IAI Actuarial Core Principles · Business Economics

Role, structure and stability of the financial system: formula sheet

Full chapter guide

Key formulas

Financial intermediation (idea): Savers → intermediary → borrowers; Intermediaries take deposits or premiums and lend or invest them. They bear part of the risk and costs of matching the two sides.
Five core functions: Savings-to-investment channel; payments; risk pooling and transfer; liquidity; price information; Use this list as a checklist for any 'role of the financial system' question.
Maturity transformation: Short-term liabilities (deposits) funding long-term assets (loans); Useful but creates liquidity risk. It is a benefit and a source of fragility.
Real rate of return (approximate): Real rate ≈ nominal rate − expected inflation; Savers care about real returns. The exact relation is (1 + real) = (1 + nominal) ÷ (1 + inflation).
Money market vs capital market: Money market: maturity ≤ 1 year. Capital market: maturity > 1 year, plus equity (no fixed maturity); One year is the usual dividing line. Equity has no maturity, so it sits in the capital market.
Primary vs secondary market: Primary: issuer receives the funds. Secondary: investors trade with each other; The issuer is not paid on secondary trades.
Core functions of intermediaries: Pooling + maturity transformation + risk diversification + lower transaction costs + information screening; Use this list to structure any 'role of intermediaries' answer.
Direct vs indirect finance: Direct: saver → borrower via markets. Indirect: saver → intermediary → borrower; Banks and insurers are indirect finance; bond issues to investors are direct finance.
Simple money multiplier: m = 1 ÷ r; r is the reserve ratio as a decimal. This is the maximum multiplier, assuming no cash leakage and no excess reserves.
Maximum total deposit creation: Total new deposits = initial deposit ÷ r; The initial deposit is included in the total. Lending created = total deposits − initial deposit.
Multiplier with cash leakage: m = (1 + c) ÷ (r + c); c is the cash-to-deposit ratio and r the reserve-to-deposit ratio. This applies to the money supply multiplier on the monetary base. State the assumption used.
Geometric series for rounds of lending: Total = D × (1 + (1 − r) + (1 − r)² + ...) = D ÷ r; Valid for 0 < r ≤ 1, so the series converges.
Bank balance sheet identity: Assets = Liabilities + Capital; Reserves and loans are assets. Deposits are liabilities.
Leverage ratio: Leverage = Total assets ÷ Equity; Higher leverage means a smaller fall in asset value wipes out equity.
Equity wipe-out fall in assets: Fall in asset value that eliminates equity (%) = 1 ÷ Leverage × 100; With leverage of 20, a 5% fall in assets removes all equity (ignoring other changes).
Solvency condition: Solvent if Assets ≥ Liabilities; insolvent if Assets < Liabilities; A bank can be solvent but illiquid if assets cannot be sold quickly at fair value.
Fractional reserve position: Liquid reserves ÷ Deposits = reserve ratio; If withdrawals exceed the reserve ratio, the bank must sell other assets or borrow.
Capital adequacy ratio: Capital ratio = Eligible capital ÷ Risk-weighted assets; Risk-weighted assets give riskier assets a higher weight. A bank must keep this ratio at or above the regulatory minimum.
Risk-weighted assets: RWA = Σ (exposure × risk weight); Sum over all asset classes. Cash and government bonds usually carry low weights; unsecured loans carry higher ones.
Leverage ratio: Leverage ratio = Tier 1 capital ÷ Total (unweighted) exposure; A simple backstop that does not depend on risk weights.
Liquidity coverage ratio: LCR = Stock of high-quality liquid assets ÷ Net cash outflows over 30 days; Must be at least 100% under the Basel standard.
Prudential split: Microprudential = safety of each firm; Macroprudential = stability of the whole system; Use this one-line contrast in any compare question.

Quick revision

The main functions are channelling savings to investment, transferring and pooling risk, providing payments and pricing assets.
Money markets deal in short-term funds; capital markets deal in long-term funds.
Financial intermediaries reduce transaction costs and information problems between savers and borrowers.
Banks lend out part of their deposits, and lending creates new deposits in the system.
The money multiplier depends on the reserve ratio; a higher reserve ratio means less money creation.
Central banks influence credit through policy rates, reserve requirements and open market operations.
A bank run happens when depositors lose confidence and withdraw funds faster than the bank can pay.
Systemic risk is the risk that one failure spreads through the whole system.
Excess leverage and asset bubbles often precede a crisis.
Capital and liquidity requirements aim to make banks able to absorb losses and meet withdrawals.
Deposit insurance reduces the chance of runs but can encourage excess risk-taking, known as moral hazard.
A central bank can act as lender of last resort to solvent but illiquid banks.

Common mistakes

Listing functions without explaining how they work. Fix: Give each function a mechanism and a benefit, even if short.
Confusing financial intermediation with direct finance. Fix: In direct finance, savers hold the borrower's securities. In intermediation, an institution stands in between and issues its own claims, such as deposits.
Saying the issuer receives money when shares are traded on a stock exchange. Fix: Remember that the issuer is paid only in the primary market. Secondary trades move money between investors.
Placing equity in the money market or calling it a short-term instrument. Fix: Maturity is the contractual term. Equity has none, so it belongs to the capital market.
Using the multiplier as the exact increase in money supply. Fix: Call 1 ÷ r the maximum. Real creation is lower because of cash holding and excess reserves.
Entering r as a percentage, such as 1 ÷ 10 instead of 1 ÷ 0.10. Fix: Always write r as a decimal or fraction before inverting.
Treating liquidity risk and solvency risk as the same thing. Fix: Liquidity is about timing of cash. Solvency is about assets versus liabilities. Check the balance sheet first.
Saying bank runs happen only to weak banks. Fix: Runs can be self-fulfilling. Because of information asymmetry, even a sound bank can face one if depositors fear others will withdraw first.
Treating microprudential and macroprudential regulation as the same thing. Fix: Ask what is being protected. One firm's solvency is micro. The stability of the whole system, including credit cycles and interconnections, is macro.
Dividing capital by total assets instead of risk-weighted assets. Fix: Multiply each exposure by its risk weight, add them up, then divide. Only the leverage ratio uses unweighted exposure.

Exam tips

Use the five-function checklist as your skeleton. Examiners reward named functions with a clear mechanism.
Always add a short example. A bank, an insurer or a stock exchange is enough.
In 'discuss' or 'evaluate' questions, include at least one limit or risk to earn the balance marks.
Keep terms exact: liquidity, maturity transformation, diversification, intermediation and price discovery.
For MCQs, watch for options that blur risk transfer with risk elimination. The system moves and shares risk but does not remove it.
Always give the dividing feature first (maturity, or who receives the funds), then examples.
In written answers, tie each institution to its type of liabilities. This is where marks separate students.
For MCQs, apply maturity and stage tests before reading options in detail.