-Interest Rsk -Foregn Exchange Rsk -Lqudty Rsk -Market Rsk -Operaton Rsk ( ) (1) Interest Rsk Reprcng (or fundng gap) model Maturty model Duraton mode

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1 Rsk Management Products to Fnancal Insttutons

2 -Interest Rsk -Foregn Exchange Rsk -Lqudty Rsk -Market Rsk -Operaton Rsk ( ) (1) Interest Rsk Reprcng (or fundng gap) model Maturty model Duraton model (2) ( Futures Forwards Optons Caps Floors Collars) (3) Foregn Exchange Rsk on-balance sheet hedge off-balance sheet hedge (4) Lqudty Rsk Lablty management reserve asset management (5) RskMetrcs Hstorcal smulaton Monte Carlo Smulaton BIS Market Rsk 1

3 Interest Rate Rsk <Example> Savngs and Loan Insttutons (S&L) S&L 1972~1982 > nterest rate volatlty Reprcng (or fundng gap) model Maturty model Duraton model Gap 1. Reprcng model (or fundng gap) (1) Reprcng Gap The reprcng gap s the dfference between assets and labltes whose nterest rate wll change durng a partcular tme perod. (2) Reprcng Gap maturty buckets reprce / maturty buckets ex 3-month T-bll s reprced every 3 months 2-year tme deposts s reprced every 2 years / book value (hstorcal value) market equty captal Gap = Asset Lablty (for each maturty bucket) Cumulatve Gap (CGAP) = 0 NII = GAP R where NII change n net nterest ncome n the bucket GAP gap between rate senstve assets and rate senstve labltes n the bucket R change n the nterest rates affectng the bucket <Example > Reprcng Gap Assets Labltes Gap CGAP 1 day day ~ 3 months months ~ 12 months years ~ 5 years Over 5 years Total

4 <Example > Calculate the reprcng gap and the mpact on the net nterest ncome of a 1% ncrease n nterest rates f rate-senstve assets total $400mllon and rate senstve labltes total $300 mllon (Ans) reprcng gap = $ 400 m -$ 300 m = $ 100 m NII = $100 m x 0.01 = $1 m <Example > Calculate the banks 6-month cumulatve gap Asset Labltes Short term loans (1yr maturty) 15 Demand deposts 60 Long term loans (2yr maturty) 25 Passbook savngs 55 3-month T-blls 10 3-month CDs 25 6-month T-notes 5 6-month CP 35 1-year T-notes 65 1-year tme deposts year T-bonds 75 2-year tme deposts year floatng rate mortgage (reprced every 6 months) 50 Equty captal 15 Total 245 Total 245 Ans Total rate senstve assets = 3 month T-blls+6 month T-notes+Floatng rate mortgage = = 65 Total rate senstve labltes = 3-month CD + 6-month CP = = 60 CGAP = = 5 mllon <Example > The fact that nvestors generally move funds out of demand deposts and nto hgher yeldng nstruments when rates rses suggests that demand deposts should be consder (a) long term nterest rate senstve assets (b) short term nterest rate senstve assets (c) long term nterest rate senstve labltes (d) short term nterest rate senstve labltes (ps) demand depost core depost 3

5 <Example > Calculate the GAP Raton n the prevous example Ans CGAP $5mllon GAP _ Rato = = = 2.04% Total _ Assets $245mllon (3) Reprcng Gap (4) Reprcng Gap gnore market value effect ncome over aggregatve bucket / match doesn t deal wth runoff mortgage 2. Maturty model (1) Reprcng model book value market rate-senstve assets rate-senstve-labltes Maturty Gap (2) (maturty) (3) Maturty Gap N M A = WAj M Aj j= 1 where M A Weghted average maturty of a portfolo of n assets WAj market value of asset j relatve to the market value of the portfolo Aj M the maturty of asset j 4

6 N M L = W j= 1 Lj M Lj where M L Weghted average maturty of a portfolo of n labltes WLj market value of lablty j relatve to the market value of the portfolo M Lj the maturty of lablty j Maturty Gap = M A - M L = the dfference between the weghted average maturty of the banks assets and ts labltes. (4)Maturty Gap ( duraton) renvestment rate <Example > If nterest rate rse, a bank wth a negatve maturty gap and postve equty captal wll experence (a) nsolvency (b) a gan n equty captal (c) a loss of equty captal (d) no change n equty captal 3. Duraton model (1) Duraton Reprcng model Maturty model / (2) Duraton Gap D A weght average (based on market value) duratons of assets D L weght average (based on market value) duratons of labltes R E = A L = [ DA ( DL k) ] A (1 + R) Leverage adjusted duraton gap [ DA ( DL k) ] sze of the fnancal nsttuton A R sze of the nterest rate shock ( 1 + R) 5

7 <Example > A bank has the followng balance sheet Asset Labltes and Equtes Assets = 250 wth duraton = 12 years Labltes = 150 wth duraton=10 years Equty = 100 Total = 250 Total = 250 Calculate the change n equty f the nterest rate ncrease from 7% to 8% Ans k=150/250= E = [( 12 ( ) ] 250 = 14. mllon <Example > Determne the leverage raton necessary to mmunze the balance sheet aganst changes n the nterest rates, holdng the asset and lablty duratons constant. Gven Duraton of assets s 10, and Duraton of labltes s 12. Ans In order to set the leverage adjusted duraton gap equal to zero, D ( D k) =0 [ ] A L 10-k*12=0 k=0.83 6

8 Futures and Forwards 1. Hedgng Futures Forward portfolo portfolo fully mmunzaton portfolo <Example 1> Jane Swanson holds a 10-year, $10 mllon face value bond. The duraton of the bond s 7 years. Suppose today the bonds have a market value of $98 per $100 face value. Swanson antcpates that nterest rate wll rse by 2% from current level of 5%. (1) Swanson P R = D P 1+ R P = 7 9,800, P = $1,306,667 (2) Swanson 3 10-year bond forward $98 (3)3 7% 10-year bond $8,493,333 ($9,800,000-$1,306,667) (4)Swanson $8,493, year bond forward Spot Forward Intal value $9,800,000 Pad by forward buyer $9,800,000 New value $8,493,333 Cost of buyng bond to delver $8,493,333 Loss -$1,306,667 Proft $1,306,667 (5) forward Swanson 2. Mcrohedng vs Macrohedgng (1)Mcrohedgng the process whereby a futures contract or other dervatves s used to hedge a specfc asset or lablty. (2)Macrohedgng the process whereby a futures contract or other dervatves s used to hedge the entre balance sheet duraton gap. 7

9 (3)Bass Rsk movement of spot asset s prce s not perfectly correlated wth the movement n the prce of asset beng hedged. 3. Routne Hedgng vs Selectve Hedgng (1)Routng Hedgng occurs when nterest rate exposure s hedged by sellng enough futures to offset the nterest rate rsk exposure of the cash postons of each asset and lablty. Not all managers seek to do ths snce reducng rsk could also reduce return. (2)Selectve Hedgng partally hedges the gap of ndvdual assets and labltes. Selectve hedgng can be used for nterest rate rsk, foregn exchange rsk and credt rsk. 4. Futures vs Forwards (1) Futures Forwards OTC Mark-to market Yes No Standardzed Customzed Counterparty default (2)Hedge rato S Hedgerato = f 5. Futures/Forwards credt rsk (1)credt forward s used to hedge aganst a reducton n a borrower s credt qualty after a loan has been ssued and the loan rate s determned. A credt forward apples a credt spread on a benchmark bond ssued by a bank borrower to compensate for possble default rsk. Credt Spread at End of Forward Credt Spread Seller Contract (Lender) S T > S F credt spread ncrease Receve ( ST S F ) MD sze S T < S F credt spread decrease Pays ( S S ) MD sze F T Credt Spread Buyer (Insurance Company) Pays ( ST S F ) MD sze Receve ( S S ) MD sze F T Note Ths forward contract has lmted maxmum loss 8

10 6. Futures Contract and Catastrophe Rsk 921 payoff loss rato 9

11 Opton, Caps, Floors, and Collars 1. opton (1)number of optons need to buy [ DA kdl ] A N P = δ D B <Example 1> Suppose a fnancal nsttuton has assets of $10 mllon and labltes of $9 mllon. The duraton of ts assets s 6 years, and the duraton of ts labltes s 4 years. There s a put opton avalable on a long-term T-bond. The delta of the opton s 0.5, and the duraton of the underlyng bond s The current value of $100,000 face value of long-term T-bond s &98,000. Calculate the number of put opton contracts needed to hedge ths poston. Ans [ DA kdl ] A [ 6 (0.9x4)] x = δ D B [ 0.5x7.73x$98,000] $10,000,000 N P = = 63contracts 2. opton (1)Credt Spread Call optons Defnton A credt spread s payoff s a functon of the yeld spread on a borrower s benchmark bond above the comparable T-bond rate. Payoff = max[(credt spread-exercse spread), 0] x nomnal value f credt spread > exercse spread, the opton s n the money, whch means the default rsk s ncrease f credt spread < exercse spread, the opton s out of the money (2)Dgtal default Opton Defnton A dgtal default opton wll pay a stated amount aganst the defaulted credt f the default happens. payoff = 0 f no default payoff = stated amount f default 10

12 3. call-spread opton (catastrophe rsk) Catastrophe (CAT)call spread opton loss rato <Example 1> Front Insurance Company buys a CAT call spread to hedge the rsk that the loss rato on ths busness may be somewhere between 90% and 120% Front opton premum loss rate < 90% opton payoff = 0 90%<loss rate<120% opton payoff = (loss rate-90%)x nomnal value 120%<loss rate opton payoff = (loss rate-120%)x nomnal value Front 120% loss rate 4.Caps, Floors, and Collars (1)Cap( ) (2)Floor( ) (3)Collar( ) ( ) 11

13 Foregn Exchange Rsk 1. Source o Foregn Exchange Rsk Exposure (1) net exposure net _ exposure = ( FX _ assets FX _ labltes ) + ( FX _ bought net _ exposure = net _ foregn _ asset + net _ FX _ bought ) A postve net exposure poston means that we are net long n a currency A negatve net exposure poston means that we are net short n a currency FX _ sold ) 2. On Balance-Sheet hedgng On Balance Sheet hedgng s acheved when a fnancal nsttuton has a matched maturty and currency foregn asset lablty book. <Example> Assume the orgnal exchange rate s USD1.70/CHF. Assume the franc deprecate to USD1.55/CHF after 1 year. Calculate net return of the bank. Assets Labltes Amount (USD) Currency Yeld Maturty Amount (USD) Currency Yeld Maturty 50 mllon USD 8% 1 year 50 mllon USD 6% 1 year 50 mllon CHF 13% 1 year 50 mllon CHF 10% 1 year Ans (1)Assets 50 mllon (n USD) Asset 50x1.08=54 50 mllon (n CHF) Asset 50/1.70=29.41CHF 13% 29.41x1.13=33.23CHF CHF 33.23x1.55=51.51USD = % (2)Labltes 50 mllon (n USD) Labltes 50x1.06=53 50 mllon (n CHF) Labltes 50/1.70=29.41CHF 10% 29.41x1.10=32.35CHF CHF 32.35x1.55=50.15USD = % (3) Net return = average return on assets average cost of funds =5.51%-3.15%=2.37% 12

14 3. Off Balance-Sheet hedgng Rather than matchng foregn assets wth foregn labltes, we may also hedge-off-balance-sheet by takng a poston n the forward/future market whle reman unhedged on the balance sheet. 4.Multcurrency Foregn Asset Lablty Poston (1) Dversfcaton (2) / (3) 13

15 Lqudty Rsk 1. Causes of Lqudty Rsk (1)From Labltes Sde as depostors or polcyholders demand payment (2)From Assets Sde cause bank has made loan commtment to borrowers. 2. Lqudty Rsk of Commercal Banks and Thrft Insttutons (1)Lqudty Rsk From Labltes Sde demand deposts s rather stable, formng the core deposts of the nsttuton lqudty rsk lablty management reserve asset management (2)Lqudty Rsk From Asset Sde loan commtment, letters of credt lablty management, reserve asset management (3)Gaugng an nsttuton s Exposure to Lqudty Rsk Source of lqudty avalable - cash equvalent, or very lqud assets(such as T-bll) - Bank s borrowng ablty of maxmum amount that the bank may readly borrow from money or captal markets. - Excess cash and reserves, defned as those exceedng requred mn amounts uses of lqudty - The amount of funds already borrowed from captal and money market - Any borrowng from the Fed already outstandng Comparng Peer Group Lqudty Ratos - Lqudty Rato = assets/labltes llqud _ assets - lqudty rsk short _ term _ depost - (peer group) lqudty rsk 14

16 Fed lqudty ndex - N - = P I = ( w ) ^ 1 P where I lqudty ndex w proporton of each asset to the total assets P value(prce)that can be realzed f lqudated mmedately P^ value(prce)that can be realzed from an orderly sale - lqudty ndex <Example> Assume that an nsttuton has only 2 equally valued assets-a T-bll that ca be lqudated at ts market value and a loan that can be lqudated at 90% of ts value. The lqudty ndex value for the nsttuton would be (a) 50% (b) 75% (c) 90% (d) 95% Fnancal Gap - Fnancal Gap = average amount of loans average amount of core depost - core depost Fnancal Gap 3. Lqudty Rsk of Lfe Insurance Companes (1) (2) 1991 Frst Executve Corporaton (3) excess reserve 4. Lqudty Rsk of Property-Casualty Insurance Companes (1) (2) (3) (premum) (4) renewals 15

17 (5) ( 911) (6) 5. Lqudty Rsk of Mutual Funds (1)Closed-end fund lqudty rsk (2)Open-end fund lqudty rsk 16

18 Market Rsk 1. market rsk (1)Management Informaton (2)Settng Lmts (3)Resource allocaton (4)Performance evaluaton (5)Regulaton market rsk nternal model Regulatory Model( BIS) 2. nternal model market rsk (1)Rsk Metrcs varance/covarance model fxed ncome, foregn exchange equtes market rsk (2)Hstorcal or Back Smulaton Approach 500 return 500 5% VaR correlaton standard devaton (3)Monte Carlo Smulaton Approach 10, VaR 3. BIS standardzed Framework market rsk (1) Standardzed Framework for fxed Income General rsk charge reflect the product of the modfed duraton and nterest rate shock antcpated for each maturty Specfc rsk charge measure the rsk of a declne n the lqudty of the tradng portfolo over the holdng perod Dsallowance factors long and short poston n dfferent maturty zone are not offset perfectly (bass rsk) Zone Dsallowance factor 1 month 12 month 40% 1 year 4 years 30% 4 years 20 years plus 30% 17

19 (2) Standardzed Framework for Foregn Exchange captal requrement = 8% of the hgher of the aggregate long and short postons (3) Standardzed Framework for Equtes 8% of net long or short poston 4% of total poston of a stock ( long poston + short poston) 18

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