Risks of Financial Institutions: what the chapter asks you to explain

The clean Chapter 7 slides begin here, after the annotated version on PDF 12–16 and the blank page 17. They repeat the same opening ideas, then continue into the remaining risk categories. The chapter is not a list of nine unrelated definitions. Its sequence asks you to explain what risk means, how a financial institution’s activities create it, how risks interact, and why losses ultimately threaten capital.

The opening management objective is to increase returns for the institution’s owners while controlling the risks taken to earn them. A bank earns interest partly because it accepts claims whose repayment, funding cost or market value is uncertain. An insurer promises compensation against uncertain events. Simply eliminating every exposure would also eliminate much of the service that makes the institution useful.

The phrase “no profit without risk” should therefore be read as a risk–return management problem, not a promise that taking more risk always produces more profit. Expected return is what is anticipated before the outcome; realized return is what actually happens. A poorly priced loan can have both substantial risk and inadequate expected compensation. The manager needs to ask whether the expected reward covers the exposure, operating costs and the capital needed to bear losses.

The title’s reference to capital anticipates the endpoint. If assets lose value or an obligation becomes more expensive, the owners’ residual claim shrinks. With assets A and liabilities L, equity is E = A − L. Equity is not a separate bag of cash: it is the balance-sheet cushion that absorbs losses. We will first identify the source of a loss, then follow its route to that cushion.

What do we mean by risk?

Financial risk is the possibility that an outcome differs from the expected outcome, especially in a way that leaves the institution worse off. Two dimensions matter: how likely the adverse event is and how large its consequence would be. A small frequent processing loss and a rare catastrophic funding failure are both risks, but they require different controls.

The source calls risk the raw material of the FI’s business. This means that useful intermediation often involves exposure rather than complete certainty. The task is to identify the exposure, price it in the terms offered to customers, manage it through limits, diversification or hedging, and hold enough capital to withstand plausible losses. Pricing risk and absorbing risk are different tasks: charging a premium does not make the bad event impossible.

The source’s arrow from higher risk to higher expected return describes the compensation investors require for bearing risk. It is not a mathematical guarantee about any realized investment. If a borrower defaults, a high contractual interest rate does not turn the missing payment into income. Nor does every extra risk earn a premium: avoidable operational mistakes may simply destroy value.

The nine risks of financial intermediation

The source presents the nine risks in the following order. For each, identify the first thing that changes. This helps distinguish the initiating risk from the later damage it causes. For example, a borrower’s missed payment begins as credit risk; the resulting cash shortage may then become liquidity risk.

1. Interest rate risk: market rates change while assets and funding reset or mature at different times. 2. Credit risk: a borrower fails to deliver promised cash flows in full. 3. Off-balance-sheet risk: a contingent commitment creates a loss or funding need when its triggering condition occurs.

4. Foreign exchange risk: exchange-rate movements change the home-currency value of net foreign-currency claims. 5. Market risk: traded positions lose value as interest rates, exchange rates, equity prices or other market prices move. 6. Country or sovereign risk: government action or sovereign default prevents or obstructs cross-border repayment.

7. Technology and operational risk: systems, processes, people or external events disrupt the institution or impose losses. 8. Liquidity risk: cash cannot be raised when required on acceptable terms, potentially forcing distressed asset sales. 9. Insolvency risk: losses exhaust the institution’s capital cushion.

These categories overlap in a causal chain. A trading system failure may create a market loss; depositors may react by withdrawing; fire-sales may then deepen the loss. Insolvency is therefore both a named risk and a possible final consequence of the others. The later slides return to this interaction explicitly.

Interest rate risk: the cost of transforming maturities

A financial institution may offer savers short-term claims while financing borrowers for longer periods. That is part of asset transformation. It is also why the asset and liability sides do not always respond to a rate change at the same moment. A loan may keep its fixed earning rate after the deposit used to fund it has matured and must be replaced.

Let M_A denote asset maturity and M_L liability maturity. When M_A > M_L, the institution is short-funded: its funding expires before its asset. Its replacement funding cost is uncertain, producing refinancing risk. When M_A < M_L, it is long-funded: the asset returns cash before the funding obligation ends. The rate earned when that cash is redeployed is uncertain, producing reinvestment risk. “Short-funded” here does not mean a short-sale trading position.

The third component is market value risk. Even before a contract matures, a new market discount rate changes the present value of its future cash flows. The institution’s assets and liabilities can both be revalued, with a net effect on equity. This is a stock-of-value question, whereas refinancing and reinvestment examples often focus on interest income over a period.

The source proposes a balance-sheet hedge: match the timing of assets and liabilities. Yet perfect matching can restrict the very maturity transformation customers want. Also, equal final maturities alone are not sufficient if coupon dates, amounts, repricing dates, currencies or embedded options differ. We begin with simple fixed-rate bullet claims so the mechanism is visible; later models refine the measurement.

Maturity mismatch: two ways to fund a loan

Both diagrams begin with a 100 loan earning 10% and 100 of deposits costing 9%. The rates and starting amounts are the same; only the maturities differ. The diagram assumes annual compounding into a single final payment. That assumption matters: it is not a loan paying its interest out to the bank every year.

In the long-funded diagram, the loan matures after one year and delivers 100 × 1.10 = 110. The deposit lasts two years and requires 100 × (1.09)² = 118.81 at year 2. The bank has 110 at year 1 but still needs to meet its year-2 obligation. What happens between those dates depends on the return earned when the 110 is reinvested.

In the short-funded diagram, the loan lasts three years and delivers 100 × (1.10)³ = 133.10 at year 3. The one-year deposit requires 109 at year 1. The institution must refinance before the loan pays. The source does not specify every future refinancing contract; the diagram identifies the exposure, not a complete three-year profit forecast.

Both sides start at 100, so this teaching balance sheet begins with E = 100 − 100 = 0. Equal amounts do not eliminate risk when timing differs. Nor should zero initial equity be read as a sensible real-bank capital policy. The next valuation example uses this deliberately stripped-down balance sheet to show the loss without an offsetting capital buffer.

Refinancing risk: the funding rate changes first

The source first gives the structural example: a ten-year fixed-rate loan is funded by a two-year deposit. At year 2 the deposit must be repaid or rolled over, but the loan continues. The uncertainty is the price and availability of the new funding used to keep financing that longer asset. If market funding rates rise, the asset’s fixed income does not automatically rise with the expense.

Example 7–1 isolates the interest spread. Initially the institution lends at 10% and borrows at 9%, giving 10% − 9% = +1 percentage point. At refinancing, the funding rate becomes 11% while the loan remains at 10%. The new spread is 10% − 11% = −1 percentage point. On a constant 100 principal for a full year, those rates imply interest income of 10 and expense first of 9, then of 11.

The change in spread is −2 percentage points: the institution has moved from a positive margin to a negative one. If instead the replacement rate fell, the same short-funded position would benefit because fixed asset income would be financed more cheaply. Risk describes uncertainty about this outcome; it does not say that the adverse direction must occur.

The source’s structural illustration uses a two-year funding maturity, while the small spread box labels successive periods “Year 1” and “Year 2.” Read them as two illustrations of the same mechanism, not one fully specified timeline. Likewise, this annual spread calculation should not be substituted for the fully compounded terminal-payoff calculation on the previous page without specifying when interest is paid and how it is financed.

Reinvestment risk: the earning rate changes first

Now reverse the timing. The source’s structural example funds a two-year loan with a ten-year fixed-rate deposit. After two years the loan is repaid, but the institution remains committed to the deposit rate. It must place the returned money into a new earning asset. The available yield may be lower than expected, or even below its continuing funding cost.

Example 7–2 uses a one-year loan at 10% and two-year funding at 9%. In the first year the annual rate spread is +1 percentage point. If the next one-year earning opportunity yields only 8%, the second-year spread becomes 8% − 9% = −1 percentage point. Here the earning rate changes first; in refinancing risk, the funding rate changed first.

Reinvestment risk also applies to cash received before final maturity. Bond coupons and monthly loan repayments must be used or reinvested when they arrive. A yield calculation made in advance may implicitly assume a reinvestment rate that is not ultimately available. Thus the realized return over the full holding period can differ from the initially expected return even when the borrower makes every promised payment.

Keep the cash-flow models separate. As an explicitly derived extension to page 24, if all 110 received at year 1 is reinvested at 8%, the year-2 amount is 110 × 1.08 = 118.80. The compounded funding obligation is 100 × 1.09² = 118.81, leaving a total terminal shortfall of 0.01. This does not contradict a −1 percentage-point second-year rate spread: the reinvested amount is 110, the annual funding base and compounding history differ, and a rate spread is not a terminal cash balance.

Market value risk: reprice the same future payments

The market value of a financial claim is the present value of its promised cash flows discounted at a current rate appropriate to its risk and maturity. For a fixed future payment, a higher required yield means a lower price today. An investor can obtain a higher return from new alternatives, so an old fixed payment must be bought more cheaply to offer that return.

The same logic applies to liabilities. A bank’s promise to pay a fixed amount in the future has an economic value to the creditor. If the required discount rate rises, that liability’s present value falls too. For the bank’s equity this is an offset: E = PV(assets) − PV(liabilities). A fall in liability value is not cash arriving at the bank, and it does not cancel the contractual payment.

The source asks what happens when a short-funded institution faces higher rates. In its simple fixed-payment example, the longer asset loses more value than the shorter liability, so economic net worth falls. The next pages calculate this rather than relying on the slogan alone. For more complex balance sheets, final maturity is only a guide; cash-flow timing, coupon rates, repricing, amounts and options determine the actual sensitivity.

Notice the distinction from the previous two examples. A bank may still earn a positive current interest spread while suffering a present-value loss on future business. Income is a flow over time; equity is a stock measured at a date. Both are important, but they answer different risk questions.

Valuing the balance sheet at market rates

The source returns to the short-funded timeline: the loan pays 133.10 in three years, while the deposit requires 109 in one year. To value a single fixed payment, divide its future value FV by the growth factor (1 + i)ⁿ. Here i is the current annual market yield for the relevant instrument, and n is the remaining number of years. Write percentages as decimals in the calculation.

PV = FV / (1 + i)ⁿ

At the original rates, the asset value is 133.10/(1.10)³ = 100. The liability value is 109/1.09 = 100. The different discount rates are intentional: the loan yields 10% and the deposit costs 9%. Each instrument is valued at its own comparable market rate, not automatically at one common rate.

Subtract the liability from the asset to obtain initial economic net worth: E₀ = 100 − 100 = 0. These are time-zero values, not the amounts paid at maturity. The 133.10 asset payoff and 109 liability payoff remain future contractual amounts.

The question then raises both rates by 100 basis points. One basis point is 0.01 percentage point, so 100 bp is 1 percentage point: 10% becomes 11%, and 9% becomes 10%. This is not a 1% proportional increase in the quoted rate. To isolate the immediate valuation effect, keep the contractual payments and remaining maturities unchanged.

A 100 basis-point rise in market rates

First revalue the fixed three-year asset at 11%: A₁ = 133.10/(1.11)³ = 97.32157285, or 97.32. Its change is 97.32157285 − 100 = −2.67842715. The denominator rises over three compounding periods, so the present-value reduction is substantial even though the rate moves by only one percentage point.

Next revalue the fixed one-year liability at 10%: L₁ = 109/1.10 = 99.09090909, or 99.09. Its change is −0.90909091. Both sides have fallen in value, but the liability’s shorter remaining cash-flow horizon makes its change smaller in this example.

Finally subtract unrounded values: E₁ = 97.32157285 − 99.09090909 = −1.76933624 ≈ −1.77. Equivalently, ΔE = ΔA − ΔL = −2.67842715 − (−0.90909091). The minus sign on ΔL matters: the liability decline partially offsets the asset loss. It does not make the entire shock beneficial.

The dollar and percentage losses happen to have the same numerical magnitudes because each side originally equals 100. That coincidence disappears with another starting balance. Also, because initial equity is zero, a percentage change in equity is undefined; report the −1.77 currency-unit change rather than dividing by zero.

The lesson is the mechanism, not a blanket maturity rule: the specified longer fixed-payoff asset is more rate-sensitive than its shorter funding liability. Capital would absorb the net loss if present. For example, adding 8 of equity-funded cash would leave equity of 8 − 1.76933624 = 6.23066376 after the same shock; it would not prevent the value loss itself.