Core Path · L2.1.01

What is risk?

10 minRiskDefinitions

Know these first

Welcome to Level 2

Level 1: Foundations of Finance showed how markets, instruments and financial firms work. Level 2: Foundations of Risk turns to the risks they carry: what risk is, its main types, who governs it, the first ways to measure it, how to reduce it and the rules that apply. It starts here, with a definition.

By the end you will be able to

  1. 1Define risk as uncertainty about outcomes that matter, and tell it apart from loss.
  2. 2Give an example of a risk that never becomes a loss, and of a loss that was never a risk.
  3. 3Separate expected loss from unexpected loss, and calculate the unexpected part.
  4. 4Explain why the same event can be a risk for one firm and not for another.

Why it matters

On the day a bank makes a loan, nothing has gone wrong. No payment is late and no money is lost. Yet the bank's risk managers are already at work. Risk is there long before any loss, and most risks never turn into losses at all.

Core explanation

Two ingredients: uncertainty and something at stake

In L1.1.08: Returns and risk: a first look you met risk as the chance that outcomes differ from what you expect, and volatility as its simplest measure. Level 2 sharpens that into a working definition: risk is uncertainty about outcomes that matter to you.

That definition has two ingredients. The first is uncertainty: more than one outcome is possible, and you do not know which one you will get. The second is exposure: something you care about is at stake, such as money, capital or a goal you have set. Take away either one and there is no risk.

Uncertainty only

You toss a coin with nothing riding on it.

Not a risk to you: nothing is at stake.

Exposure only

A fixed fee is due next month.

A cost, not a risk: there is only one outcome.

Both

A bank lends to a firm that may not repay.

A risk: several outcomes, and money at stake.

Risk is not loss

In everyday speech the two words are used almost as one. In risk management they are kept apart. A loss is an outcome: money that has gone, measured after the event. Risk is about the whole range of outcomes, judged before the event.

RiskLoss
WhenBefore the eventAfter the event
What it describesA range of possible outcomesOne outcome that happened
Can it exist alone?Yes: a risky bet can end in a gainYes: a certain cost is a loss with no risk
Measured byHow wide the outcomes spread, how likely and how bad the bad ones areThe amount lost

Pick a place for £10,000 below and look at the range of outcomes first. Then let a year pass and see which one you get.

ExploreBefore the year, and after it

£10,000 in each · illustrative

Where the money goes

Before: the risk

A wide spread: big gains and big losses are both possible.

Worst year−£3,000
Best year+£3,900
Spread£6,900
Losing years2 of 5

After: the outcome

Nothing has happened yet. Let a year pass.

The five equally likely outcomes, in £. The bar is the spread; the tick is the average.
−4k−2k0+2k+4kbreak-even

The share fund is just as risky in a year when it gains 39% as in a year when it loses 30%: the spread of outcomes was the same before the year began. The fixed fee loses money every year, yet carries no risk, because nothing about it is uncertain.

Expected and unexpected losses

A bank that lends to thousands of households knows some will not repay. It plans for an average level of losses, the expected loss, and builds it into its interest rates, just as you saw for bond spreads in L1.4.07: Credit ratings and credit spreads. An expected loss is a cost of doing business. The risk is the part nobody can plan for exactly: the unexpected loss, when losses come in above the plan.

Outcomes better than planned count too. A trading desk that earns three times its budget took more risk than anyone thought. This is upside risk, and risk managers question it as closely as a shortfall.

Risk to whom?

Because risk needs exposure, the same event can be a risk for one firm and not for another. When interest rates rise, a holder of long-dated fixed-rate bonds loses, as L1.4.06: The price-yield relationship showed, while a saver whose deposit rate resets upwards gains. Before asking “how risky is this?”, a risk manager asks “risky for whom, and against which goal?”

Sort itRisk, loss or neither?

0 of 7 right

Decide whether each situation is a risk (uncertain, with something at stake), a loss (an outcome that has happened) or not a risk at all.

  1. A bank has lent €2m to a builder who might not repay.

  2. The builder goes bust, and the bank recovers only €1.2m of the €2m.

  3. An insurer pays office rent fixed at £3m a year under a ten-year lease.

  4. A Japanese exporter will be paid US$5m in three months and does not know the exchange rate then.

  5. A trader's bond position fell $3m in value yesterday.

  6. You watch a football match with no bet on it.

  7. A life insurer does not know how many policyholders will die this year.

Think firstTrickier cases

The formal version

The international risk management standard, ISO 31000, defines risk as the “effect of uncertainty on objectives”. Uncertainty is the first ingredient; the objectives are what is at stake. The effect can be good or bad.

For losses on a loan book or an insurance portfolio, the split used above is written in full as:

Unexpected loss=Actual loss−Expected loss\text{Unexpected loss} = \text{Actual loss} - \text{Expected loss}

Expected loss is planned for and charged to customers. Unexpected loss can be positive (worse than planned) or negative (better). Risk managers try to measure how large the unexpected loss could be, and how likely; that leads to the risk measures of M2.5: First risk measures.

Worked example

One mortgage book, a good year and a bad year

A bank has a £500m mortgage book and £40m of capital set aside for it. From past experience it expects losses of 0.4% of the book a year and has built that into its mortgage rates. Amounts in £ millions; illustrative. Try each step before revealing it.

Expected and unexpected losses

Step 1 of 5
  1. 1

    The expected loss

    0.4% × £500m = £2.0m a year. This is a cost, covered by the interest customers pay.

Regulatory lens

Bank capital rules build in exactly this split. Under the Basel framework's internal ratings-based approach, expected losses are meant to be covered by provisions and pricing, and the capital requirement is set to absorb unexpected losses. M2.7: Introduction to regulation introduces the Basel rules, and Level 4 covers the calculations.

Sparks

SparkTo dare
In Against the Gods (1996), Peter Bernstein traces the word “risk” to the early Italian risicare, “to dare”. In that sense risk is a choice you make, not a fate you suffer: the starting point of risk management.
SparkOne event, two sides
Every financial contract has two sides. When a borrower defaults, the lender loses; when oil prices jump, an airline loses and an oil producer gains. Much of finance is about moving risk to whoever is best placed, or best paid, to carry it.

Key takeaways

  • Risk is uncertainty about outcomes that matter: it needs both uncertainty and exposure.
  • A loss is one outcome, seen after the event. Risk is the range of outcomes, judged before it.
  • A risk can end in a gain, and a certain cost is a loss with no risk.
  • Expected losses are a cost to price in; the risk is the unexpected loss, which capital must absorb.
  • Risk depends on whose exposure you look at: the same event hurts some and helps others.

Reaction

Check what stuck

Question 1 · objective 1

Which of these is a risk, in the sense used in this course?

Question 2 · objective 2

A share fund returned +12% last year. Was holding it risky?

Question 3 · objective 3

A bank has a $200m book of business loans and expects losses of 1% a year, which it has priced in. This year losses are 2.5% of the book. What is the unexpected loss, in $m?

$m

Question 4 · objective 2

A firm must pay a fixed fee of 2% of its fund each year, whatever happens. This fee is:

Question 5 · objective 4

Interest rates rise unexpectedly. For whom is this a loss?

Glossary

Risk
Uncertainty about outcomes that matter to you: more than one outcome is possible, and something you care about is at stake.
Uncertainty
Not knowing which of several possible outcomes will happen.
Exposure
What you stand to gain or lose: the money, capital or objective that an uncertain outcome would affect.
Loss
A fall in value that has actually happened: one outcome, measured after the event.
Expected loss
The average loss you plan for over a period. Lenders and insurers price it in as a cost of doing business.
Unexpected loss
How far the actual loss turns out above the expected loss. This is the part that capital must absorb.
Upside risk
The chance of an outcome better than expected. It is still risk: the outcome was uncertain.

Deep Dives & Origins

Deep Dives

  • Bernstein, P. L., Against the Gods: The Remarkable Story of Risk, John Wiley & Sons, 1996. Beginner, narrative.
  • Hull, J. C., Risk Management and Financial Institutions, 6th edition, Wiley, 2023, chapter 1. Intermediate.

Origins

  • International Organization for Standardization, ISO 31000:2018, Risk management: Guidelines.
  • Basel Committee on Banking Supervision, An Explanatory Note on the Basel II IRB Risk Weight Functions, July 2005.
  • Bernstein, P. L., Against the Gods: The Remarkable Story of Risk, Wiley, 1996.

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Reading an annual report

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Risk and uncertainty