Understanding Banking Theories: Deposit Expansion, GAP, Duration Analysis, and Principal-Agent Dynamics

1. Chapter 17:Learning Objectives • Theories of the Banking Firm: • Multiple deposit expansion • A graphical exposition and some applications • GAP & Duration Analysis • The Principal-Agent View

2. A Simplified Balance Sheet Liabilities Assets DEP=Deposits ADV=Bank of Canada Advances CUR=Cash RES=Target reserves L=Loans SEC= Securities

3. Multiple Expansion of Deposits: The Basics

4. Multiple Deposit Expansion • Based on the assumption of a reserve requirement. No longer formally exists in Canada BUT banks need to keep reserves • Reserve target and Excess reserves: the starting point of the multiple expansion approach • A Banking system with a single bank vs. multiple banks: does it make a difference? Not really. • Initial assumptions: • banks maintain target reserves at all times • there are no “cash drains” in the banking system

5. The Deposit Multiplier • The basic theory predicts that inflows or outflows of funds lead to deposits in the banking system to rise or fall by a multiple of the original change • The basic theory also has implications for changes in the money supply which is linked to CUR and DEP

6. Multiple Deposit Expansion:The Basics M1=money supply=CUR+DEP RES=rr • DEP, where rr= target reserve ratio rr is FIXED  DEP = (1/rr) • RES  A more flexible model DEP = (1/(rr+er(R)) • RES Where er=excess reserve ratio

7. Multiple Deposit Expansion: Examples • Effect of a currency drain  reduces multiplier • Effect of a change in the composition of deposits  different deposits may have different target reserves which also can affect the multiplier [TABLE 17.3] • Transfer of deposits among different types of financial institutions can affect multiplier if, for regulatory or other reasons, target reserves differ across institution types [TABLE 17.4]

8. Deposit expansion: Change in deposit composition

9. Impact of shift between bank and near bank

10. A Simple Theory of the Banking Firm • Assumes there is a behavioural relationship between DEP and other economic variables such as interest rates, income and wealth  EQUATION 17.10 • Assumes that the objective of the banking firm is to maximize profits MR=MC is the required condition FIGURE 17.1 • Profits are the difference between Revenues and Costs which are assumed, for simplicity, to be a function of Deposits, asset returns and deposit costs  EQUATION 17.13

11. MCDEP Interest rate ACDEP Ra Spread ARDEP RDEP MRDEP Deposits DEP* Figure 17.1. Profit Maximization of the Banking Firm

12. Applications of the Banking Firm Model • Helps explain the spread and its link to the degree of “competitiveness” in the financial sector [FIGURE 17.2] • Helps explain how the banking firm reacts to changing costs or technological developments • Is more useful as a pedagogical device than in practice

13. MC Interest rate R’a AC • • • R*a • 1 Ra† MR†=AR† 3 (Competitive Case) 4 • R+DEP • AR R*DEP • • R’DEP 2 R’DEP MR(Monopoly power Case) Deposits DEP’ DEP* DEP† Figure 17.2. The Impact of Government Regulations on the Market for Deposits

14. A More Practical Alternative:GAP and Duration Analysis • Not all assets / liabilities are equally sensitive to interest rate changes • Profitability in the short-run will be a function of changes in the “value” of those components in the balance sheet which are sensitive to interest rates  GAP= IRSA - IRSL • Not all assets / liabilities have the same term to maturity. This can affect the “price” of balance sheet items  DURATION and duration GAP concepts  dur GAP= durA (A/L) - durL

15. GAP Analysis: Numerical Example

16. Duration Analysis: The Basic formulas Stream of income is written P= $X1/ (1+R) + $X2 / (1+R)2 +…+ $Xn/(1+R)n Duration = A weighted average (weights are years before income is received) as a percent of the price of the asset Or Dur = 1 [$X1/(1+R)]/P + 2 [$X2/(1+R)2]/P +…+n [$Xn/(1+R)n]/P

17. The Principal - Agent Approach to the Banking Firm • Banks are typically owned by Shareholders and run by Managers • The two groups may have conflicting objectives • shareholders want to maximize the stream of dividends • managers may wish to maximize their income, perks • Table 17.6: a numerical example • If we think of the relationship between the two groups are a “game” we can develop policies to ensure that the banking firm’s profits are maximized

18. Principal-Agent Problem:Ilustration

19. Summary • Understanding the behaviour of banks can be accomplished in a number of ways: • multiple expansion of deposits approach • the theory of the banking firm approach • GAP and DURATION analysis • Principal-Agent approach • Each theory focuses on different aspects of banking firm behaviour