MRM FRM-GARP Oct-2001 Zvi Wiener 02-588-3049 Market Risk Management.

MRM FRM-GARP Oct-2001 Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Market Risk Management

MRM FRM-GARP Oct-2001 Introduction to Market Risk Measurement Following Jorion 2001, Chapter 11 Financial Risk Manager Handbook

http://www.tfii.orgZvi Wiener - MRM slide 3 Old ways to measure risk notional amounts sensitivity measures (duration, Greeks) scenarios ALM, DFA assume linearity do not describe probability

http://www.tfii.orgZvi Wiener - MRM slide 4 1938Bonds 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-30 1994Risk Metrics 1997CreditMetrics, CreditRisk+

http://www.tfii.orgZvi Wiener - MRM slide 5 How much can we lose? Everything correct, but useless answer. How much can we lose realistically?

http://www.tfii.orgZvi Wiener - MRM slide 6 What is the current Risk? duration, convexity volatility delta, gamma, vega rating target zone Bonds Stocks Options Credit Forex Total?

http://www.tfii.orgZvi Wiener - MRM slide 7 Standard Approach

http://www.tfii.orgZvi Wiener - MRM slide 8 Modern Approach Financial Institution

http://www.tfii.orgZvi Wiener - MRM 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.

http://www.tfii.orgZvi Wiener - MRM 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.

http://www.tfii.orgZvi Wiener - MRM slide 11 Profit/Loss VaR 1% VaR 1%

http://www.tfii.orgZvi Wiener - MRM 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.

http://www.tfii.orgZvi Wiener - MRM slide 13 Returns year 1% of worst cases

http://www.tfii.orgZvi Wiener - MRM slide 14 Main Ideas A few well known risk factors Historical data + economic views Diversification effects Testability Easy to communicate

http://www.tfii.orgZvi Wiener - MRM 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!

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM slide 19 Other Measures of Risk The entire distribution The expected left tail loss The standard deviation The semi-standard deviation

http://www.tfii.orgZvi Wiener - MRM slide 20 Profit/Loss Risk Measures

http://www.tfii.orgZvi Wiener - MRM 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!

http://www.tfii.orgZvi Wiener - MRM 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?

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM 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.

http://www.tfii.orgZvi Wiener - MRM 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.

http://www.tfii.orgZvi Wiener - MRM 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.

http://www.tfii.orgZvi Wiener - MRM 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. 2.33 B. 3.16 C. 7.25 D. 10

http://www.tfii.orgZvi Wiener - MRM 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. 2.33 B. 3.16 C. 7.25 D. 10

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM slide 31 Basel Rules MRC Market Risk Charge = MRC SRC - specific risk charge, k  3.

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM slide 33 VaR system Risk factors Historical data Model Distribution of risk factors VaR method Portfolio positions Mapping Exposures VaR

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM 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!

http://www.tfii.orgZvi Wiener - MRM slide 38 Stress-testing scenario analysis stressing models, volatilities and correlations developing policy responses

http://www.tfii.orgZvi Wiener - MRM 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.

http://www.tfii.orgZvi Wiener - MRM 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

http://www.tfii.orgZvi Wiener - MRM 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.

http://www.tfii.orgZvi Wiener - MRM 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.

MRM FRM-GARP Oct-2001 Identification of Risk Factors Following Jorion 2001, Chapter 12 Financial Risk Manager Handbook

http://www.tfii.orgZvi Wiener - MRM slide 44 Absolute and Relative Risk Absolute risk - measured in dollar terms Relative risk - measured relative to benchmark index and is often called tracking error.

http://www.tfii.orgZvi Wiener - MRM slide 45 Directional Risk Directional risk involves exposures to the direction of movements in major market variables. beta for exposure to stock market duration for IR exposure delta for exposure of options to undelying

http://www.tfii.orgZvi Wiener - MRM slide 46 Non-directional Risk Non-linear exposures, volatility exposures, etc. residual risk in equity portfolios convexity in interest rates gamma - second order effects in options vega or volatility risk in options

http://www.tfii.orgZvi Wiener - MRM slide 47 Market versus Credit Risk Market risk is related to changes in prices, rates, etc. Credit risk is related to defaults. Many assets have both types - bonds, swaps, options.

http://www.tfii.orgZvi Wiener - MRM slide 48 Risk Interaction You buy 1M GBP at 1.5 $/GBP, settlement in two days. We will deliver $1.5M in exchange for 1M GBP. Market risk Credit risk Settlement risk (Herstatt risk) Operational risk

http://www.tfii.orgZvi Wiener - MRM slide 49 Exposure and Uncertainty Losses can occur due to a combination of A. exposure (choice variable) B. movement of risk factor (external variable) Dollar duration

http://www.tfii.orgZvi Wiener - MRM slide 50 Exposure and Uncertainty Market loss = Exposure * Adverse movement in risk factor

http://www.tfii.orgZvi Wiener - MRM slide 51 Specific Risk Market exposureSpecific risk Specific risk - risk due to issuer specific price movements

http://www.tfii.orgZvi Wiener - MRM slide 52 FRM-97, Question 16 The risk of a stock or bond which is NOT correlated with the market (and thus can be diversified) is known as: A. interest rate risk. B. FX risk. C. model risk. D. specific risk.

http://www.tfii.orgZvi Wiener - MRM slide 53 Continuous process - diffusion Discontinuities Jumps in prices, interest rates Price impact and liquidity market closure discontinuity in payoff: binary options loans

http://www.tfii.orgZvi Wiener - MRM slide 54 Emerging Markets Emerging stock market - definition by IFC (1981) International Finance Corporation. Stock markets located in developing countries (countries with GDP per capita less than $8,625 in 1993).

http://www.tfii.orgZvi Wiener - MRM slide 55 Liquidity Risk Difficult to measure. Very unstable. Market depth can be used as an approximation. Liquidity risk consists of both asset liquidity and funding liquidity!

http://www.tfii.orgZvi Wiener - MRM slide 56 Funding Liquidity Risk of not meeting payment obligations. Cash flow risk! Liquidity needs can be met by using cash selling assets borrowing

http://www.tfii.orgZvi Wiener - MRM slide 57 Highly liquid assets tightness - difference between quoted mid market price and transaction price. depth - volume of trade that does not affect prices. resiliency - speed at which price fluctuations disappear.

http://www.tfii.orgZvi Wiener - MRM slide 58 Flight to quality Shift in demand from low grade towards high grade securities. Low grade market becomes illiquid with depressed prices. Spread between government and corporate issues increases.

http://www.tfii.orgZvi Wiener - MRM slide 59 On-the-run recently issued most active very liquid after a new issue appears they become off- the-run liquidity premium can be compensated by repos/reverse repos

http://www.tfii.orgZvi Wiener - MRM slide 60 FRM-98, Question 7 Which of the following products has the least liquidity? A. US on-the-run Treasuries B. US off-the-run Treasuries C. Floating rate notes D. High grade corporate bonds

http://www.tfii.orgZvi Wiener - MRM slide 61 FRM-98, Question 7 Which of the following products has the least liquidity? A. US on-the-run Treasuries B. US off-the-run Treasuries C. Floating rate notes D. High grade corporate bonds

http://www.tfii.orgZvi Wiener - MRM slide 62 FRM-97, Question 54 “Illiquid” describes an instrument which A. does not trade in an active market B. does not trade on any exchange C. can not be easily hedged D. is an over-the-counter (OTC) product

http://www.tfii.orgZvi Wiener - MRM slide 63 FRM-97, Question 54 “Illiquid” describes an instrument which A. does not trade in an active market B. does not trade on any exchange C. can not be easily hedged D. is an over-the-counter (OTC) product

http://www.tfii.orgZvi Wiener - MRM slide 64 FRM-98, Question 6 A finance company is interested in managing its balance sheet liquidity risk. The most productive means of accomplishing this is by: A. purchasing market securities B. hedging the exposure with Eurodollar futures C. diversifying its sources of funding D. setting up a reserve

http://www.tfii.orgZvi Wiener - MRM slide 65 FRM-98, Question 6 A finance company is interested in managing its balance sheet liquidity risk. The most productive means of accomplishing this is by: A. purchasing market securities B. hedging the exposure with Eurodollar futures C. diversifying its sources of funding D. setting up a reserve

http://www.tfii.orgZvi Wiener - MRM slide 66 FRM-00, Question 74 In a market crash the following is usually true? I. Fixed income portfolios hedged with short Treasuries and futures lose less than those hedged with IR swaps given equivalent duration. II. Bid offer spreads widen due to less liquidity. III. The spreads between off the run bonds and benchmark issues widen. A. I, II & IIIC. I & III B. II & IIID. None of the above

http://www.tfii.orgZvi Wiener - MRM slide 67 FRM-00, Question 74 In a market crash the following is usually true? I. Fixed income portfolios hedged with short Treasuries and futures lose less than those hedged with IR swaps given equivalent duration. II. Bid offer spreads widen due to less liquidity. III. The spreads between off the run bonds and benchmark issues widen. A. I, II & IIIC. I & III B. II & IIID. None of the above

MRM FRM-GARP Oct-2001 Sources of Risk Following Jorion 2001, Chapter 13 Financial Risk Manager Handbook

http://www.tfii.orgZvi Wiener - MRM slide 69 Currency Risk free movements of currency devaluation of a fixed or pegged currency regime change (Israel, Europe)

http://www.tfii.orgZvi Wiener - MRM slide 70 Currency Volatility End 99End 96 Argentina0.350.4 Australia7.68.5 Canada5.13.6 Switzerland1010 Denmark9.87.8 Britain6.59.1 Hong Kong0.30.3 Indonesia241.6 Japan116.6 Korea6.94.5

http://www.tfii.orgZvi Wiener - MRM slide 71 Currency Volatility End 99End 96 Mexico7.57 Malaysia0.11.6 Norway7.67.6 New Zealand13.47.9 Philippines5.50.6 Sweden8.56.4 Singapore3.81.8 Thailand9.71.2 Taiwan1.80.9 Euro9.88.3 S. Africa4.28.4

http://www.tfii.orgZvi Wiener - MRM slide 72 FRM-97, Question 10 Which currency pair would you expect to have the lowest volatility? A. USD/DEM B. USD/CAD C. USD/JPY D. USD/ITL

http://www.tfii.orgZvi Wiener - MRM slide 73 FRM-97, Question 10 Which currency pair would you expect to have the lowest volatility? A. USD/DEM B. USD/CAD C. USD/JPY D. USD/ITL

http://www.tfii.orgZvi Wiener - MRM slide 74 FRM-97, Question 14 What is the implied correlation between JPY/DEM and DEM/USD when given the following volatilities for foreign exchange rates? JPY/USD 8%, JPY/DEM 10%, DEM/USD 6% A. 60% B. 30% C. -30% D. -60%

http://www.tfii.orgZvi Wiener - MRM slide 75 Cross Rate volatility JPY/USD = xJPY/DEM = yDEM/USD = z

http://www.tfii.orgZvi Wiener - MRM slide 76 Fixed Income Risk Arises from potential movements in the level and volatility of bond yields. Factors affecting yields inflationary expectations term spread higher volatility of the low end of TS

http://www.tfii.orgZvi Wiener - MRM slide 77 Volatilities of IR/bond prices Price volatility in %End 99End 96 Euro 30d0.220.05 Euro 180d0.300.19 Euro 360d0.520.58 Swap 2Y1.571.57 Swap 5Y4.234.70 Swap 10Y8.479.82 Zero 2Y1.551.64 Zero 5Y4.074.67 Zero 10Y7.769.31 Zero 30Y20.7523.53

http://www.tfii.orgZvi Wiener - MRM slide 78 Duration approximation What duration makes bond as volatile as FX? What duration makes bond as volatile as stocks? A 10 year bond has yearly price volatility of 8% which is similar to major FX. 30-year bonds have volatility similar to equities (20%).

http://www.tfii.orgZvi Wiener - MRM slide 79 Models of IR Normal model  (  y) is normally distributed. Lognormal model  (  y/y) is normally distributed. Note that:

http://www.tfii.orgZvi Wiener - MRM slide 80 Time adjustment Square root of time adjustment is more questionable for bond prices than for other assets there is a strong evidence of mean reversion bond prices converge approaching maturity (bridge effect) - strong for short bonds, weak for long.

http://www.tfii.orgZvi Wiener - MRM slide 81 Volatilities of yields Yield volatility in %, 99  (  y/y)  (  y) Euro 30d452.5 Euro 180d100.62 Euro 360d90.57 Swap 2Y12.50.86 Swap 5Y130.92 Swap 10Y12.50.91 Zero 2Y13.40.84 Zero 5Y13.90.89 Zero 10Y13.10.85 Zero 30Y11.30.74

http://www.tfii.orgZvi Wiener - MRM slide 82 FRM-99, Question 86 For computing the market risk of a US T-bond portfolio it is easiest to measure: A. yield volatility, because yields have positive skewness. B. price volatility, because bond prices are positively correlated. C. yield volatility for bonds sold at a discount and price volatility for bonds sold at a premium. D. yield volatility because it remains more constant over time than price volatility, which must approach zero at maturity.

http://www.tfii.orgZvi Wiener - MRM slide 83 FRM-99, Question 86 For computing the market risk of a US T-bond portfolio it is easiest to measure: A. yield volatility, because yields have positive skewness. B. price volatility, because bond prices are positively correlated. C. yield volatility for bonds sold at a discount and price volatility for bonds sold at a premium. D. yield volatility because it remains more constant over time than price volatility, which must approach zero at maturity.

http://www.tfii.orgZvi Wiener - MRM slide 84 FRM-99, Question 80 You have position of $20M in the 6.375% Aug-27 US T-bond. Calculate daily VaR at 95% assume that there are 250 business days in a year. Price 98 8/32Accrued 1.43% Yield 6.509%Duration 13.133 Modified Dur. 12.719Yield volatility 12% A. $291,400 B. $203,080 C. $206,036 D. $206,698

http://www.tfii.orgZvi Wiener - MRM slide 85 FRM-99, Question 80 Value of the position Daily yield volatility

http://www.tfii.orgZvi Wiener - MRM slide 86 Correlations Eurodeposit block zero-coupon Treasury block very high correlations within each block and much lower across blocks.

http://www.tfii.orgZvi Wiener - MRM slide 87 Principal component analysis level risk factor 94% of changes slope risk factor (twist) 4% of changes curvature (bend or butterfly) See book by Golub and Tilman.

http://www.tfii.orgZvi Wiener - MRM slide 88 FRM-00, Question 96 Which statement about historic US Treasuries yield curves is TRUE?

http://www.tfii.orgZvi Wiener - MRM slide 89 FRM-00, Question 96 A. Changes in the long-term yield tend to be larger than in short-term yield. B. Changes in the long-term yield tend to be approximately the same as in short-term yield. C. The same size yield change in both long-term and short-term rates tends to produce a larger price change in short-term instruments when all securities are traded near par. D. The largest part of total return variability of spot rates is due to parallel changes with a smaller portion due to slope changes and the residual due to curvature changes.

http://www.tfii.orgZvi Wiener - MRM slide 90 FRM-00, Question 96 A. Changes in the long-term yield tend to be larger than in short-term yield. B. Changes in the long-term yield tend to be approximately the same as in short-term yield. C. The same size yield change in both long-term and short-term rates tends to produce a larger price change in short-term instruments when all securities are traded near par. D. The largest part of total return variability of spot rates is due to parallel changes with a smaller portion due to slope changes and the residual due to curvature changes.

http://www.tfii.orgZvi Wiener - MRM slide 91 FRM-97, Question 42 What is the relationship between yield on the current inflation-proof bond issued by the US Treasury and a standard Treasury bond with similar terms? A. The yields should be about the same. B. The yield on the inflation protected bond should be approximately the yield on treasury minus the real interest. C. The yield on the inflation protected bond should be approximately the yield on treasury plus the real interest. D. None of the above.

http://www.tfii.orgZvi Wiener - MRM slide 92 Credit Spread Risk Prepayment Risk (MBS and CMO) seasoning current level of interest rates burnout (previous path) economic activity seasonal patterns OAS = option adjusted spread = spread over equivalent Treasury minus the cost of the option component.

http://www.tfii.orgZvi Wiener - MRM slide 93 FRM-99, Question 71 You held mortgage interest only (IO) strips backed by Fannie Mae 7 percent coupon. You want to hedge this by shorting Treasury interest strips off the 10- year on-the-run. The curve steepens as 1 month rate drops, while the 6 months to 10 year rates remain stable. What will be the effect on the value of your portfolio? A. Both IO and the hedge appreciate in value. B. Almost no change in both (may be a small appreciation). C. Not enough information to find changes in both. D. The IO will depreciate, the hedge will appreciate.

http://www.tfii.orgZvi Wiener - MRM slide 94 FRM-99, Question 71 You held mortgage interest only (IO) strips backed by Fannie Mae 7 percent coupon. You want to hedge this by shorting Treasury interest strips off the 10- year on-the-run. The curve steepens as 1 month rate drops, while the 6 months to 10 year rates remain stable. What will be the effect on the value of your portfolio? A. Both IO and the hedge appreciate in value. B. Almost no change in both (may be a small appreciation). C. Not enough information to find changes in both. D. The IO will depreciate, the hedge will appreciate.

http://www.tfii.orgZvi Wiener - MRM slide 95 FRM-99, Question 73 A fund manager attempting to beat his LIBOR based funding costs, holds pools of adjustable rate mortgages and is considering various strategies to lower the risk. Which of the following strategies will NOT lower the risk? A. Enter a total rate of return swap swapping the ARMs for LIBOR plus a spread. B. Short US government bonds C. Sell caps based on the projected rate of mortgage paydown. D. All of the above.

http://www.tfii.orgZvi Wiener - MRM slide 96 FRM-99, Question 73 A fund manager attempting to beat his LIBOR based funding costs, holds pools of adjustable rate mortgages and is considering various strategies to lower the risk. Which of the following strategies will NOT lower the risk? A. Enter a total rate of return swap swapping the ARMs for LIBOR plus a spread. B. Short US government bonds. C. Sell caps based on the projected rate of mortgage paydown. D. All of the above. He should buy caps, not sell!

http://www.tfii.orgZvi Wiener - MRM slide 97 Fixed income portfolio risk Yield curve component (government) Credit spread (of the class of similar rating) Specific spread

http://www.tfii.orgZvi Wiener - MRM slide 98 Equity risk Market risk (beta based relative to an index) Specific risk

http://www.tfii.orgZvi Wiener - MRM slide 99 FRM-97, Question 43 Which of the following statements about SP500 is true? I. The index is calculated using market prices as weights. II. The implied volatilities of options of the same maturity on the index are different. III. The stocks used in calculating the index remain the same for each year. IV. The SP500 represents only the 500 largest US corporations. A. II only.B. I and II. C. II and III.D. III and IV only.

http://www.tfii.orgZvi Wiener - MRM slide 100 FRM-97, Question 43 Which of the following statements about SP500 is true? I. The index is calculated using market prices as weights. II. The implied volatilities of options of the same maturity on the index are different. III. The stocks used in calculating the index remain the same for each year. IV. The SP500 represents only the 500 largest US corporations. A. II only.B. I and II. C. II and III.D. III and IV only. values

http://www.tfii.orgZvi Wiener - MRM slide 101 Forwards and Futures The forward or futures price on a stock. e -rt the present value in the base currency. e -yt the cost of carry (dividend rate). For a discrete dividend (individual stock) we can write the right hand side as S t - D, where D is the PV of the dividend.

http://www.tfii.orgZvi Wiener - MRM slide 102 FRM-97, Question 44 A trader runs a cash and future arbitrage book on the SP500 index. Which of the following are the major risk factors? I. Interest rate II. Foreign exchange III. Equity price IV. Dividend assumption risk A. I and II only. B. I and III only. C. I, III, and IV only. D. I, II, III, and IV.

http://www.tfii.orgZvi Wiener - MRM slide 103 FRM-97, Question 44 A trader runs a cash and future arbitrage book on the SP500 index. Which of the following are the major risk factors? I. Interest rate II. Foreign exchange III. Equity price IV. Dividend assumption risk A. I and II only. B. I and III only. C. I, III, and IV only. D. I, II, III, and IV.

http://www.tfii.orgZvi Wiener - MRM slide 104 In an equilibrium the following holds (Sharpe) CAPM

http://www.tfii.orgZvi Wiener - MRM slide 105 APT Arbitrage Pricing Theory

http://www.tfii.orgZvi Wiener - MRM slide 106 FRM-98, Question 62 In comparing CAPM and APT, which of the following advantages does APT have over CAPM? I. APT makes less restrictive assumptions about investor preferences toward risk and return. II. APT makes no assumption about the distribution of security returns. III. APT does not rely on the identification of the true market portfolio, and so the theory is potentially testable. A. I only.B. II and III only. C. I, and III only.D. I, II, and III.

http://www.tfii.orgZvi Wiener - MRM slide 107 FRM-98, Question 62 In comparing CAPM and APT, which of the following advantages does APT have over CAPM? I. APT makes less restrictive assumptions about investor preferences toward risk and return. II. APT makes no assumption about the distribution of security returns. III. APT does not rely on the identification of the true market portfolio, and so the theory is potentially testable. A. I only.B. II and III only. C. I, and III only.D. I, II, and III.

http://www.tfii.orgZvi Wiener - MRM slide 108 Commodity Risk Base metal - aluminum, copper, nickel, zinc. Precious metals - gold, silver, platinum. Energy products - natural gas, heating oil, unleaded gasoline, crude oil. Metals have 12-25% yearly volatility. Energy products have 30-100% yearly volatility (much less storable). Long forward prices are less volatile then short forward prices.

http://www.tfii.orgZvi Wiener - MRM slide 109 FRM-97, Question 12 Which of the following products should have the highest expected volatility? A. Crude oil B. Gold C. Japanese Treasury Bills D. DEM/CHF

http://www.tfii.orgZvi Wiener - MRM slide 110 FRM-97, Question 12 Which of the following products should have the highest expected volatility? A. Crude oil B. Gold C. Japanese Treasury Bills D. DEM/CHF

http://www.tfii.orgZvi Wiener - MRM slide 111 FRM-97, Question 23 Identify the major risks of being short $50M of gold two weeks forward and being long $50M of gold one year forward. I. Spot liquidity squeeze. II. Spot risk. III. Gold lease rate risk. IV. USD interest rate risk. A. II only.B. I, II, and III only. C. I, III, and IV only.D. I, II, III, and IV.

http://www.tfii.orgZvi Wiener - MRM slide 112 FRM-97, Question 23 Identify the major risks of being short $50M of gold two weeks forward and being long $50M of gold one year forward. I. Spot liquidity squeeze. II. Spot risk. III. Gold lease rate risk. IV. USD interest rate risk. A. II only.B. I, II, and III only. C. I, III, and IV only.D. I, II, III, and IV. Spot risk is eliminated by offsetting positions

MRM FRM-GARP Oct-2001 Hedging Linear Risk Following Jorion 2001, Chapter 14 Financial Risk Manager Handbook

http://www.tfii.orgZvi Wiener - MRM slide 114 Hedging Taking positions that lower the risk profile of the portfolio. Static hedging Dynamic hedging

http://www.tfii.orgZvi Wiener - MRM slide 115 Unit Hedging with Currencies A US exporter will receive Y125M in 7 months. The perfect hedge is to enter a 7-months forward contract. Such a contract is OTC and illiquid. Instead one can use traded futures. CME lists yen contract with face value Y12.5M and 9 months to maturity. Sell 10 contracts and revert in 7 months.

http://www.tfii.orgZvi Wiener - MRM slide 116 Market data07mP&L time to maturity92 US interest rate6%6% Yen interest rate5%2% Spot Y/$125.00150.00 Futures Y/$124.07149.00

http://www.tfii.orgZvi Wiener - MRM slide 117 Stacked hedge - to use a longer horizon and to revert the position at maturity. Strip hedge - rolling over short hedge.

http://www.tfii.orgZvi Wiener - MRM slide 118 Basis Risk Basis risk arises when the characteristics of the futures contract differ from those of the underlying. For example quality of agricultural product, types of oil, Cheapest to Deliver bond, etc. Basis = Spot - Future

http://www.tfii.orgZvi Wiener - MRM slide 119 Cross hedging Hedging with a correlated (but different) asset. In order to hedge an exposure to Norwegian Krone one can use Euro futures. Hedging a portfolio of stocks with index future.

http://www.tfii.orgZvi Wiener - MRM slide 120 FRM-00, Question 78 What feature of cash and futures prices tend to make hedging possible? A. They always move together in the same direction and by the same amount. B. They move in opposite direction by the same amount. C. They tend to move together generally in the same direction and by the same amount. D. They move in the same direction by different amount.

http://www.tfii.orgZvi Wiener - MRM slide 121 FRM-00, Question 78 What feature of cash and futures prices tend to make hedging possible? A. They always move together in the same direction and by the same amount. B. They move in opposite direction by the same amount. C. They tend to move together generally in the same direction and by the same amount. D. They move in the same direction by different amount.

http://www.tfii.orgZvi Wiener - MRM slide 122 FRM-00, Question 17 Which statement is MOST correct? A. A portfolio of stocks can be fully hedged by purchasing a stock index futures contract. B. Speculators play an important role in the futures market by providing the liquidity that makes hedging possible and assuming the risk that hedgers are trying to eliminate. C. Someone generally using futures contract for hedging does not bear the basis risk. D. Cross hedging involves an additional source of basis risk because the asset being hedged is exactly the same as the asset underlying the futures.

http://www.tfii.orgZvi Wiener - MRM slide 123 FRM-00, Question 17 Which statement is MOST correct? A. A portfolio of stocks can be fully hedged by purchasing a stock index futures contract. B. Speculators play an important role in the futures market by providing the liquidity that makes hedging possible and assuming the risk that hedgers are trying to eliminate. C. Someone generally using futures contract for hedging does not bear the basis risk. D. Cross hedging involves an additional source of basis risk because the asset being hedged is exactly the same as the asset underlying the futures.

http://www.tfii.orgZvi Wiener - MRM slide 124 FRM-00, Question 79 Under which scenario is basis risk likely to exist? A. A hedge (which was initially matched to the maturity of the underlying) is lifted before expiration. B. The correlation of the underlying and the hedge vehicle is less than one and their volatilities are unequal. C. The underlying instrument and the hedge vehicle are dissimilar. D. All of the above.

http://www.tfii.orgZvi Wiener - MRM slide 125 FRM-00, Question 79 Under which scenario is basis risk likely to exist? A. A hedge (which was initially matched to the maturity of the underlying) is lifted before expiration. B. The correlation of the underlying and the hedge vehicle is less than one and their volatilities are unequal. C. The underlying instrument and the hedge vehicle are dissimilar. D. All of the above.

http://www.tfii.orgZvi Wiener - MRM slide 126 The Optimal Hedge Ratio  S - change in $ value of the inventory  F - change in $ value of the one futures N - number of futures you buy/sell

http://www.tfii.orgZvi Wiener - MRM slide 127 The Optimal Hedge Ratio Minimum variance hedge ratio

http://www.tfii.orgZvi Wiener - MRM slide 128 Hedge Ratio as Regression Coefficient The optimal amount can also be derived as the slope coefficient of a regression  s/s on  f/f:

http://www.tfii.orgZvi Wiener - MRM slide 129 Optimal Hedge One can measure the quality of the optimal hedge ratio in terms of the amount by which we have decreased the variance of the original portfolio. If R is low the hedge is not effective!

http://www.tfii.orgZvi Wiener - MRM slide 130 Optimal Hedge At the optimum the variance is

http://www.tfii.orgZvi Wiener - MRM slide 131 FRM-99, Question 66 The hedge ratio is the ratio of the size of the position taken in the futures contract to the size of the exposure. Denote the standard deviation of change of spot price by  1, the standard deviation of change of future price by  2, the correlation between the changes in spot and futures prices by . What is the optimal hedge ratio? A. 1/  1 /  2 B. 1/  2 /  1 C.  1 /  2 D.  2 /  1

http://www.tfii.orgZvi Wiener - MRM slide 132 FRM-99, Question 66 The hedge ratio is the ratio of the size of the position taken in the futures contract to the size of the exposure. Denote the standard deviation of change of spot price by  1, the standard deviation of change of future price by  2, the correlation between the changes in spot and futures prices by . What is the optimal hedge ratio? A. 1/  1 /  2 B. 1/  2 /  1 C.  1 /  2 D.  2 /  1

http://www.tfii.orgZvi Wiener - MRM slide 133 FRM-99, Question 66 The hedge ratio is the ratio of derivatives to a spot position (vice versa) that achieves an objective such as minimizing or eliminating risk. Suppose that the standard deviation of quarterly changes in the price of a commodity is 0.57, the standard deviation of quarterly changes in the price of a futures contract on the commodity is 0.85, and the correlation between the two changes is 0.3876. What is the optimal hedge ratio for a three-month contract? A. 0.1893 B. 0.2135 C. 0.2381 D. 0.2599

http://www.tfii.orgZvi Wiener - MRM slide 134 FRM-99, Question 66 The hedge ratio is the ratio of derivatives to a spot position (vice versa) that achieves an objective such as minimizing or eliminating risk. Suppose that the standard deviation of quarterly changes in the price of a commodity is 0.57, the standard deviation of quarterly changes in the price of a futures contract on the commodity is 0.85, and the correlation between the two changes is 0.3876. What is the optimal hedge ratio for a three-month contract? A. 0.1893 B. 0.2135 C. 0.2381 D. 0.2599

http://www.tfii.orgZvi Wiener - MRM slide 135 Example Airline company needs to purchase 10,000 tons of jet fuel in 3 months. One can use heating oil futures traded on NYMEX. Notional for each contract is 42,000 gallons. We need to check whether this hedge can be efficient.

http://www.tfii.orgZvi Wiener - MRM slide 136 Example Spot price of jet fuel $277/ton. Futures price of heating oil $0.6903/gallon. The standard deviation of jet fuel price rate of changes over 3 months is 21.17%, that of futures 18.59%, and the correlation is 0.8243.

http://www.tfii.orgZvi Wiener - MRM slide 137 Compute The notional and standard deviation f the unhedged fuel cost in $. The optimal number of futures contracts to buy/sell, rounded to the closest integer. The standard deviation of the hedged fuel cost in dollars.

http://www.tfii.orgZvi Wiener - MRM slide 138 Solution The notional is Qs=$2,770,000, the SD in $ is  (  s/s)sQ s =0.2117  $277  10,000 = $586,409 the SD of one futures contract is  (  f/f)fQ f =0.1859  $0.6903  42,000 = $5,390 with a futures notional fQ f = $0.6903  42,000 = $28,993.

http://www.tfii.orgZvi Wiener - MRM slide 139 Solution The cash position corresponds to a liability (payment), hence we have to buy futures as a protection.  sf = 0.8243  0.2117/0.1859 = 0.9387  sf = 0.8243  0.2117  0.1859 = 0.03244 The optimal hedge ratio is N* =  sf Q s  s/Q f  f = 89.7, or 90 contracts.

http://www.tfii.orgZvi Wiener - MRM slide 140 Solution  2 unhedged = ($586,409) 2 = 343,875,515,281 -  2 SF /  2 F = -(2,605,268,452/5,390) 2  hedged = $331,997 The hedge has reduced the SD from $586,409 to $331,997. R 2 = 67.95%(= 0.8243 2 )

http://www.tfii.orgZvi Wiener - MRM slide 141 FRM-99, Question 67 In the early 90s, Metallgesellshaft, a German oil company, suffered a loss of $1.33B in their hedging program. They rolled over short dated futures to hedge long term exposure created through their long- term fixed price contracts to sell heating oil and gasoline to their customers. After a time, they abandoned the hedge because of large negative cashflow. The cashflow pressure was due to the fact that MG had to hedge its exposure by: A. Short futures and there was a decline in oil price B. Long futures and there was a decline in oil price C. Short futures and there was an increase in oil price D. Long futures and there was an increase in oil price

http://www.tfii.orgZvi Wiener - MRM slide 142 FRM-99, Question 67 In the early 90s, Metallgesellshaft, a German oil company, suffered a loss of $1.33B in their hedging program. They rolled over short dated futures to hedge long term exposure created through their long- term fixed price contracts to sell heating oil and gasoline to their customers. After a time, they abandoned the hedge because of large negative cashflow. The cashflow pressure was due to the fact that MG had to hedge its exposure by: A. Short futures and there was a decline in oil price B. Long futures and there was a decline in oil price C. Short futures and there was an increase in oil price D. Long futures and there was an increase in oil price

http://www.tfii.orgZvi Wiener - MRM slide 143 Duration Hedging Dollar duration

http://www.tfii.orgZvi Wiener - MRM slide 144 Duration Hedging If we have a target duration D V * we can get it by using

http://www.tfii.orgZvi Wiener - MRM slide 145 Example 1 A portfolio manager has a bond portfolio worth $10M with a modified duration of 6.8 years, to be hedged for 3 months. The current futures prices is 93-02, with a notional of $100,000. We assume that the duration can be measured by CTD, which is 9.2 years. Compute: a. The notional of the futures contract b.The number of contracts to by/sell for optimal protection.

http://www.tfii.orgZvi Wiener - MRM slide 146 Example 1 The notional is: (93+2/32)/100  $100,000 =$93,062.5 The optimal number to sell is: Note that DVBP of the futures is 9.2  $93,062  0.01%=$85

http://www.tfii.orgZvi Wiener - MRM slide 147 Example 2 On February 2, a corporate treasurer wants to hedge a July 17 issue of $5M of CP with a maturity of 180 days, leading to anticipated proceeds of $4.52M. The September Eurodollar futures trades at 92, and has a notional amount of $1M. Compute a. The current dollar value of the futures contract. b. The number of futures to buy/sell for optimal hedge.

http://www.tfii.orgZvi Wiener - MRM slide 148 Example 2 The current dollar value is given by $10,000  (100-0.25(100-92)) = $980,000 Note that duration of futures is 3 months, since this contract refers to 3-month LIBOR.

http://www.tfii.orgZvi Wiener - MRM slide 149 Example 2 If Rates increase, the cost of borrowing will be higher. We need to offset this by a gain, or a short position in the futures. The optimal number of contracts is: Note that DVBP of the futures is 0.25  $1,000,000  0.01%=$25

http://www.tfii.orgZvi Wiener - MRM slide 150 FRM-00, Question 73 What assumptions does a duration-based hedging scheme make about the way in which interest rates move? A. All interest rates change by the same amount B. A small parallel shift in the yield curve C. Any parallel shift in the term structure D. Interest rates movements are highly correlated

http://www.tfii.orgZvi Wiener - MRM slide 151 FRM-00, Question 73 What assumptions does a duration-based hedging scheme make about the way in which interest rates move? A. All interest rates change by the same amount B. A small parallel shift in the yield curve C. Any parallel shift in the term structure D. Interest rates movements are highly correlated

http://www.tfii.orgZvi Wiener - MRM slide 152 FRM-99, Question 61 If all spot interest rates are increased by one basis point, a value of a portfolio of swaps will increase by $1,100. How many Eurodollar futures contracts are needed to hedge the portfolio? A. 44 B. 22 C. 11 D. 1100

http://www.tfii.orgZvi Wiener - MRM slide 153 FRM-99, Question 61 The DVBP of the portfolio is $1,100. The DVBP of the futures is $25. Hence the ratio is 1100/25 = 44

http://www.tfii.orgZvi Wiener - MRM slide 154 FRM-99, Question 109 Roughly how many 3-month LIBOR Eurodollar futures contracts are needed to hedge a position in a $200M, 5 year, receive fixed swap? A. Short 250 B. Short 3,200 C. Short 40,000 D. Long 250

http://www.tfii.orgZvi Wiener - MRM slide 155 FRM-99, Question 109 The dollar duration of a 5-year 6% par bond is about 4.3 years. Hence the DVBP of the fixed leg is about $200M  4.3  0.01%=$86,000. The floating leg has short duration - small impact decreasing the DVBP of the fixed leg. DVBP of futures is $25. Hence the ratio is 86,000/25 = 3,440. Answer A

http://www.tfii.orgZvi Wiener - MRM slide 156 Beta Hedging  represents the systematic risk,  - the intercept (not a source of risk) and  - residual. A stock index futures contract

http://www.tfii.orgZvi Wiener - MRM slide 157 Beta Hedging The optimal N is The optimal hedge with a stock index futures is given by beta of the cash position times its value divided by the notional of the futures contract.

http://www.tfii.orgZvi Wiener - MRM slide 158 Example A portfolio manager holds a stock portfolio worth $10M, with a beta of 1.5 relative to S&P500. The current S&P index futures price is 1400, with a multiplier of $250. Compute: a. The notional of the futures contract b. The optimal number of contracts for hedge.

http://www.tfii.orgZvi Wiener - MRM slide 159 Example The notional of the futures contract is $250  1,400 = $350,000 The optimal number of contracts for hedge is The quality of the hedge will depend on the size of the residual risk in the portfolio.

http://www.tfii.orgZvi Wiener - MRM slide 160 A typical US stock has correlation of 50% with S&P. Using the regression effectiveness we find that the volatility of the hedged portfolio is still about (1-0.5 2 ) 0.5 = 87% of the unhedged volatility for a typical stock. If we wish to hedge an industry index with S&P futures, the correlation is about 75% and the unhedged volatility is 66% of its original level. The lower number shows that stock market hedging is more effective for diversified portfolios.

http://www.tfii.orgZvi Wiener - MRM slide 161 FRM-00, Question 93 A fund manages an equity portfolio worth $50M with a beta of 1.8. Assume that there exists an index call option contract with a delta of 0.623 and a value of $0.5M. How many options contracts are needed to hedge the portfolio? A. 169 B. 289 C. 306 D. 321

http://www.tfii.orgZvi Wiener - MRM slide 162 FRM-00, Question 93 The optimal hedge ratio is N = -1.8  $50,000,000/(0.623  $500,000)=289

MRM FRM-GARP Oct-2001 VaR methods Following Jorion 2001, Chapter 17 Financial Risk Manager Handbook

http://www.tfii.orgZvi Wiener - MRM slide 164 Risk Factors There are many bonds, stocks and currencies. The idea is to choose a small set of relevant economic factors and to map everything on these factors. Exchange rates Interest rates (for each maturity and indexation) Spreads Stock indices

http://www.tfii.orgZvi Wiener - MRM slide 165 How to measure VaR Historical Simulations Variance-Covariance Monte Carlo Analytical Methods Parametric versus non-parametric approaches

http://www.tfii.orgZvi Wiener - MRM slide 166 Historical Simulations Fix current portfolio. Pretend that market changes are similar to those observed in the past. Calculate P&L (profit-loss). Find the lowest quantile.

http://www.tfii.orgZvi Wiener - MRM slide 167 Example 4.00 4.20 4.10 4.15 Assume we have $1 and our main currency is SHEKEL. Today $1=4.30. Historical data: 4.30*4.20/4.00 = 4.515 4.30*4.20/4.20 = 4.30 4.30*4.10/4.20 = 4.198 4.30*4.15/4.10 = 4.352 P&L 0.215 0 -0.112 0.052

http://www.tfii.orgZvi Wiener - MRM slide 168 today USD NIS 2000 100 -120 2001 200 100 2002-300 -20 2003 20 30

http://www.tfii.orgZvi Wiener - MRM slide 169 today Changes in IR USD: +1%+1% +1% +1% NIS: +1% 0% -1% -1%

http://www.tfii.orgZvi Wiener - MRM slide 170 Returns year 1% of worst cases

http://www.tfii.orgZvi Wiener - MRM slide 171 Profit/Loss VaR 1% VaR 1%

http://www.tfii.orgZvi Wiener - MRM slide 172 Variance Covariance Means and covariances of market factors Mean and standard deviation of the portfolio Delta or Delta-Gamma approximation VaR 1% =  P – 2.33  P Based on the normality assumption!

http://www.tfii.orgZvi Wiener - MRM slide 173  Variance-Covariance 2.33   -2.33  1%

http://www.tfii.orgZvi Wiener - MRM slide 174 Monte Carlo

http://www.tfii.orgZvi Wiener - MRM slide 175 Monte Carlo Distribution of market factors Simulation of a large number of events P&L for each scenario Order the results VaR = lowest quantile

http://www.tfii.orgZvi Wiener - MRM slide 176 Monte Carlo Simulation

http://www.tfii.orgZvi Wiener - MRM slide 177 Weights Since old observations can be less relevant, there is a technique that assigns decreasing weights to older observations. Typically the decrease is exponential. See RiskMetrics Technical Document for details.

http://www.tfii.orgZvi Wiener - MRM slide 178 Stock Portfolio Single risk factor or multiple factors Degree of diversification Tracking error Rare events

http://www.tfii.orgZvi Wiener - MRM slide 179 Bond Portfolio Duration Convexity Partial duration Key rate duration OAS, OAD Principal component analysis

http://www.tfii.orgZvi Wiener - MRM slide 180 Options and other derivatives Greeks Full valuation Credit and legal aspects Collateral as a cushion Hedging strategies Liquidity aspects

http://www.tfii.orgZvi Wiener - MRM slide 181 Credit Portfolio rating, scoring credit derivatives reinsurance probability of default recovery ratio

http://www.tfii.orgZvi Wiener - MRM slide 182 Reporting Division of VaR by business units, areas of activity, counterparty, currency. Performance measurement - RAROC (Risk Adjusted Return On Capital).

http://www.tfii.orgZvi Wiener - MRM slide 183 Backtesting Verification of Risk Management models. Comparison if the model’s forecast VaR with the actual outcome - P&L. Exception occurs when actual loss exceeds VaR. After exception - explanation and action.

http://www.tfii.orgZvi Wiener - MRM slide 184 Backtesting Green zone - up to 4 exceptions Yellow zone - 5-9 exceptions Red zone - 10 exceptions or more OK increasing k intervention

http://www.tfii.orgZvi Wiener - MRM slide 185 Stress Designed to estimate potential losses in abnormal markets. Extreme events Fat tails Central questions: How much we can lose in a certain scenario? What event could cause a big loss?

http://www.tfii.orgZvi Wiener - MRM slide 186 Local Valuation Simple approach based on linear approximation. Full Valuation Requires repricing of assets.

http://www.tfii.orgZvi Wiener - MRM slide 187 Delta-Gamma Method The valuation is still local (the bond is priced only at current rates).

http://www.tfii.orgZvi Wiener - MRM slide 188 FRM-97, Question 13 An institution has a fixed income desk and an exotic options desk. Four risk reports were produced, each with a different methodology. With all four methodologies readily available, which of the following would you use to allocate capital? A. Simulation applied to both desks. B. Delta-Normal applied to both desks. C. Delta-Gamma for the exotic options desk and the delta-normal for the fixed income desk. D. Delta-Gamma applied to both desks.

http://www.tfii.orgZvi Wiener - MRM slide 189 An institution has a fixed income desk and an exotic options desk. Four risk reports were produced, each with a different methodology. With all four methodologies readily available, which of the following would you use to allocate capital? A. Simulation applied to both desks. B. Delta-Normal applied to both desks. C. Delta-Gamma for the exotic options desk and the delta-normal for the fixed income desk. D. Delta-Gamma applied to both desks. FRM-97, Question 13 Bad question!

http://www.tfii.orgZvi Wiener - MRM slide 190 Mapping Replacing the instruments in the portfolio by positions in a limited number of risk factors. Then these positions are aggregated in a portfolio.

http://www.tfii.orgZvi Wiener - MRM slide 191 Delta-Normal method Assumes linear exposures risk factors are jointly normally distributed The portfolio variance is Forecast of the covariance matrix for the horizon

http://www.tfii.orgZvi Wiener - MRM slide 192 Delta-normalHistor.MC Valuationlinearfullfull Distributionnormalactualgeneral Extreme eventslow prob.recent possible Ease of comput.Yesintermed.No CommunicabilityEasyEasyDifficult VaR precisionBaddependsgood Major pitallsnonlinearityunstablemodel fat tails risk

http://www.tfii.orgZvi Wiener - MRM slide 193 FRM-97, Question 12 Delta-Normal, Historical-Simulations, and MC are various methods available to compute VaR. If underlying returns are normally distributed, then the: A. DN VaR will be identical to HS VaR. B. DN VaR will be identical to MC VaR. C. MC VaR will approach DN VaR as the number of simulations increases. D. MC VaR will be identical to HS VaR.

http://www.tfii.orgZvi Wiener - MRM slide 194 FRM-97, Question 12 Delta-Normal, Historical-Simulations, and MC are various methods available to compute VaR. If underlying returns are normally distributed, then the: A. DN VaR will be identical to HS VaR. B. DN VaR will be identical to MC VaR. C. MC VaR will approach DN VaR as the number of simulations increases. D. MC VaR will be identical to HS VaR.

http://www.tfii.orgZvi Wiener - MRM slide 195 FRM-98, Question 6 Which VaR methodology is least effective for measuring options risks? A. Variance-covariance approach. B. Delta-Gamma. C. Historical Simulations. D. Monte Carlo.

http://www.tfii.orgZvi Wiener - MRM slide 196 FRM-98, Question 6 Which VaR methodology is least effective for measuring options risks? A. Variance-covariance approach. B. Delta-Gamma. C. Historical Simulations. D. Monte Carlo.

http://www.tfii.orgZvi Wiener - MRM slide 197 FRM-99, Questions 15, 90 The VaR of one asset is 300 and the VaR of another one is 500. If the correlation between changes in asset prices is 1/15, what is the combined VaR? A. 525 B. 775 C. 600 D. 700

http://www.tfii.orgZvi Wiener - MRM slide 198 FRM-99, Questions 15, 90

http://www.tfii.orgZvi Wiener - MRM slide 199 Example On Dec 31, 1998 we have a forward contract to buy 10M GBP in exchange for delivering $16.5M in 3 months. S t - current spot price of GBP in USD F t - current forward price K - purchase price set in contract f t - current value of the contract r t - USD risk-free rate, r t * - GBP risk-free rate  - time to maturity

http://www.tfii.orgZvi Wiener - MRM slide 200

http://www.tfii.orgZvi Wiener - MRM slide 201 The forward contract is equivalent to a long position of SP* on the spot rate a long position of SP* in the foreign bill a short position of KP in the domestic bill

http://www.tfii.orgZvi Wiener - MRM slide 202 On the valuation date we have S = 1.6595, r = 4.9375%, r* = 5.9688% V t = $93,581 - the current value of the contract

MRM FRM-GARP Oct-2001 Zvi Wiener 02-588-3049 Market Risk Management.

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MRM FRM-GARP Oct-2001 Zvi Wiener 02-588-3049 Market Risk Management.

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