useless answer. How much can we lose realistically?

Ch. 11, HandbookZvi Wiener slide 6 What is the current Risk? duration, convexity volatility delta, gamma, vega rating target zone Bonds Stocks Options Credit Forex Total?

Ch. 11, HandbookZvi Wiener slide 7 Standard Approach

Ch. 11, HandbookZvi Wiener slide 8 Modern Approach Financial Institution

Ch. 11, HandbookZvi Wiener slide 9 Definition VaR is defined as the predicted worst-case loss at a specific confidence level (e.g. 99%) over a certain period of time.

Ch. 11, HandbookZvi Wiener slide 10 Definition (Jorion) VaR is the maximum loss over a target horizon such that there is a low, prespecified probability that the actual loss will be larger.

Ch. 11, HandbookZvi Wiener slide 11 Profit/Loss VaR 1% VaR 1%

Ch. 11, HandbookZvi Wiener slide 12 Meaning of VaR A portfolio manager has a daily VaR equal $1M at 99% confidence level. This means that there is only one chance in 100 that a daily loss bigger than $1M occurs, 1% VaR under normal market conditions.

Ch. 11, HandbookZvi Wiener slide 13 Returns year 1% of worst cases

Ch. 11, HandbookZvi Wiener slide 14 Main Ideas A few well known risk factors Historical data + economic views Diversification effects Testability Easy to communicate

Ch. 11, HandbookZvi Wiener slide 15 History of VaR 80’s - major US banks - proprietary 93 G-30 recommendations 94 - RiskMetrics by J.P.Morgan 98 - Basel SEC, FSA, ISDA, pension funds, dealers Widely used and misused!

Ch. 11, HandbookZvi Wiener slide 16 FRM-99, Question 89 What is the correct interpretation of a $3 overnight VaR figure with 99% confidence level? A. expect to lose at most $3 in 1 out of next 100 days B. expect to lose at least $3 in 95 out of next 100 days C. expect to lose at least $3 in 1 out of next 100 days D. expect to lose at most $6 in 2 out of next 100 days

Ch. 11, HandbookZvi Wiener slide 17 FRM-99, Question 89 What is the correct interpretation of a $3 overnight VaR figure with 99% confidence level? A. expect to lose at most $3 in 1 out of next 100 days B. expect to lose at least $3 in 95 out of next 100 days C. expect to lose at least $3 in 1 out of next 100 days D. expect to lose at most $6 in 2 out of next 100 days

Ch. 11, HandbookZvi Wiener slide 18 VaR caveats VaR does not describe the worst loss VaR does not describe losses in the left tail VaR is measured with some error

Ch. 11, HandbookZvi Wiener slide 19 Other Measures of Risk The entire distribution The expected left tail loss The standard deviation The semi-standard deviation

Ch. 11, HandbookZvi Wiener slide 20 Profit/Loss Risk Measures

Ch. 11, HandbookZvi Wiener slide 21 Properties of Risk Measure Monotonicity (X R(Y)) Translation invariance R(X+k) = R(X)-k Homogeneity R(aX) = a R(X) (liquidity??) Subadditivity R(X+Y)  R(X) + R(Y) the last property is violated by VaR!

Ch. 11, HandbookZvi Wiener slide 22 No subadditivity of VaR Bond has a face value of $100,000, during the target period there is a probability of 0.75% that there will be a default (loss of $100,000). Note that VaR 99% = 0 in this case. What is VaR 99% of a position consisting of 2 independent bonds?

Ch. 11, HandbookZvi Wiener slide 23 FRM-98, Question 22 Consider arbitrary portfolios A and B and their combined portfolio C. Which of the following relationships always holds for VaRs of A, B, and C? A. VaR A + VaR B = VaR C B. VaR A + VaR B  VaR C C. VaR A + VaR B  VaR C D. None of the above

Ch. 11, HandbookZvi Wiener slide 24 FRM-98, Question 22 Consider arbitrary portfolios A and B and their combined portfolio C. Which of the following relationships always holds for VaRs of A, B, and C? A. VaR A + VaR B = VaR C B. VaR A + VaR B  VaR C C. VaR A + VaR B  VaR C D. None of the above

Ch. 11, HandbookZvi Wiener slide 25 Confidence level low confidence leads to an imprecise result. For example 99.99% and 10 business days will require history of 100*100*10 = 100,000 days in order to have only 1 point.

Ch. 11, HandbookZvi Wiener slide 26 Time horizon long time horizon can lead to an imprecise result. 1% - 10 days means that we will see such a loss approximately once in 100*10 = 3 years. 5% and 1 day horizon means once in a month. Various subportfolios may require various horizons.

Ch. 11, HandbookZvi Wiener slide 27 Time horizon When the distribution is stable one can translate VaR over different time periods. This formula is valid (in particular) for iid normally distributed returns.

Ch. 11, HandbookZvi Wiener slide 28 FRM-97, Question 7 To convert VaR from a one day holding period to a ten day holding period the VaR number is generally multiplied by: A B C D. 10

Ch. 11, HandbookZvi Wiener slide 29 FRM-97, Question 7 To convert VaR from a one day holding period to a ten day holding period the VaR number is generally multiplied by: A B C D. 10

Ch. 11, HandbookZvi Wiener slide 30 Basel Rules horizon of 10 business days 99% confidence interval an observation period of at least a year of historical data, updated once a quarter

Ch. 11, HandbookZvi Wiener slide 31 Basel Rules MRC Market Risk Charge = MRC SRC - specific risk charge, k  3.

Ch. 11, HandbookZvi Wiener slide 32 FRM-97, Question 16 Which of the following quantitative standards is NOT required by the Amendment to the Capital Accord to Incorporate Market Risk? A. Minimum holding period of 10 days B. 99% one-tailed confidence interval C. Minimum historical observations of two years D. Update the data sets at least quarterly

Ch. 11, HandbookZvi Wiener slide 33 VaR system Risk factors Historical data Model Distribution of risk factors VaR method Portfolio positions Mapping Exposures VaR

Ch. 11, HandbookZvi Wiener slide 34 FRM-97, Question 23 The standard VaR calculation for extension to multiple periods also assumes that positions are fixed. If risk management enforces loss limits, the true VaR will be: A. the same B. greater than calculated C. less then calculated D. unable to determine

Ch. 11, HandbookZvi Wiener slide 35 FRM-97, Question 23 The standard VaR calculation for extension to multiple periods also assumes that positions are fixed. If risk management enforces loss limits, the true VaR will be: A. the same B. greater than calculated C. less then calculated D. unable to determine

Ch. 11, HandbookZvi Wiener slide 36 FRM-97, Question 9 A trading desk has limits only in outright foreign exchange and outright interest rate risk. Which of the following products can not be traded within the current structure? A. Vanilla IR swaps, bonds and IR futures B. IR futures, vanilla and callable IR swaps C. Repos and bonds D. FX swaps, back-to-back exotic FX options

Ch. 11, HandbookZvi Wiener slide 37 FRM-97, Question 9 A trading desk has limits only in outright foreign exchange and outright interest rate risk. Which of the following products can not be traded within the current structure? A. Vanilla IR swaps, bonds and IR futures B. IR futures, vanilla and callable IR swaps C. Repos and bonds D. FX swaps, back-to-back exotic FX options No limits!

Ch. 11, HandbookZvi Wiener slide 38 Stress-testing scenario analysis stressing models, volatilities and correlations developing policy responses

Ch. 11, HandbookZvi Wiener slide 39 Scenario Analysis Moving key variables one at a time Using historical scenarios Creating prospective scenarios The goal is to identify areas of potential vulnerability.

Ch. 11, HandbookZvi Wiener slide 40 FRM-97, Question 4 The use of scenario analysis allows one to: A. assess the behavior of portfolios under large moves B. research market shocks which occurred in the past C. analyze the distribution of historical P&L D. perform effective back-testing

Ch. 11, HandbookZvi Wiener slide 41 FRM-98, Question 20 VaR measure should be supplemented by portfolio stress-testing because: A. VaR measures indicate that the minimum is VaR, they do not indicate the actual loss B. stress testing provides a precise maximum loss level C. VaR measures are correct only 95% of time D. stress testing scenarios incorporate reasonably probable events.

Ch. 11, HandbookZvi Wiener slide 42 FRM-00, Question 105 VaR analysis should be complemented by stress-testing because stress-testing: A. Provides a maximum loss in dollars. B. Summarizes the expected loss over a target horizon within a minimum confidence interval. C. Assesses the behavior of portfolio at a 99% confidence level. D. Identifies losses that go beyond the normal losses measured by VaR.