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SM-85-7 c E E o u c .2 > a) at c V E k. * a O a> t/) a A Series of Occasional Papers in Draft Form Prepared by M em bers 'o A N O TE ON M ANAGING D EPO SIT FLO W S W IT H CASH A N D F U T U R E S M A R K E T D EC ISIO N S G. D. Koppenhaver so > so so < m OS > z * o ■n n X n > n o SM-85-7 A Note on Managing Deposit Flows with Cash and Futures Market Decisions* by G. D. Koppenhaver Research Department Federal Reserve Bank of Chicago 230 South LaSalle Street Chicago, Illinois (312) 322-5858 March 1984 Revised August 1984 *The author 1s grateful to an anonymous reviewer for helpful comments. The views expressed here are those of the author and are not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System. A Note on Managing Deposit Flows with Cash and Futures Market Decisions Abstract As deposit markets become less regulated, financial Intermediaries must focus more of their attention on the explicit pricing of deposit accounts. An Implication of pricing deposits 1s that the Intermediary faces a random source of funds when future deposit supplies are unknown. This note shows that financial future contracts can be used to hedge the risk of deposit withdrawals, allowing the financial firm to set lower deposit rates than 1t would without futures trading. A model of risk averse banking behavior 1s constructed to determine the relationship between hedging deposit withdrawals and setting deposit rates. Using the certificate of deposit futures contract to hedge demand and savings deposit withdrawals, an empirical application of the model reveals that the possible gains 1n profitability from setting deposit rates and hedging withdrawals are small but statistically significant. 1 A Note on Managing Deposit Flows with Cash and Futures Market Decisions With the recent deregulation of deposit accounts and the increased competition in the banking industry, financial firms are focusing more attention on the pricing of their deposits.1 Highly concentrated demand, savings, and time deposit markets permit this price-setting behavior, and traditionally, depository financial intermediaries agree to accept whatever quantity of deposits forthcoming at a predetermined deposit rate. behavioral mode is prone to problems of bank liquidity, however. This Setting deposit rates ex ante, the intermediary is uncertain about the quantity and mix of liabilities it will have on its balance sheet ex post. As a solution to this liquidity problem, bank liability management can be used to fill out the financial firm's balance sheet ex post. The essence of most ex post liability management strategies is the selection and use of perfectly competitive funds markets where the desired quantity of funds can always be purchased or sold. This implies that if a deposit rate-setting bank has access to a perfect funds market, variations in the cost of funds are a secondary problem to variations in deposit quantities; the bank's main concern is filling out its balance sheet (see Mason (1979)). This note presents an alternative to the ex post liability management policies used to satisfy an intermediary's balance sheet constraint. A position in a financial futures market is used jointly with deposit ratesetting to hedge, ex ante, the quantity of funds forthcoming. That is, the futures hedge is an anticipatory hedge of a liability quantity risk faced by the financial intermediary. Hedging permits the separation of withdrawal risk considerations from profitability considerations in setting deposit rates. Ex ante liability management through financial futures hedging and deposit rate 2 setting becomes a substitute tool for controlling thrift liquidity relative to ex post liability management. This application of financial futures hedging is different than the literature on the anticipatory hedging of bank liability interest rates (see Franckle and Senchack (1982), Parker and Daigler (1981), and Speakes (1983)) because it explicitly considers the management of the deposit quantity risk faced by rate-setting intermediaries. Futhermore, cash and futures market decisions are determined simultaneously. I. A Model of Deposit Flow Hedging It is assumed the bank uses two tools to manage deposit flow uncertainty: trading CO futures contracts and setting deposit interest rates. To manage deposit withdrawals, the bank can buy CD futures contracts and raise deposit interest rates. The purchase of futures contracts represents an anticipatory hedge of deposit outflows (a funding hedge) because it acts as an alternative source of funds. If withdrawals are closely associated with a fall in market interest rates, the profits from a long (buy) futures position augment the reduced cash market sources of funds. face of deposit outflows. Bank profits can be sustained in the Conversely, expected deposit inflows and higher market interest rates create less need for a funding hedge; the long position should be reduced or possibly changed to a short (sell) position to increase bank profitability. In conjunction with the funding hedge, the bank can raise (lower) deposit interest rates to counter expected deposit withdrawals (inflows), assuming a positive interest elasticity of deposit supply. Assume the bank has a one-period planning horizon. At the beginning of the period, the bank must decide on the CD futures position, X, and the deposit interest rate, R^. At this time, the bank knows the current CD futures price, (1-R^), the rate on purchased funds, RB>RQ , and the 3 loan revenue at the end of the period, R|_L, but does not know the level of deposits, D, or the CD futures price, (1-Rx), at the end of the period (Tildes indicate random variables realized in the future.) When deposits are realized and the futures position is offset, bank borrowing, B, takes place to fill out the balance sheet. perfectly competitive. The market for these funds is assumed to be Let D be D = D(R0)+e, aD/aRp > o, aD/ae > o (l) where 0 is the random change in deposits over the planning period, unknown ex ante but with a known subjective probability distribution. Bank profits at the end of the period are given by:3 n = R i_l + [(1-Rx) - (1-Rx)]x - Rb B - RpD = RLL * (RX - Rx)X - RBB - RpD. (2) Note that if futures prices fall and interest rates rise at the end of the period, selling futures contracts (X < 0) at the start of the period is profitable, while if prices rise and interest rates fall, buying futures contracts (X > 0) is profitable. For simplicity, initial margins and variation margin calls are ignored. The bank's problem is to make two ex ante decisions, X and Rp, and one ex post decision, B, that will maximize the expected utility of profit subject to the balance sheet constraint at the end of the period. These decisions are based on the bank's subjective expectation about future events, described by the joint cumulative density F(Rx,o). It is assumed that this joint distribution does not change over the planning period. The decision problem can be written* Maximize E[max U(n)| F(Rx,e)] x,Rpa o B a o subject to: L=(Rx-Rx)X+B+D (3) 4 where E Is the expectations operator, and U Is a risk averse utility function such that U'(n) > 0 and U"(n) < 0 (a prime Indicates derivation). Assuming bank management 1s constant absolute risk averse and the joint distribution of random variables 1s normal, the objective function 1n expression (3) can be rewritten 1n a mean-variance expected utility framework, after substituting for B from the balance sheet constraint. The optimal solutions can easily be shown to be 5 X* „ E(RX - RX) ( H R B) + (RB - R$)Cov[e,Rx ] YVar[Rx] R0 = Rb + ED(ae - 1) (4) Var[Rx ] + X* Cov[e,Rx ] YVar[e] (5) Var[e] where y 1s the Index of risk aversion, Var represents variance, Cov represents covariance, a* = (RB - Rq )/Rb , and c = (aD/aRQ)(Rq /D)• The variable a* 1s Interpreted as the bank's percentage funding margin on a dollar of deposits; e Is a constant deposit rate elasticity of deposit supply. Both a* and e are non-negative. In the right hand side of equation (4), the optimal futures position 1s written as the sum of two terms: term. an expectations term and a deposit risk Initially, let the expectations term be zero. In a banking Industry offering unregulated deposit Instruments, Cov[e,Rx] > 0 1f futures markets move 1n the same direction as cash market rates. That 1s, deposit outflow are associated with lower CD rates, deposits Inflows with higher CD rates. Since (Rb - Rq ) > 0, the optimal futures position represents a long hedge of the anticipated risk. If deposit outflows and lower Interest rates occur, the profits from a long hedge substitute for the loss of deposits. A non zero expectations term reinforces the Incentive to take a long position 1f rates are expected to fall. 5 In the absence of futures trading, the solution to the f1rm-theoret1c model would be given 1n equation (5) with the third term on the right hand side equal to zero. + * If 0 < e < 1/a , then (Rg - Rq ) > 0. In the the nonhedging solution, expected deposit outflows are managed by raising deposit rates, expected deposit Inflows by lowering deposit rates. These qualitative effects are preserved when futures trading 1s Introduced, but deposit Interest rates with a funding hedge (X*> 0) are lower than deposit rates without hedging. Low deposit rates may exacerbate the risk of bank deposit withdrawals; hedging the withdrawal risk 1n the futures market makes low deposit rates less risky. Alternatively, a large expected rise 1n Interest rates could result 1n a short futures position (X*< 0). Deposit Interest rates would then be set higher with futures trading than without futures trading. A short futures position offers no protection from deposit withdrawals and 1s speculative; to compensate, the level of deposit rates must be raised. In this model, offering higher deposits rates to gain deposits occurs only 1n conjunction with futures speculation; futures market risk 1s substituted for deposit market risk 1n maximizing expected utility. II. Quantity Risks and the CD Futures Market This section estimates the hedging effectiveness of the CD futures market by comparing the performance of the optimal strategy 1n equations (4) and (5) with a routine hedging strategy and a nonhedging strategy. f1rm-spec1f1c data for L, Cov[e,Rx], ED, and Var[e]. This requires It 1s unlikely that any existing financial Intermediary faces a situation exactly satisfying the assumptions of the model, but equations (4) and (5) can be simulated using Report of Condition data compiled by the Federal Reserve. Commercial banks with domestic assets greater than $750 million report their assets and liabilities an a mid-weekly basis (170 banks total).6 Since the model 1n section one assumes a single homogeneous source of deposits, the average bank's 6 sum of demand and savings deposits is used to calculate e = D-D and Var[e]. To capture the effects of changing deposit volitility, all variances and covariances are recalculated for each new hedging period. Rl is taken to be the weekly average prime rate on business loans; Rg is taken to be the rate on three-month CDs. Gross loans excluding federal funds sold are used to measure bank lending. The simulation period begins in September 1981 and ends in June 1983. Wednesday settlement prices for the nearby CD futures contract were collected from the Wall Street Journal to calculate E(Rx - Rx). Var[Rx], and Cov[e,Rx]. The time period contains 46 non-overlapping opportunities for hedging as a result. Ex post values were used for expected CD futures interest rates and expected deposits. Two elements of equations (4) and (5) remain to be specified. is the value of the constant absolute risk averse index, y. The first Rather than make an ad hoc assumption about any particular index value, the simulation is run with a variety of values ranging between lxlO-^ and lxl0~7. The simulation results reported below are for two index values, lxlO-4*8 and lxlO-5*4 . Values larger than lxlO-4*8 did not significantly change the results, while values smaller than lxlO-5*4 generated negative deposit rates.7 The second variable to be specified is the elasticity of deposit supply, c . Since the simulation explicitly prices the total of demand and savings deposits, a proxy for e could be obtained from estimates of the interest elasticity of money demand. Barro and Santomero (1972) find the interest elasticity of household money demand to be -1/2, although their elasticity is with respect to the interest rate differential between savings and loan share dividends and commercial bank demand deposit rates. If the level of share dividend rates is used, they estimate an interest elasticity of -1. In light 7 of this, simulation results are reported for four different elasticities of deposit supply, ranging from .1 to 1.0. The smallest elasticity measures come from estimates of the short-rate Interest elasticity of money demand and the largest from estimates of the long-rate elasticity and the work of Barro and Santomero. Results are also reported with e =1.5, for comparison purposes. Table 1 presents the simulation results.8 of hedge positions placed by the bank. Column (2) represents the number Column (3) 1s the proportion of total demand and savings deposits hedged 1n the CD futures market.9 Column (4) is the ratio of the optimal hedge, determined in equations (11) and (12), to the routine hedge of deposit withdrawal risk, X, A routine hedge is defined as a hedge equal to 100% of the absolute value of the deposit change. In the fifth * ★ column, H(X ,Rg) 1s the percentage change 1n the variability of unhedged * profits when the optimal decisions X * and Rg are used. Columns ( 6 ) , (7), and (8) are defined similarly but with respect to combinations of the optimal, nonhedging, and routine hedging decisions. Rg and Rg are the deposit Interest rates simulated for the nonhedging and routine hedging situations, respectively. * * In column ( 9 ) , P(X ,Rg) represents the percentage change 1n JL bank profits when the optimal decisions X ★ — and Rg are used. — P(X, Rg) in column (10) 1s defined similarly with respect to the routine hedging decisions. Finally, column (11) contains the mean difference (Rg - Rg) , for the respective simulations. After a close examination of Table 1, several comments can be made. * First, * the optimal strategy 1n equations (11) and (12), (X , Rg), implies a small futures trading position relative both to total deposits and to the routine hedging position. Note that the futures positions are long hedges, Indicating Cov[e,Rx] 1s positive on average. Second, at low elasticities of supply, Implementing the ( X* , Rg) strategy 1s likely to Increase the 8 variability of bank profits (column (5)). However, the increase in the variability of profits is due to the increased variability of deposit rates in the presence of futures rather than a lack of hedging effectiveness in the CD futures market. This is verified in column (6) where the percent change in the variability of unhedged profits is calculated assuming deposit rates are set at the higher, nonhedging level. Third, hedging deposit withdrawals and jointly setting deposit rate is likely to increase bank profits, especially at lower elasticities of deposit supply. The percentage increase in profits is estimated at less than 100 basis points and is always significant (column (9)). pertains to the routine hedging results. The fourth and final comment Columns (7), (8), and (10) show that the performance of a routine hedging strategy is highly variable, depending on the value of the risk aversion index. Routine hedging may increase or decrease the variability of unhedged profits, although the level of profits is never significantly affected. . * In sum, the possible hedging effectiveness of the optimal strategy (X ,Rq ) and the CD futures market is somewhat difficult to interpret. On the one hand, the simultaneous decisions to hedge deposit withdrawals and set'deposit interest rates tend to increase the variability of unhedged profits. Even after adjusting for the increased variability of profits resulting from the deposit rate decision, the percent reduction in the variability of profits when hedging deposit withdrawals is substantially smaller than the results reported by Ederington (1979) and Franckle (1980) for hedging pure interest rate risk. The results in Table 1 imply the link between deposit flows and CD futures rates is not very strong, at least for the average bank reporting weekly asset and liability positions to the Federal Reserve. On the other hand, if the purpose of the hedge is to maintain the intermediary's level of profits in the face of deposit withdrawals, the optimal strategy (X*,Rq ) 9 Table 1 Average Two-Week Futures Trading and Interest Rate Results, Septerriber 1981 - June 1983 (2) (1) c N (3) (4) X*/D X*/X A. (5) 1h (x *, r J,) (6) H(X*,Rq ) (7) (8) H(X,R0) H(X,Rq ) (9) a. * P(X*,RD) (10) (ID P(X,Rd) o * D(Rq ,Rd ) Constant Absolute Risk Aversion Index; = 1 x 10--4.8 .1 45 .92% (. 14)a 47.98% (5.31) 2.77% (.43) -2.08% (.32) 11.16% (2.46) 11.30% (2.59) .78% (.11) -.15%* (.25) .06% (.01) .3 45 .88 (.13) 46.48 (5.28) 2.25 (.34) -2.08 (.32) 13.06 (2.78) 13.15 (2.96) .68 (.10) -.13* (.24) .05 (.01) .5 45 .84 (.13) 45.18 (5.28) 2.04 (.32) -2.08 (.32) 15.12 (3.13) 15.21 (3.34) .63 (.09) -.12* (-23) .05 (.01) 1.0 43 .80 (.12) 44.23 (5.30) 1.47 (.30) -2.18 (.32) 21.74 (4.35) 21.53 (4.67) .53 (.08) -.06* (.23) .04 (.01) 1.5 43 .74 (.11) 42.07 (5.32) 1.30 (.26) -2.18 (.32) 27.82 (5.58) 27.74 (5.93) .48 (.07) -.08* (.21) .03 (.01) B. Constant Absolute Risk Aversion Index = 1 x 10--5.4 .1 43 2.48% (.37) 83.87% (4.44) 1.08% (.25) -1.61% (.25) -3.57* (1.94) -1.48% (.26) .92% (.12) -1.05*% (.92) .15% (.02) .3 43 1.95 (.30) 74.79 (5.02) .06 (.20) -1.81 (.27) -1.54* (.78) -1.13 (.36) .51 (.10) -.14* (.24) .06 (.01) .5 43 1.72 (.28) 69.75 (5.23) -.25* (.20) -1.85 (.28) -1.15* (.80) -.70 (.48) .44 (.09) -.15* (.24) .05 (.01) 1.0 42 1.45 (.24) 62.67 (5.62) -.48 (.22) -1.88 (.28) -.04* (.95) -.80* (.91) .36 (.08) -.21* (.24) .03 (.01) 1.5 40 1.33 (.22) 58.65 (5.83) -.57 (.21) -1.87 (.25) 2.58* (1.39) 3.23 (1.55) .51 (.22) -.16* (.24) .03 (.01) aStandard error of the mean. *Not different from zero at the 5% significance level. 10 appears to perform well. The question of what the appropriate measure of hedging effectiveness should be when cash and futures decisions are made jointly merits further research. Ill Implications The results presented here have two important implications. To begin with, the need for financial futures hedging by financial intermediaries is often questioned because any hedge of the interest rate risk associated with an existing cash market position can be duplicated by the purchase and sale of cash market instruments with different maturities. However, even if the interest rate sensitivities of a financial firm's assets and liabilities are perfectly matched, the presence of deposit flow uncertainty justifies a role for financial futures hedging as it is viewed here. In the extreme, a Phoenix savings and loan association could benefit from hedging deposit withdrawals if it is faced with liquidity risk problems. This use of hedging by a Phoenix is in contrast to Guttentag's (1983) argument that a Phoenix may want to hedge its interest rate risk to stabilize the income of the FSLIC. The results presented here also have implications for public policy. With respect to the regulation of financial futures trading by intermediaries, the analysis here indicates that while the futures hedge lowers the variability of unhedged profits when considered in isolation, the interaction of the futures decision and other joint decisions can increase the variability of unhedged profits. Should banks be required to make futures trading decisions without regard to other cash market decisions and vice versa? If so, the gains from preventing joint cash and futures market decisions must be greater than the suboptimal allocation of financial resources resulting from sequential decision-making. 11 VI. Footnotes throughout this paper the terms "bank", "financial firm," and "financial intermediary" are used synonymously. 2 The framework used here is related to the model developed by Sealey (1980). 3 This model ignores the quantity risks associated with bank loans such as default and prepayment risk. The model here also treats the two cash market sources of funds, B and D, as discount instruments. If interest is not paid on bank liabilities when the level of deposits is revealed, the model would have to be recast in a two-period framework, complicating the analysis. *The balance sheet constraint is expression (3) explicitly treats futures trading profits (losses) as a source (use) of funds. In reality, a bank's futures position is treated as an off-balance sheet item with trading profits and losses appearing in the income statement. Dropping (Rx-Rx)X from the balance sheet constraint would make no difference in the qualitative results presented below. 5a sufficient condition for a maximum in expression (4) is that the utility function demonstrate risk aversion. 6This data was obtained from the Federal Reserve Bulletin, volumes 67-69. 7The static simulation was conducted using the SAS/ETS procedure SIMNLIN with 100 maximum iterations for the algorithm. 12 ®A few of the bank specific Items used 1n the simulation are as follows (means over the simulation period with standard error in parentheses). L (in millions) 2,828 (15) g D (in millions) $1,605 (32) Cov[0,Rx] 57,097 (10,240) For the purposes of the simulation, the optimal futures hedge expressed in equation (11) was restricted to be no larger in absolute value than the routine hedge, although it could be smaller. This restriction was imposed so that the bank's futures trading position would conform to the current regulatory guidelines for bank use of financial futures. These guidelines were issued simultaneously by all those bank regulatory agencies in November 1979 (revised in March 1980) and require that financial futures positions be a bona fide hedge of overall exposure, leaving the specifics of the hedging program up to the individual bank. For national banks, consult Banking Circular No. 79 issued by the Comptroller of the Currency; for insured nonmember banks, consult Banking Letter No. 17-80 issued by the FOIC. 13 V. References Barro, R. J. and A. J. Santomero, 1972, Household money holdings and the demand deposit rate. Journal of Honey, Credit and Banking 4, 397-413. Ederington, L., 1979, The hedging performance of the new futures markets, Journal of Finance 34, 154-170. Franckle, C., 1980, The hedging performance of the new futures markets: comment, Journal of Finance 35, 1273-1279. Franckle, C. and A. Senchack, Jr., 1981, Economic considerations in the use of interest rate futures, Journal of Futures Markets 2, 107-116. Guttentag, J. M., 1983, A note on hedging and solvency: the case of a phoenix, Journal of Futures Markets 3, 137-141. Mason, J. M., 1979, Modeling mutual funds and commercial banks: a comparative analysis, Journal of Banking and Finance 3, 347-353. Parker, J. and R. Daigler, 1981, Hedging money market CDs with Treasury bill futures, Journal of Futures Markets 1, 597-606. Sealey, C., Jr., 1980, Deposit rate-setting, risk aversion, and the theory of depository financial intermediaries, Journal of Finance 35, 1139-1154. Speakes, J.K., 1983, The phased-in money market certificate hedge, Journal of Futures Markets 3, 185-190.
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