FRM Zvi Wiener Financial Risk Management
Zvi WienerFRM-1 slide 2 Risk Business Risk Operational Risk Financial Risk credit risk market risk liquidity risk Legal Risk
Zvi WienerFRM-1 slide 3 Crouhy, Galai, Mark, Risk Management, McGraw Hill, Golub, Tilman, Risk Management Approaches for Fixed Income Markets, Wiley, Jorion, Value at Risk, McGraw Hill,
Zvi WienerFRM-1 slide 4 Derivatives ($ million) Shova Shell, Japan1,580 Kashima Oil, Japan1,450 Metallgesellschaft1,340 Barings, U.K.1,330 Codelco, Chile200 Procter & Gamble, US157
Zvi WienerFRM-1 slide 5 Barings February 26, year old bank 28 year old Nick Leeson $1,300,000,000 loss bought by ING for $1.5
Zvi WienerFRM-1 slide 6 Public Funds ($ million) Orange County1,640 San Diego357 West Virginia279 Florida State Treasury200 Cuyahoga County137 Texas State55
Zvi WienerFRM-1 slide 7 Orange County Bob Citron, the county treasures $7.5B portfolio (schools, cities) borrowed $12.5B, invested in 5yr. notes interest rates increased reported at cost - big mistake! realized loss of $1.64B
Zvi WienerFRM-1 slide 8 Barings$1.3B Bank Negara, Malaysia 92$3B Banesto, Spain$4.7B Credit Lyonnais$10B S&L, U.S.A.$150B Japan$500B Financial Losses
Zvi WienerFRM-1 slide 9 Metallgesellshaft 14th largest industrial group 58,000 employees offered long term oil contracts hedge by long-term forward contracts short term contracts were used (rolling hedge) 1993 price fell from $20 to $15 $1B margin call in cash
Zvi WienerFRM-1 slide 10
Zvi WienerFRM-1 slide 11 Risk Management and Risk Measurement
Zvi WienerFRM-1 slide 12 Basic Statistics Certainty and uncertainty Probabilities, distribution, PDF, CDF Mean, variance Multivariable distributions Covariance, correlation, beta Quantile
Zvi WienerFRM-1 slide 13 A100 km.B 100 km/hr 50 km/hr 1 – 1002 – 503 – 50 ( )/3 = km/hr.
Zvi WienerFRM-1 slide % 2.+10% 3.-50% 4.+20% 1.-2% 2.+1% 3.-1% 4.+1% 1.4*1.1*0.5*1.2 = *1.01*0.99*1.01 =
Zvi WienerFRM-1 slide 15 Probabilities Certainty Uncertainty Probabilities
Zvi WienerFRM-1 slide 16 Probabilities Mean Variance
Zvi WienerFRM-1 slide 17 Probabilities % 30% 10%
Zvi WienerFRM-1 slide 18 Probabilities
Zvi WienerFRM-1 slide 19 Probabilities
Zvi WienerFRM-1 slide 20 Probabilities
Zvi WienerFRM-1 slide 21 Sample Estimates Sometimes one can use weights
Zvi WienerFRM-1 slide 22 Normal Distribution N( , )
Zvi WienerFRM-1 slide 23 Normal Distribution N( , )
Zvi WienerFRM-1 slide 24 Normal Distribution quantile 1%
Zvi WienerFRM-1 slide 25 Lognormal Distribution
Zvi WienerFRM-1 slide 26 Covariance Shows how two random variables are connected For example: independent move together move in opposite directions covariance(X,Y) =
Zvi WienerFRM-1 slide 27 Correlation -1 1 = 0 independent = 1 perfectly positively correlated = -1 perfectly negatively correlated
Zvi WienerFRM-1 slide 28 Properties
Zvi WienerFRM-1 slide 29 Time Aggregation Assuming normality
Zvi WienerFRM-1 slide 30 Time Aggregation Assume that yearly parameters of CPI are: mean = 5%, standard deviation (SD) = 2%. Then daily mean and SD of CPI changes are:
Zvi WienerFRM-1 slide 31 Portfolio 2 (A+B) = 2 (A) + 2 (B) + 2 (A) (B) rfrf A B
Zvi WienerFRM-1 slide 32 $ £ $¥ £¥ £$ $ £¥ £ $¥ ¥ $£
Zvi WienerFRM-1 slide 33 12 11 22 John Zerolis "Triangulating Risk", Risk v.9 n.12, Dec. 1996
Zvi WienerFRM-1 slide 34 Useful Books Duffie D., Dynamic Asset Pricing Theory. Duffie D., Security Markets, Stochastic Models. Shimko D. Finance in Continuous Time, A Primer. Kolb Publishing Company, 1992.
Zvi WienerFRM-1 slide 35 Binomial Tree
Zvi WienerFRM-1 slide 36
Zvi WienerFRM-1 slide 37 Example We will receive n dollars where n is determined by a die. What would be a fair price for participation in this game?
Zvi WienerFRM-1 slide 38 Example 1 ScoreProbability 11/6 21/6 31/6 41/6 51/6 61/6 Fair price is 3.5 NIS. Assume that we can play the game for 3 NIS only.
Zvi WienerFRM-1 slide 39 Example If there is a pair of dice the mean is doubled. What is the probability to gain $5?
Zvi WienerFRM-1 slide 40 Example 1,12,13,14,15,16,1 1,22,23,24,25,26,2 1,32,33,34,35,36,3 1,42,43,44,45,46,4 1,52,53,54,55,56,5 1,62,63,64,65,66,6 All combinations: 36 combinations with equal probabilities
Zvi WienerFRM-1 slide 41 Example 1,12,13,14,15,16,1 1,22,23,24,25,26,2 1,32,33,34,35,36,3 1,42,43,44,45,46,4 1,52,53,54,55,56,5 1,62,63,64,65,66,6 All combinations: 4 out of 36 give $5, probability = 1/9
Zvi WienerFRM-1 slide 42 All combinations: 1 out of 9 give $5, probability = 1/9 Additional information: the first die gives 4. 1,12,13,14,15,16,1 1,22,23,24,25,26,2 1,32,33,34,35,36,3 1,42,43,44,45,46,4 1,52,53,54,55,56,5 1,62,63,64,65,66,6
Zvi WienerFRM-1 slide 43 All combinations: 4 out of 24 give $5, probability = 1/6 Additional information: the first die gives 4. 1,12,13,14,15,16,1 1,22,23,24,25,26,2 1,32,33,34,35,36,3 1,42,43,44,45,46,4 1,52,53,54,55,56,5 1,62,63,64,65,66,6
Zvi WienerFRM-1 slide 44 Example
Zvi WienerFRM-1 slide 45 Example we pay NIS
Zvi WienerFRM-1 slide 46 P&L
Zvi WienerFRM-1 slide 47 Example 1 (2 cubes)
Zvi WienerFRM-1 slide 48 Example 1 (5 cubes)
Zvi WienerFRM-1 slide 49 Breakfast $2 $450%
Zvi WienerFRM-1 slide 50 Lunch $5 $1150%
Zvi WienerFRM-1 slide 51
Zvi WienerFRM-1 slide 52 Lunch Breakfast $2$4 $5$7$9 $11$13$15 50% = $11 = ?? 50%
Zvi WienerFRM-1 slide 53 Correlation =+1 $2$4 $5$7$9 $11$13$15 Lunch Breakfast 50% = $11 = $450%
Zvi WienerFRM-1 slide 54 Correlation =-1 $2$4 $5$7$9 $11$13$15 Lunch Breakfast 50% = $11 = $250%
Zvi WienerFRM-1 slide 55 Correlation =0 $2$4 $5$7$9 $11$13$15 Lunch Breakfast 50% = $11 = $3.1650%
Zvi WienerFRM-1 slide 56 How much can we lose? Everything correct, but useless answer. How much can we lose realistically?
Zvi WienerFRM-1 slide 57 What is the current Risk? duration, convexity volatility delta, gamma, vega rating target zone Bonds Stocks Options Credit Forex Total?
Zvi WienerFRM-1 slide 58 Standard Approach
Zvi WienerFRM-1 slide 59 Modern Approach Financial Institution
Zvi WienerFRM-1 slide 60 interest rates and dollar are NOT independent Value Interest Rate dollar