Assessing Credit Risk in Derivatives

Assessing Credit Risk in Derivatives Daniel Moore Director Structured Product Trading Scotia Capital Acknowledgements and Disclaimer • The presenter gratefully acknowledges the invaluable contributions of his colleagues in the Risk Management Analytics department (including Abdalla Ruken, Niall Whelan, and Alexander Bondarenko) at the Bank of Nova Scotia without whom this work (especially the hard bits) would not be possible. All mistakes, of course, remain those of the presenter. Not an offer, recommendation, general solicitation or official confirmation of terms. Prepared from generally available information believed to be reliable. No representation of accuracy or completeness. Indicated returns not guaranteed. Assumption changes may materially impact returns. Price/availability subject to change without notice. Past performance not indicative of future results. • What is a Total Return Swap? •An agreement where one party pays the total return of an underlying asset while receiving either a fixed or floating payment in return Distributions and Realized/Unrealized Gains Total Return Payer Realized/Unrealized Losses Total Return Receiver LIBOR + Spread Total of Return Asset Reference Asset Uses of Total Return Swaps Total Return Receiver Total Return Payer •Leverage  Little or no initial cash payment •Ability to hedge both the price and default risk (unlike CDS). •By entering into a TRS that matures before the asset, you can guarantee a return and temporarily short the asset •Ability to hedge an unrecognized loss on a bond without risking further losses •Spread Income •Customize maturity dates that are not readily available in the market •Possibility of higher return on capital •Off balance sheet exposure •Reduction in administrative costs since TRS is an off balance sheet transaction Uses of TRS! TRS vs. CDO Loans Second Loss (TR seller) Loans Senior Tranches TRS TR payment (First Loss) Collateral CDO Equity Tranche (First Loss) Equity Investment •MTM •Cash flows may mimic assets •Flexible Terms, maturity, unwind •Accrual •Cash flows don‟t match buys and sells •Fixed terms – many investors •Commonly only equity exposure •Off Balance Sheet •Any tranche (subject to investor availability) •On Balance Sheet Economics Very Similar Credit Risk Defined •Rating agencies and BIS decompose credit risk into three factors Expected Future Loss(EL) = PD ● LGD ● Exposure at Default •If collateral is posted, the net exposure decreases, which leads to a lower EL EL = PD ● LGD ● (Exposure-Collateral)+ •Banks typically decompose this risk into two factors •Deemed Risk -“loan equivalent exposure,” a measure of exposure at default -calculated as the 95th percentile of the amount BNS stands to lose -does not reflect security, collateral or credit rating •Customer and Facility IG codes / Ratings -Really, a proxy for rating -A combination of LGD and PD -This Customer IG code measures the probability that the customer will default. Other factors such as the amount of collateral posted, MTM triggers and mutual puts are taken into account to upgrade the Customer IG into a Facility IG. Potential Future Exposure a) No Collateral TRS MTM (seller) -10 -5 Original Asset Value ($100) +5 +10 Probability 10% 20% Buyer has exposure to seller 40% 20% Seller has exposure to buyer 10% b) With Collateral TRS MTM (seller) -10 -5 Probability 10% Buyer has exposure to seller 20% Original Asset Value ($100) +5 +10 $6 Collateral posted by buyer 40% Seller has no net exposure 20% 10% Seller has exposure to buyer Deemed Risk: In Math  DR =20 Or   MTM  P( x) 1 P  95 dx DR = Ω(P=95) Also  Expected Gross Exposure =   ( MTM )   P( x)dx  ( MTM  Collateral)   P( x)dx Expected Net Exposure =   Log-Normal Distribution • Then, the results are analytic. • For example, an equity TRS, Forward, or Call/ Put, with no up front margin: DR  20  2   ( r  2 / 2 ) T  X    rT  ( r  / 2 ) T  X     KN    S0e N   T  T      S0 Recipe for Deemed Risk AHA! now the way is CLEAR Steps to Calculate Deemed Risk for a TRS on a portfolio of loans 1. 2. 3. 4. 5. 6. Build database of price histories for loans Period of Risk : Discovery Period + Grace and Cure + Asset Liquidity Sample independent return histories over the POR for portfolios of varying number of assets, industries, WARF‟s. Calculate the total return over this period and store 40% Wash, rinse, repeat -> Create a Distribution of Portfolio returns Add stress events 35% 30% 25% 20% 15% 10% 5% 0% W ARF 2220 W ARF 3490 0 Loss 10% Loss 20% Loss a) Use Moody‟s Binomial Expansion Method to calculate effective # of assets eg: diversification 5% by obligor / 20% by industry 5 industries, each of 4 assets Diversified score for 4 assets = 2.33 Neff = 5 ● 2.33 = 11.67 a) Probability of „j‟ defaults is: Pj  N! p j  (1  p) N  j j!( N  j )! A Bit More Math • Weighted Average Rating Factor – Allows us to treat a portfolio as if it were a single security, with equivalent rating equal to the WARF. • Effective Number of Assets / Diversity Score – Simple example: all assets in one industry: N_eff = S&P Rating AAA AA+ AA AAA+ A ABBB+ BBB BBBBB+ BB BBB+ B BCCC+ CCC CCCCC C D NR NR NA NA Moody's Rating Rating Factor Aaa 1 Aa1 10 Aa2 20 Aa3 40 A1 70 A2 120 A3 180 Baa1 260 Baa2 360 Baa3 610 Ba1 940 Ba2 1350 Ba3 1780 B1 2220 B2 2720 B3 3490 Caa1 4770 Caa2 6500 Caa3 8070 Ca 10000 Caa 10000 D 10000 NR 610 NR 610 NA 610 NA 610  f ^2 i Num Assets in Industry Diversity Score Contribution 1 1.00 2 1.50 3 2.00 4 2.33 5 2.67 6 3.00 7 3.25 8 3.50 9 3.75 10 4.00 Layering in Defaults • Need a way to convolute defaults with spread moves Loss Prob 92% Defaults 0 •Sort the spread scenarios, adding the Loss On Default amount to the spread loss. 0% 7% 7.0% 1 12.4% 0.24% 2 16.5% … 0.005% … 3 … Does it work? •Deemed Risk for various portfolios of hedge funds. •Diversification by Number of Funds (1-36), and by Strategies (1-12) •Period of Risk = 3mo. Deemed Risk and Diversification 120.00% 100.00% 80.00% Num Strategies DR 60.00% 40.00% 20.00% 0.00% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Num Funds Examples: 1) T=2yr, no resets, Nf = 12, Ns = 5. Effective Nf=10.7, ENs = 3.9  DR = 34.8% 2) Same trade, Monthly resets, WAL = 5mo (POR=6mo)  DR = 17.4% Effect of Margin • As defined, up front collateral does not affect Deemed Risk / Loan Equivalent Amount. • However, variation margin triggers can affect the Period of Risk. • The maximum likely exposure becomes: Trigger + DR(Liquidity Period) • For example: 25% up front, termination trigger at 5% decline, the Deemed Risk is 5% + DR(2 weeks). • Recouponing triggers have a similar effect. What is Facility IG Really? •Assumption: Dealing with a Customer IG of x is equivalent to dealing with a worse customer that has a Facility IG of x •This statement is really about the equivalency of the expected losses. Example: EL (Cust IG 85, Facility IG 90, DR=$100) = EL (Cust IG 90, no security, DR=$100) Or PD (Cust IG) ● LGD ● (MTM-Collateral)+ = PD (Facility IG) ● LGD ● (MTM)+ thus PD (Facility IG) = PD (Cust IG) ● (MTM-Collateral)+ MTM+ AHA! More Clarity! Upgrade Factor Who Expects a Loss? How to Calculate Facility IG code from EL Steps to Calculate Upgrade Factor for a TRS on a portfolio of loans 1. 2. Go back to the previously calculated Distribution of Portfolio returns For a given amount of security and Period of Risk, Calculate the average secured exposure and unsecured exposure. The Upgrade Factor is the ratio of these: Average Exposure (Secured) / Average Exposure (Unsecured) Year Rating Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1 Caa2 Caa3 1 2 3 4 0.000% 0.000% 0.000% 0.001% 0.000% 0.002% 0.006% 0.012% 0.001% 0.004% 0.014% 0.026% 0.002% 0.011% 0.033% 0.056% 0.003% 0.020% 0.064% 0.104% 0.006% 0.039% 0.122% 0.190% 0.021% 0.083% 0.198% 0.297% 0.050% 0.154% 0.308% 0.457% 0.094% 0.259% 0.457% 0.660% 0.231% 0.578% 0.941% 1.309% 0.479% 1.111% 1.722% 2.310% 0.858% 1.909% 2.849% 3.740% 1.546% 3.031% 4.329% 5.385% 2.574% 4.609% 6.369% 7.618% 3.938% 6.419% 8.553% 9.972% 6.391% 9.136% 11.567% 13.222% 9.560% 12.779% 15.751% 17.863% 14.300% 17.875% 21.450% 24.134% 28.045% 31.355% 34.348% 36.433% 5 0.002% 0.017% 0.037% 0.078% 0.144% 0.257% 0.402% 0.605% 0.869% 1.678% 2.904% 4.626% 6.523% 8.866% 11.391% 14.878% 19.973% 26.813% 38.402% Moody's Idealized Expected Loss Table . 3. Use the Upgrade Factor to Get a Facility Rating Take the Counterparty Rating as a given, and look up the EL. • • Upgrade the EL by the Upgrade Factor Reverse Lookup the Facility Rating from the upgraded EL • NB: This is similar to the approach taken for rating secured loans by the agencies. Show me the Money For example: TRS on portfolio of Loans, 1 year term 15 Loans, Diversity Score of 10, Average Rating B-/B3, Collateral = 14% cash Customer is a hedge fund, rated Baa2/BBB internally. •Customer EL = 0.0935% •EL(unsecured) = 1.0644% •EL(secured) = 0.0079% •Facility EL = 0.0935% * (0.00779 / 1.0644) = 0.00069% FACILITY RATING is Aa2 / AA Questions?