Free sample chapter from FRM Level I: Financial Markets and Products I.

Chapter 1: Banks — Risks, Capital and the Business Model

Chapter 1: Banks — Risks, Capital and the Business Model

A bank is the only kind of firm whose product is its balance sheet. A manufacturer's balance sheet records what it owns in order to make something else; a bank's balance sheet is the business. Every risk in this chapter, and most of the products in the six chapters that follow, exist because a bank funds long, illiquid, uncertain assets with short, liquid, certain liabilities — and is paid for the difference.

Our subject is Ravensmoor Financial Group, the mid-sized bank holding company that runs through this whole series. Its chief risk officer, Ingrid Halvorsen, is preparing for a board meeting with two items on the agenda. The first is routine: confirm that the group is adequately capitalised. The second is not: the board wants to know whether last year's securitization programme — which the finance division has reported as releasing $60.80 million of capital — was worth doing.

By the end of this chapter you will have answered both, and the second answer will be roughly half the number the board was given.

Learning Objectives

1.1 The Risks a Bank Runs, and Where They Come From

The exam asks you to identify a bank's major risks and explain how they arise. The second half is what earns marks: every risk below is the by-product of a specific activity, and naming the activity is how you tell two risks apart when a question describes a loss without labelling it.

Credit risk The risk that a borrower or counterparty fails to make a payment it owes. It arises from lending, from holding bonds, and from any derivative or settlement exposure where the bank is owed money it has not yet received.

Credit risk is Ravensmoor's largest exposure and the reason $2,400 million of commercial loans sits on its balance sheet. It arises whenever the bank has performed its side of a bargain before the counterparty has performed theirs. Note that this includes positions that look like market risk: a profitable interest rate swap is a credit exposure to the counterparty for the amount by which it is in the money.

Market risk is the risk of loss from movements in prices — interest rates, equity prices, exchange rates, commodity prices, credit spreads. It arises from positions the bank holds deliberately for trading, and from positions it holds structurally. A bank that funds thirty-year fixed-rate mortgages with overnight deposits has an interest rate position whether or not anyone intended to take one.

Operational risk is the risk of loss from failed internal processes, people and systems, or from external events. It arises from everything — which is what makes it hard. Fraud, a mispriced trade booked into the wrong system, a failed settlement, a cyber intrusion, a fine for mis-selling, a fire in a data centre. The curriculum's own examples run from rogue trading to natural disaster.

Liquidity risk has two distinct forms, and conflating them is a classic exam error:

• Funding liquidity risk is the risk of being unable to meet obligations as they fall due. It arises from the maturity transformation at the heart of banking: deposits are repayable on demand and loans are not.
• Market (or trading) liquidity risk is the risk of being unable to exit a position at anything near its marked value. It arises from position size relative to market depth, and it shows up precisely when it is least welcome, because everyone wants to sell the same thing at once.

Beyond those four, a bank also runs business and strategic risk (revenues fall because the business model stops working), reputational risk (customers and counterparties withdraw because of what the bank is believed to have done), and legal and compliance risk (losses from litigation, regulatory penalties, or contracts that turn out not to say what the bank thought).

These risks interact rather than stack. A credit shock becomes a liquidity shock when funders notice, and a liquidity shock becomes a market loss when assets have to be sold into it. That interaction is why a bank holds capital centrally rather than per desk, which is the subject of the rest of this chapter.

1.2 Ravensmoor's Balance Sheet, and the Number Regulators Look At

Here is the group as Halvorsen's team reports it, in millions of dollars.

A regulator does not ask how large the balance sheet is. It asks how risky it is, and it does so with a deliberately crude instrument: every asset is multiplied by a risk weight, and the results are added.

Risk-weighted assets (RWA) The sum of a bank's exposures, each multiplied by a weight reflecting its riskiness. Cash and government securities of high-quality sovereigns carry a 0% weight; ordinary corporate loans carry 100%; some exposures carry more. Capital requirements are expressed as percentages of this total, not of total assets.

1.3 Two Things Called Capital

Ravensmoor's board is about to be shown two capital numbers for the same loan book, and they will not match. They are not meant to. They answer different questions, and a candidate who cannot say which question each one answers will lose marks on this reading every time.

Economic capital The amount of capital a firm judges it needs to absorb unexpected losses to a confidence level of its own choosing, usually one tied to the credit rating it wants to keep. It is computed from the firm's own loss distribution: the distance from the mean of that distribution to a chosen high quantile.

Regulatory capital The amount of capital a supervisor requires the firm to hold, computed by applying a prescribed rule to prescribed exposure measures. It is a minimum imposed from outside, and the firm does not get to choose the confidence level, the model, or in many cases the inputs.

The distinction the exam tests most often is what each number is for.

Both numbers sit above expected loss, and both exclude it. This is the second most tested point in the reading.

1.4 The Basel Regulations and What Motivated Them

Regulatory capital rules are easier to remember if you know what each generation was a reaction to. The exam asks for the requirements and their motivations.

Four features of the current framework carry most of the exam's weight:

The three minimum ratios are nested. Common equity tier 1 — ordinary shares and retained earnings, the capital that absorbs loss while the bank is still a going concern — must be at least 4.50% of RWA. Tier 1, which adds certain perpetual instruments, must be at least 6.00%. Total capital, which adds tier 2 instruments such as subordinated debt, must be at least 8.00%. On Ravensmoor's $3,000 million of RWA those are $135 million, $180 million and $240 million.

The buffers sit on top and bite gradually. The capital conservation buffer of 2.50% is not a minimum whose breach closes the bank; it is a region within which distributions — dividends, buybacks, bonuses — are progressively restricted. That design is deliberate: a hard minimum gives a bank in trouble an incentive to shrink lending abruptly, while a buffer gives it a reason to retain earnings instead.

The leverage ratio is a deliberate crosscheck. Tier 1 capital divided by total exposure, with no risk weights at all, must be at least 3%. Its entire purpose is to catch the case where the risk weights are wrong. A bank stuffed with assets the model calls safe can satisfy a risk-based ratio and still be one bad assumption from insolvency.

The liquidity standards are separate from capital. The liquidity coverage ratio requires enough high-quality liquid assets to survive thirty days of a prescribed stress; the net stable funding ratio requires long-term assets to be funded with stable liabilities. Neither is a capital rule, and both exist because the crisis killed solvent banks.

1.5 The Same Loan Book, Measured Twice

Now put the two definitions to work on one portfolio.

ead, pd, lgd = 2400.0, 0.0180, 0.45
loss_999, risk_weight = 181.19, 1.00

el = ead * pd * lgd
economic = loss_999 - el
reg_min = 0.0800 * ead * risk_weight
reg_buffered = 0.1050 * ead * risk_weight

print(f"expected loss (provisioned) : ${el:7,.2f}M")
print(f"economic capital at 99.9%   : ${economic:7,.2f}M")
print(f"regulatory at 8.00%         : ${reg_min:7,.2f}M  gap ${reg_min - economic:6,.2f}M  ({reg_min / economic - 1:+.2%})")
print(f"regulatory at 10.50%        : ${reg_buffered:7,.2f}M  gap ${reg_buffered - economic:6,.2f}M  ({reg_buffered / economic - 1:+.2%})")
print(f"binding requirement         : {'regulatory' if reg_min > economic else 'economic'}")
# Output:
# expected loss (provisioned) : $  19.44M
# economic capital at 99.9%   : $ 161.75M
# regulatory at 8.00%         : $ 192.00M  gap $ 30.25M  (+18.70%)
# regulatory at 10.50%        : $ 252.00M  gap $ 90.25M  (+55.80%)
# binding requirement         : regulatory

Hold on to that gap, because it is an incentive. Every dollar by which the regulatory number exceeds the economic one is a dollar of capital the bank must hold but does not believe it needs. A bank facing that gap has three options: hold the capital and accept a lower return on equity, take more risk on the same risk-weighted footprint — since the weight does not change when the book gets worse — or move the exposure off the balance sheet. §1.10 is what happens when Ravensmoor chooses the third.

1.6 Deposit Insurance and the Put the Insurer Wrote

Ravensmoor funds $2,400 million of its balance sheet with insured customer deposits. Those depositors do not monitor the bank, do not read its accounts, and would not withdraw if they did. That is the point of deposit insurance: it stops runs by removing the reason to run.

It also creates the cleanest example of moral hazard in the curriculum.

Moral hazard A change in behaviour caused by being insulated from the consequences of that behaviour. Insurance creates it whenever the premium does not vary with the insured party's own choices.

Think about who holds what. Insured depositors hold a claim that pays in full whatever happens, so they are indifferent to the bank's asset risk and will lend to it at the same rate regardless. Shareholders hold the residual, which is a call option on the bank's assets: they take the whole upside and their downside stops at zero. The deposit insurer holds the other side of that option — it has, in effect, written a put on the bank's assets, struck at the value of the insured deposits.

A put written on a more volatile asset is worth more. So the insurer's liability rises with the bank's asset risk while, under a flat premium, its income does not.

from scipy.stats import norm

assets, deposits, premium_rate = 2600.0, 2400.0, 0.0010

def expected_claim(vol):
    sd = assets * vol
    d = (assets - deposits) / sd
    return sd * norm.pdf(d) - (assets - deposits) * norm.cdf(-d)

premium = premium_rate * deposits
for vol in (0.03, 0.06):
    claim = expected_claim(vol)
    sd = assets * vol
    print(f"asset vol {vol:>5.0%}: sd ${sd:6,.2f}M  P(shortfall) {norm.cdf(-(assets - deposits) / sd):7.4%}  "
          f"expected claim ${claim:6.4f}M  fair premium {claim / deposits:.4%}")
print(f"flat premium paid by both  : ${premium:.2f}M")
print(f"ratio of expected claims   : {expected_claim(0.06) / expected_claim(0.03):.2f}x")
print(f"safe bank overpays ${premium - expected_claim(0.03):.4f}M, "
      f"risky bank underpays ${expected_claim(0.06) - premium:.4f}M")
# Output:
# asset vol    3%: sd $ 78.00M  P(shortfall) 0.5172%  expected claim $0.1279M  fair premium 0.0053%
# asset vol    6%: sd $156.00M  P(shortfall) 9.9912%  expected claim $7.3777M  fair premium 0.3074%
# flat premium paid by both  : $2.40M
# ratio of expected claims   : 57.67x
# safe bank overpays $2.2721M, risky bank underpays $4.9777M

The consequence is a subsidy that flows from prudent banks to risky ones, and an incentive for any bank to take more asset risk than it otherwise would — because the extra risk is funded at an insured deposit rate that does not move. Four things are done about it, and the exam expects you to be able to name them:

• Risk-based premiums. Tie the assessment to the bank's own risk profile and capital, so the price moves with the risk. In practice the range is narrow relative to the range of real risk, so this mitigates rather than solves.
• Capital requirements. Force shareholders to keep more of their own money at stake, which shrinks the value of the put by moving the strike further away.
• Supervision and prompt corrective action. Intervene while the bank is still solvent, imposing restrictions as capital ratios decline rather than waiting for failure.
• Coverage limits. Cap the insured amount per depositor, so that large depositors retain a reason to monitor — although in a crisis those are precisely the depositors who run.

1.7 How an Investment Bank Raises Money for a Client

Ravensmoor Securities, the group's investment banking arm, brings issuers to market. The curriculum names five arrangements, and the discriminator between them is always the same: who bears the risk that the securities do not sell at the expected price.

Private placement Securities are sold directly to a small number of large, sophisticated investors rather than offered to the public. Registration requirements are lighter and the process is faster and cheaper, but the investor base is narrower and the securities are less liquid, so the issuer typically accepts a lower price.

Public offering Securities are registered and offered to investors at large, usually through an underwriting syndicate. The process is slower and more expensive, with disclosure obligations, but it reaches the deepest pool of capital and produces a liquid, tradable security.

Within a public offering, the underwriter's role can be structured two ways.

Firm commitment. The underwriter buys the entire issue from the company at an agreed price and resells it to the public. The issuer's proceeds are certain the moment the agreement is signed. If the offering is mispriced, the loss is the underwriter's.

Best efforts. The underwriter acts as an agent, promising only to use its best efforts to place the securities, and earns a commission on what it sells. The issuer takes the price and quantity risk.

Dutch auction. Investors submit bids stating a quantity and a price. The bids are ranked from highest price down, and the clearing price is the price at which cumulative demand first covers the offering. Every successful bidder pays that same clearing price, whatever they bid.

1.8 Conflicts of Interest Inside a Banking Group

Ravensmoor lends money, manages other people's money, and underwrites securities. Each of those is a respectable business. The trouble is that each one gives the group information or influence that could be used to the advantage of one client and the detriment of another.

The curriculum frames this as conflicts between three divisions.

There is also a conflict between the bank and its own clients: the bank trades for its own account in the same securities it recommends, executes, and holds for customers.

The controls are the exam's answer and they layer:

• Information barriers. Restrict the flow of confidential information between divisions, supported by restricted and watch lists that block trading and research in names where the bank holds inside information.
• Separation of function and reporting line. Research is compensated and supervised outside investment banking, so an analyst's pay does not depend on deal fees. After the 2003 global research settlement this became a formal requirement rather than a courtesy.
• Legal separation. Distinct entities for distinct businesses, with their own capital and boards — the extreme version being the Glass-Steagall separation of commercial and investment banking in the United States, repealed in 1999 and partly reintroduced in different form afterwards.
• Disclosure and consent. Where a conflict cannot be eliminated, it is disclosed and the affected client consents — the mechanism the GARP Code of Conduct relies on.
• Supervision and escalation. A conflicts register, independent compliance review, and a route by which an employee can raise a conflict without going through the person who benefits from it.

1.9 The Banking Book and the Trading Book

Every position a bank holds sits in one of two books, and which one decides how it is valued, how it is capitalised, and — as Ravensmoor is about to discover — whether it appears in the right risk report at all.

Banking book Positions the bank intends to hold to maturity or for the longer term — chiefly loans and deposits. They are carried at amortised cost with provisions for credit losses, so day-to-day price movements do not reach the income statement, and they attract credit risk capital.

Trading book Positions held with intent to trade — to profit from short-term price movements or to hedge other trading positions. They are marked to market, so every price movement hits the income statement immediately, and they attract market risk capital.

The boundary matters because the two capital treatments can give very different answers for the same economic exposure, which creates an incentive to place a position on the more favourable side. Before the crisis this was a well-worn route: credit exposures that would have attracted a full credit risk charge in the banking book were booked as trading positions and capitalised on a value-at-risk model calibrated to a calm period. The Fundamental Review of the Trading Book tightened the boundary precisely for that reason, making the classification harder to change after the fact and requiring supervisory approval to move a position across.

1.10 Originate-to-Distribute, and What Ravensmoor's Programme Was Worth

Originate-to-distribute A banking model in which loans are made with the intention of selling them on — through outright sale, securitization, or credit derivatives — rather than holding them to maturity. The bank earns origination and servicing fees, recycles its funding and its capital into new lending, and transfers some part of the credit risk to investors.

The benefits are real and the exam expects them: the bank's funding and capital are no longer tied up for the life of the loan, so the same balance sheet supports more lending; fee income replaces spread income and is less capital-hungry; the bank can shed concentrations it cannot otherwise diversify away; and credit reaches borrowers who could not have been funded from deposits alone.

The drawbacks are equally examinable, and all of them are versions of one problem — the originator no longer bears the consequence of a bad loan:

• Weakened screening and monitoring. Underwriting standards slip when the loan is going to be sold in ninety days. This is the mechanism behind the subprime deterioration of 2004-2007.
• Asymmetric information and adverse selection. The originator knows which loans are worse and keeps or sells accordingly. Investors, knowing this, discount the whole pool.
• Opacity. Repackaging into tranches, and tranches into further structures, made the ultimate exposure very hard to locate.
• Warehousing risk. Between origination and distribution the loans sit on the bank's balance sheet, and that pipeline is exactly what froze in 2007.
• Implicit recourse and reputational risk. Banks that had legally sold exposures supported the vehicles anyway, because failing to do so would have destroyed their franchise.
• Procyclicality. The model works in good markets and stops working in bad ones, withdrawing credit precisely when it is most needed.

Now to Halvorsen's second board question. Last year Ravensmoor sold $600 million of loans into a securitization and bought credit protection on a further $200 million single-name concentration. The finance division reported the programme as releasing $60.80 million of regulatory capital.

credit_rwa, min_ratio = 2500.0, 0.0800
sold, tranche, tranche_weight = 600.0, 30.0, 12.5
cds_notional, protection_weight = 200.0, 0.20

claimed = min_ratio * (sold + cds_notional * (1 - protection_weight))
sale_rwa = -sold + tranche * tranche_weight
cds_rwa = cds_notional * protection_weight - cds_notional
delivered = min_ratio * -(sale_rwa + cds_rwa)

ead, pd, lgd = 2400.0, 0.0180, 0.45
el = ead * pd * lgd
el_transferred = cds_notional * pd * lgd        # only the hedged slice leaves

print(f"claimed relief            : ${claimed:6,.2f}M")
print(f"  sale, gross             : ${min_ratio * sold:6,.2f}M")
print(f"  retained tranche RWA    : ${tranche * tranche_weight:6,.2f}M  -> claws back ${min_ratio * tranche * tranche_weight:5,.2f}M")
print(f"  hedge                   : ${min_ratio * -cds_rwa:6,.2f}M")
print(f"delivered relief          : ${delivered:6,.2f}M   overstated by ${claimed - delivered:5,.2f}M")
print(f"credit RWA                : ${credit_rwa:,.2f}M -> ${credit_rwa + sale_rwa + cds_rwa:,.2f}M")
print(f"expected loss transferred : ${el_transferred:5,.2f}M of ${el:,.2f}M = {el_transferred / el:.2%}")
print(f"relief per dollar of EL   : {delivered / el_transferred:,.2f}x")
# Output:
# claimed relief            : $ 60.80M
#   sale, gross             : $ 48.00M
#   retained tranche RWA    : $375.00M  -> claws back $30.00M
#   hedge                   : $ 12.80M
# delivered relief          : $ 30.80M   overstated by $30.00M
# credit RWA                : $2,500.00M -> $2,115.00M
# expected loss transferred : $ 1.62M of $19.44M = 8.33%
# relief per dollar of EL   : 19.01x

1.11 Putting It All Together

Halvorsen's board memo has to hold four numbers in one frame, and the frame is the chapter.

The group is adequately capitalised, with little room. $3,000 million of risk-weighted assets requires $315 million of total capital once the conservation buffer is included, against $330 million held — a surplus of $15 million, or half a percent of RWA. That is enough to satisfy the requirement and not enough to absorb a bad quarter without restricting distributions.

The binding constraint on the loan book is the regulator's, not the bank's. Ravensmoor's own model says $161.75 million of capital covers a one-in-a-thousand year on the commercial book; the rules require $192.00 million at the minimum and $252.00 million with the buffer. The $30.25 million gap is not an error by either party. It is the price of a rule that has to work for every bank, applied to a book that happens to be better than the average one the rule was written for.

That gap is a standing incentive to move exposure off the balance sheet, and Ravensmoor acted on it. The programme was worth doing and worth reporting honestly: $30.80 million of capital released, the CET1 ratio up from 8.50% to 9.75%, and 8.33% of the book's expected loss genuinely transferred. What cannot be defended is the $60.80 million figure, which counted the sale and ignored what was kept.

And the cheapest funding on the balance sheet is cheap because someone else is bearing part of its risk. $2,400 million of insured deposits fund the group at a rate that does not vary with what the group does with the money. The flat premium means a bank with twice Ravensmoor's asset volatility would pay the same $2.40 million for an expected claim 57.67 times larger. Every capital rule in §1.4 exists, in the end, to make that arrangement survivable.

The thread running through all four is the one this course keeps returning to: a market — or a regulator, or an insurer — lets you move a risk, at a price, and never all of it. The securitization moved a third of the notional and a twelfth of the risk. The credit default swap moved credit exposure from borrowers to Meridian Bank rather than removing it. Deposit insurance moved run risk from the bank to the insurer, and created a new risk in doing so. Each transfer is real, each is partial, and each leaves a residue that someone owns whether or not the reporting says so.

Chapter Summary

• A bank's major risks are credit, market, operational and liquidity — and liquidity splits into funding and market liquidity risk. Classify by cause, not symptom: a limit breach followed by a market loss is an operational failure.
• Risk-weighted assets weight each exposure by its riskiness; zero-weighted assets consume no capital. Ravensmoor's $3,000 million of assets produce $2,500 million of credit RWA, plus $200 million of market risk and $300 million of operational risk RWA, for $3,000 million in total.
• Economic capital is the firm's own answer, measured from its loss distribution as the distance from the mean to a chosen quantile: $181.19 − $19.44 = $161.75 million at 99.9%. Regulatory capital is a rule applied to a weighted exposure: $192.00 million at 8.00%, $252.00 million with the conservation buffer. Both sit above expected loss, which is provisioned rather than capitalised.
• The Basel minimum ratios are CET1 4.50%, Tier 1 6.00% and total capital 8.00% of RWA, with a 2.50% conservation buffer restricting distributions rather than forcing closure, a countercyclical buffer of 0-2.50%, a 3% leverage ratio that ignores risk weights as a crosscheck, and the LCR and NSFR liquidity standards.
• Deposit insurance is a written put, struck at insured deposits. Its value rises with asset volatility while a flat premium does not: for two banks with identical deposits, expected claims of $0.13 million and $7.38 million against the same $2.40 million premium — a ratio of 57.67 times. Risk-based premiums, capital requirements, supervision and coverage limits mitigate it.
• Financing arrangements differ in who bears price risk. Firm commitment: the underwriter, which is why the $15.00 million spread becomes a $15.00 million loss if the issue clears $1.50 below the purchase price. Best efforts: the issuer. Dutch auction: the issuer, with every successful bidder paying the clearing price of $29.00 regardless of what they bid.
• Conflicts of interest across lending, securities services and investment banking are managed with information barriers, separation of research from banking, legal separation, disclosure and consent, and independent supervision.
• The banking book holds positions intended to be held, at amortised cost, with credit risk capital; the trading book holds positions intended to be traded, marked to market, with market risk capital. The boundary invites arbitrage, which is why it is now hard to cross.
• Originate-to-distribute recycles capital and funding but weakens screening, because the originator no longer bears the consequence. Ravensmoor's programme delivered $30.80 million of relief against $60.80 million claimed — the difference being a $30 million retained tranche at a 1250% risk weight, which is a full deduction because 1/0.08 = 12.5 — and transferred 8.33% of the book's expected loss, or $19.01 of capital relief per dollar of expected loss moved.

What's Next

Chapter 2 moves from the bank to the three institutions that hold everybody else's savings: insurers, pension plans and funds. The arithmetic changes — mortality tables, combined ratios, incentive fees — but the question does not. Ravensmoor General's combined ratio turns out to be exactly 100.00%, which means its underwriting breaks even to the cent and every dollar of its profit is investment income earned on policyholders' money. The Absolute Return Fund's 2-and-20 takes 40.52% of a three-year gross gain while the investor carries the whole of the drawdown.

The Core Equity Fund, whose beta of 1.15 does all the work in Chapter 5, is introduced there as a product: its net asset value, its fee drag, and what its reported performance would look like if the funds that closed were still in the index.

Concept Checks

Fast recall before the exam-format questions — no calculator needed.

Exam-Style Practice

Standalone four-option questions at the real exam's pace — 2.4 minutes each.

Get the full course: FRM Level I: Financial Markets and Products I