Chapter 24 - MANAGING RISK WITH DERIVATIVES       

FIs can use derivatives to manage interest rate, credit and FX risk.  Also, derivatives generate fee income and profits ($4B QI 2001) for FIs, see "In the News 24-1" on p. 621.    

Spot Market: Cash transactions for immediate delivery (1-3 days) of commodities, securities (bonds, stocks), FX. 

Forward Market:  Agree on P and Q, for future delivery (1 week to 10 years), often customized, nonstandardized contracts for FX, commodities, securities.  Actual exchange of commodity, FX, securities takes place, on expiration (settlement) date.  Secondary markets for forward contracts are usually thin or nonexistent.  Some possibility for default.

Futures Markets:  Exchange-traded standardized securities (size and settlement date), organized exchanges, active secondary market, daily settlement to eliminate default risk, cash settlement, daily price limits.  $3T market for FIs.

Hedging with Forward Contracts

Naive Hedge - Full (100%) "perfect" hedge of a cash asset with a forward or futures contract.  Example: Portfolio managers holds $1m face value 20-year T-Bonds, current price is 97%, or $970,000.  Interest rates are 8%, but the FI forecasts that interest rates will rise to 10% over the next 3 months, causing a large capital loss for FI.  D = 9 years.  To calculate the possible capital loss:    

            Δ% PV Bond =  -  D  *   ΔR / (1 + R) 

            %P =  - 9  *   ( .02 / 1.08)  =  -16.6667%

            $970,000 -  16.6667% =  $808,333 (or a loss $161,667) 

            $97 - 16.6667%  =  $80.8333

Manager can make an off-balance-sheet hedge with a forward contract.  Manager is worried about interest rates rising and bond prices falling, so would want to take a short position and sell T-Bonds forward 3 months, and find a buyer to go long at 97 for $1m face value of T-Bonds in 3 months.  The buyer could be someone who is worried about interest rates going down in the next three months, i.e., a life insurance company planning to invest $1m in three months.  Assume that the life insurance does not have the same forecast about interest rates rising.  Payoff Diagram: 

Suppose that interest rates do rise and the FI has a capital loss of 16.67%, or $161,667, because the P went from 97 to 80.333.  However, they can now buy $1m of face value 20-year bonds in spot mkt at $80.833 (80.333% of face), or $808,333, and can sell to the forward contract buyer at 97, or $970,000, for a gain of $161,667 (off-balance-sheet) to exactly offset the capital loss (on balance sheet).  Any other change in interest rates would result in an off-balance-sheet gain (loss) to exactly offest the loss (gain) on-balance-sheet.     

Result: Naive hedge that immunizes the FI against interest rate risk by using a forward contract perfectly matched to the asset or transaction being hedged. 

Hedging with Futures.  Most FIs can more easily hedge using futures contracts instead of forward contracts.  Why? 

Microhedge is a hedge of a specific account, asset or transaction.  The hedger will normally select a futures contract on an underlying instrument that is as similar as possible to the account to be hedged.  Perfect matches are sometimes not possible for financial futures, and cross-hedges are common, e.g., an FI uses a general T-bond futures contracts to hedge specific interest rate risk for mortgages, CDs, or commercial loans.  The risk that remains from cross-hedging is called basis risk - the residual risk that the price of the asset being hedged (mortgage portfolio, corporate bonds), and the futures contract price (T-Bonds), will not move together perfectly over time.  The more similar the asset and the futures instruments, the less the basis risk.

Examples: a) Using S&P 500 Index futures (or other index futures) for portfolio insurance over the next 6 months; to the degree that the portfolio being hedged and the S&P500 (or other stock index) don't move perfectly together, there is basis risk.  b) GM uses a 3 month T-bond futures contract to hedge interest rate risk for its long-term corporate debt (bonds) to be issued in 3 months. 

Macrohedge is a hedge of an FI's entire balance sheet or portfolio using derivatives, i.e., hedging the overall duration gap of a balance sheet to manage, control or eliminate interest rate risk.  Result: Possible immunization, stability of bank value. 

Question: What if a bank/FI was able to eliminate ALL risk? Return? Response of shareholders? 

Risk-Return Tradeoff.  Optimal amount of risk is not zero, fully hedged balance sheet probably not optimal.  Selective or microhedging probably more likely.  Depends on managerial interest rate expectations, managerial objectives, risk-return tradeoff.  Remember from CH 1 that one of services that FIs provide for the economy is "maturity intermediation," bearing the risk of the maturity mismatch between deposits and loans.   

Accounting Rules for Hedging.  FASB rulings favor microhedges.  Under current FASB rules, gains and losses on futures used in microhedges and the instrument being hedged are marked to market and thus go through the income statement.  Since these should be offsetting that is not a particular problem.  Macrohedges may generate hedging gains or losses on futures contracts, that are recognized in earnings but are not offset because many accounts are carried at book value.  This can be upsetting to management.

Policies of Bank Regulators (Fed, FDIC, OCC). Regulations generally: a) encourage futures for hedging purposes and discourage futures for speculation, b) require disclosure of significant risk positions to shareholders, and c) establish trading limits for derivatives.  

Microhedging with Futures.  Strategy: Take a position in futures contract to offset a loss on the balance sheet due to change interest rate changes.  Example: Table 24-1 on p. 626, Sept. Eurodollar futures at 97.65 for a $1m contract.  Interest rate is 100 - 97.65 = 2.35%.  You can go long or short on the Futures Price of 97.65.  See Figure 24-1 on p. 627. 

1. Assume it is May and an investment of $1m will take place in September.  Worried about interest rates _______, Bond Prices _________.  Go _______ on ED futures.  If interest rates fall below 2.35% to 2%, there will be a gain on the futures contract (.98 - .9765) x $1m = $3,500 that will offset the reduced interest income of $3,500 ($1m x .35%) from the fall in interest rates from 2.35% to 2%.

$1m x .02 (market rate) = $20,000 interest + $3,500 gain on futures = $23,500 / $1m = .0235 or 2.35%

2. $1m needs to be borrowed in September.  Worried about interest rates _______, Bond Prices _________.  Go _______ on ED futures.  If interest rates rise above 2.35% to 2.50%, there will be a gain on the futures contract (.9765 - .9750) x $1m = $1,500 that will offset the increased interest expense of $1,500 ($1m x .15%) from the rise in interest rates from 2.35% to 2.50%.

$1m x .025 (market rate) = $25,000 interest expense - $1500 gain on futures = $23,500 / $1m = .0235 or 2.35%.

3. For an FI with a duration gap: D_A >  D_L(long term loans, short term deposits/RSLs) it is worried about interest rates _____________ and would go ____________ .  For an FI with a duration gap: D_A <  D_L, (short term loans/RSA, long term deposits), it is worried about interest rates _____________ and would go ____________ .   

Macrohedging with Futures (Appendix). 

Review Example 23-3 on p. 607, Duration Gap Analysis for FI. 

FI's exposure to interest rate risk can be measured by its Duration Gap, which takes into account the usual duration/maturity mismatch: D_A > D_L. 

    Equity (E) = Assets (A) - Liabilities (L), and

    ΔE  =  ΔA  -   ΔL

    ΔE =   -( D_A  -  k D_L)  *  A  *    ΔR     

                                                     1 + R

where k = L/A = Measure of the FI's leverage, or D/A ratio. 

Interest Rate Risk Exposure ( ΔE, Changes in Net Worth):

        ΔE = - Adjusted Duration Gap * Asset Size * Interest Rate Shock

Using Duration Gap.  a) If Duration Gap is POS (D_A > D_L), the bank is worried about an INCREASE in interest rates, because an INCREASE in interest rates will DECREASE the Value of the Bank (E).  Interest Rates and Bank Value are inversely (neg.) related.

In Example 23-3, Duration Gap is Pos (D_A= 5 YRs and D_L = 3 YRs).  If interest rates rise from 10% to 11%, the value of the bank will fall by -$2.09m, from $10m to $7.91m, a 21% loss of capital for ONLY a 1% increase in interest rates. 

         ΔE = -2.3 yrs x  $100m  x  .01/1.10 = -$2.09m

For a 2% increase:

        ΔE = -2.3 yrs x  $100m x  .02/1.10 = -$4.18m

For a 3% increase:

        ΔE = -2.3 yrs x  $100m x  .03/1.10 = -$6.27m

Question: What interest rate increase would reduce E to 0 (ΔE = -$10m) and wipe out the bank's equity?

a.        -$10m = -2.3 yrs x $100m x (ΔR / 1.10), solve for ΔR = .0478 or 4.78%  or

b.        $10m / $2.09m = 4.78X * .01 = .0478 or 4.78%

To counter this effect, the bank could adjust the Duration Gap to immunize against interest rate changes/risk.  Alternatively, the bank could hedge interest rate risk on its balance sheet using T-bond futures contracts.  

Strategy: Construct a hedge with futures contracts in dollar amount, F, so that  ΔF =  ΔE, and then any loss on the balance sheet (-ΔE) will be offset by a gain on the futures positions (+ΔF) in the exact same amount.  If  ΔE = -$2.091m, then ΔF = +$2.091m, and the portfolio will be immunized. 

            F($) = (# Futures Contracts N_F x  Price of each contract P_F) = Dollar value of the futures contracts

            ΔF    =   -D_F  *      ΔR        ,  or 

             F                         1 + R

           ΔF  =   -D_F  *  F    *       ΔR     

                                              1 + R

Once we know ΔF (based on ΔE), D_F, Price per Futures Contract (P_F), R, and ΔR, we can solve for the last important variable: # Futures Contracts for an immunization hedge. 

In Table 24-1 (p. 626), September 20-year, T-bond futures contracts are selling for 100-28 or 100 28/32, or 100.875% of face value, or $100,875 for one futures contract.  See payoff diagram Figure 24-A1.  Suppose that D = 9.5 years for these T-bonds.  How many contracts (N_F) should be used to hedge ΔE = -$2.091m against interest rates going from 10% to 11%?   Immunization Approach:

        ΔF  =   -D_F  *   F    *       ΔR     

                                             1 + R

        $2.091m  = 9.5  x  ($100,875 x N_F )  x   (.01 / 1.10)

          N  = 240 contracts OR

We want  ΔF =  ΔE

        -( D_A  -  k D_L)  *  A  *    ΔR     =    -D_F  *   F    *       ΔR     

                                             1 + R                                   1 + R

Since the term ΔR / 1 + R is common to both equations, those terms cancel and we have the Immunization Formula:

        Adjusted Duration Gap * Assets($)  = D_F   x   F($)

                2.3 YRS x $100m =  9.5 YRS x F, and we solve for F. 

            F = $24.2105m TOTAL FUTURE CONTRACT VALUE ($) TO IMMUNIZE

                $24.2105m / $100,875 = 240 T-Bond Futures Contract

If interest rates do go up to 11%, the value of the bank falls by ΔE = -$2.091m, On Balance Sheet.  The Off Balance Sheet futures payoff is as follows:

        ΔF = 9.5 x  (240  x  $100,875) x (.01/1.10) =  +$2.091m   

New Example 24-4, p. 4 in Appendix 24A:

Assume that P_F = $97,000 and D_F = 9.5 years. 

        $2.091m  = 9.5  x   (97,000 x N )  x   (.01 / 1.10)

        N = 249.60 or 249 contracts  OR

           2.3 YRS x $100m =  9.5 YRS x F

        F = $24.2105m / $97,000 = 249 Contracts

If interest rates do go up to 11%, the value of the bank falls by ΔE = -$2.091m, see Table 24-A1, On Balance Sheet.  The Off Balance Sheet futures payoff is as follows for the short position:

        ΔF = 9.5 x  (249  x  $97,000) x (.01/1.10) =  $2.086m

Difference between -$2.091m and +$2.086m ($5,000) is due to rounding contracts down to 249 from 249.60. 

BASIS RISK

Comes about because of imperfect cross-hedging.