---
title: "How Pay Works"
book: "The Industry: Firms, Roles and Careers"
subject: quant
language: en
chapter: 13
exercises: 8
source: https://one-course.com/books/quant/17/en/chapter/13-how-pay-works
---

# Chapter 13 — How Pay Works

Each March, New York’s State Comptroller estimates the average bonus paid to the city’s securities industry employees during the bonus season just ended. For 2021 it was $257 500; for 2022, $180 000, 30% less; for 2024, $244 700, 31.5% more than the year before. An average bonus is a headline, and it hides the structure that decides what pay is worth to the person who receives it: how much of it is fixed, how much depends on a formula or on a manager’s judgement, how much is deferred and in what, and what is lost on leaving. This chapter takes pay apart from the employee’s side. Book 16, chapter 10, designed the same machinery from the firm’s side, with its bonus pools, payout formulas and deferral schedules; here the question is what an offer is worth, and to whom.

## 13.1 Base and bonus: the two-part structure and why it exists

**Definition 13.1 (Base salary, total compensation).**

*Base salary* is the fixed annual pay set in the employment contract and paid in instalments whatever the year’s results. *Total compensation* is base salary plus the variable pay awarded for a year, cash and deferred, at the value at which it is awarded, with benefits stated separately; it is the figure offers are compared on, and it counts deferred awards before any [forfeiture](#def-in-how-pay-works-rsu) or change in value.

Pay in trading has two parts because the firm’s revenue has two parts: a cost base it must meet in any year, and a result that swings with markets (chapter 12 measured the swing by kind of firm). A variable award lets the firm share the good years and cut in the bad ones without cutting headcount, which is Book 16’s compensation ratio at work. For the employee the same structure transfers risk: the base is a floor, and the rest moves with the firm’s year, the desk’s and the individual’s.

**As of March 2026 — New York City’s securities industry bonus.**

| bonus year | 2021 | 2022 | 2023 | 2024 | 2025 |
| --- | --- | --- | --- | --- | --- |
| average bonus, first estimate ($) | 257 500 | 180 000 | 176 500 | 244 700 | 246 900 |

New York State Comptroller, annual estimates published each March (2022–2026); each release’s own figure for its year, except 2022, which is the figure the 2024 release gives for the previous year. The 2026 release reports the 2025 average as 6% above 2024’s, so the 2024 estimate had been revised down. The bonus pool was a record $49.2 billion for 2025. In 2024 the city’s average securities industry salary, bonuses included, was $505 677, and bonuses were about 42% of the industry’s wages.

Two things in the box matter for what follows. The average mixes every job in the industry, from operations to senior traders, so it describes no one; and bonuses were about two-fifths of the industry’s wages, so the variable part is not a detail. Chapter 14 gives the levels; this chapter gives the structure.

## 13.2 Formulaic and discretionary pay from the employee’s side

A variable award is either computed by a formula from a measured result, or set by a manager’s judgement within a pool (Book 16, chapter 10, defines the *formulaic payout* and the *discretionary bonus*). The platforms of chapter 5 pay portfolio managers a payout rate of their book’s profit (Book 16, chapter 3); a bank’s or a market maker’s employee is usually paid from a discretionary pool. From the employee’s side the difference is three things.

- **Shape.** A payout of a share of positive profit and nothing below zero is an option on the book’s result: convex, with a long right tail and a mass at zero. A discretionary award is smoother, because the manager spreads the pool and weighs more than one year.
- **Whose risk.** A formula exposes the employee to the book’s result, including luck; discretion exposes the employee to the pool, which follows the firm’s and the desk’s year, and to the manager’s judgement.
- **What ends it.** A formulaic book can be closed by a loss limit (chapter 5’s drawdown ladders), ending the job and the payout together; a discretionary employee’s award can go to zero in a bad year without the job ending.

The certainty equivalent (Book 4, chapter 9) turns these differences into money: the sure amount a person with a stated relative risk aversion would accept in place of the uncertain package. Two people offered the same package can value it differently, because their risk aversion and their other wealth differ.

## 13.3 Deferral, vesting, forfeiture and clawback: what deferred pay is worth

Part of a variable award is often deferred: awarded now, paid later in tranches under a vesting schedule, and held meanwhile in cash, in the firm’s shares or in units of its funds (Book 16, chapter 10, defines deferred compensation, the vesting schedule, malus and clawback).

**Definition 13.2 (Restricted stock unit, forfeiture, good-leaver provision).**

A *restricted stock unit* (RSU) is a promise to deliver one share of the employer’s stock, or its cash value, when the unit vests, subject to conditions such as continued employment. *Forfeiture* is the loss of unvested awards, usually on leaving the firm voluntarily or on dismissal for cause. A *good-leaver provision* is a term of an award that lets some leavers, typically on retirement, death, disability or redundancy, keep unvested awards, which then vest on the original schedule or at once.

**As of October 2025 — Deferral rules for banks and one bank’s awards.**

**EU** (Directive 2013/36/EU, Article 94, as amended in 2019): for staff whose work has a material impact on the firm’s risk, variable pay may not exceed 100% of fixed pay (200% with shareholder approval); at least 50% of variable pay is in shares or equivalent instruments; at least 40% is deferred over not less than four to five years, vesting no faster than pro rata, and at least 60% of a particularly high amount. **UK** (PRA PS21/25 and FCA PS25/15, in force for performance years starting after 16 October 2025): a four-year minimum deferral for all material risk takers; 40% deferral on the first £660 000 of a bonus and 60% on the part above it; the bonus cap was removed from 31 October 2023. **One US bank** (its Form 10-K for 2025): RSUs without performance conditions “generally vest and underlying shares of common stock are delivered (net of required withholding tax) over a three-year period”, with vesting accelerated on “retirement, death, disability and, in certain cases, conflicted employment”.

What a deferred award is worth to the employee depends on four things, which the chapter’s build values together.

1. **Time.** A dollar in four years is worth less than a dollar now; at 5% a year, a tranche vesting in four years is worth 82 cents of award.
2. **The instrument.** Deferred shares carry the stock’s risk: with 30% volatility, a tranche’s value at vesting ranges widely even with no expected change.
3. **Leaving.** Unvested tranches are forfeited on a voluntary move, so their value is weighted by the probability of staying; a [good-leaver provision](#def-in-how-pay-works-rsu) removes that weight for the leavers it covers.
4. **Malus and clawback.** An award can be reduced before vesting (malus) or recovered after it (clawback) for misconduct or a later loss; the chapter’s model treats these as rare and states them rather than pricing them.

Tax follows the vesting, not the award. In the United States, property subject to “a substantial risk of [forfeiture](#def-in-how-pay-works-rsu)” is not income “until it becomes substantially vested”, and then its market value is; a deferred award’s tax is paid on its value when it vests, which is why a bank delivers shares “net of required withholding tax”. Chapter 15 gives the rules of other locations.

**Example 13.3 (The handcuff).**

The chapter’s illustrative bank offer defers 40% of each award into the firm’s stock, vesting in equal tranches over four years. For someone who stays, the unvested balance at grant value grows to about $90 000 at the end of the first year, $158 000 after two, $203 000 after three and levels off near $226 000 from the fourth, when each year’s new deferral is matched by vesting ([Figure 13.1](#fig-in-how-pay-works-unvested)). Leaving at the end of year two forfeits a present value of about $129 000; at the end of year four, $170 000.

![The illustrative bank offer’s deferred awards: 40% of each year’s award deferred into stock and vesting over four years. The balance a leaver walks away from builds for four years, then levels off. Parameters are illustrative; data: 20 000 simulated careers, through in_pay.bank_unvested and forfeit_by_year.](https://one-course.com/images/onecourse/chapters/quant-17/in-how-pay-works/fig-78f52d1153da.svg)

***Figure 13.1.** The illustrative bank offer’s deferred awards: 40% of each year’s award deferred into stock and vesting over four years. The balance a leaver walks away from builds for four years, then levels off. Parameters are illustrative; data: 20 000 simulated careers, through `in_pay.bank_unvested` and `forfeit_by_year`.*

## 13.4 Sign-ons, guarantees and buyouts

**Definition 13.4 (Sign-on bonus, guaranteed bonus).**

A *sign-on bonus* is a payment on joining, usually repayable in full or in part if the employee leaves within a stated period. A *guaranteed bonus* is a variable award whose minimum for a stated year, usually the first, is fixed in the offer.

A hiring firm uses the two to solve two problems. The sign-on pays for what the candidate gives up by moving, and its repayment clause keeps them for its term; the guarantee removes the first year’s risk, when a new joiner has no track record at the firm and a partial year to build one. A third instrument, the *deferral buyout* of Book 16, chapter 10, replaces the unvested awards the candidate forfeits by leaving, usually as new awards on the old vesting dates. From the candidate’s side the arithmetic is the handcuff of the example above run backwards: a candidate who leaves the illustrative bank at the end of year two forfeits awards with a grant value of about $158 000, and a buyout of that size on the same dates makes the move neutral for the deferred part. The candidate should also ask what repayment and [forfeiture](#def-in-how-pay-works-rsu) terms apply to the buyout itself, because a buyout is usually deferred again.

The EU’s rules for banks limit what a guarantee may do: guaranteed variable pay “is exceptional, occurs only when hiring new staff and where the institution has a sound and strong capital base and is limited to the first year of employment”; outside the firms such rules cover it is a matter of contract. Chapter 28 returns to buyouts and notice periods when it follows moves between firms, and Book 18 to how offers are negotiated.

## 13.5 Partnership, equity and carried interest

**Definition 13.5 (Partnership share, carried interest).**

A *partnership share* is a member’s entitlement to a share of a partnership’s profit, fixed by the partnership agreement, in return for capital contributed and work; it is paid as [members’ remuneration](https://one-course.com/books/quant/17/en/chapter/11-reading-a-trading-firms-accounts#def-in-reading-a-trading-firms-accounts-members) (chapter 11) rather than as salary. *Carried interest* is a share of a fund’s profits, typically above a hurdle, paid to its managers through an interest in the fund’s general partner rather than as a fee.

Ownership pays differently from employment. A partner in a limited liability partnership (Book 16, chapter 2) shares the profit after costs, including the pay of the employees, and bears its losses up to the capital put in; chapter 11 showed that in some trading partnerships most of the profit goes to a corporate member rather than to individuals. Equity in a private firm is worth what the firm will pay for it on the terms of its agreements, which usually restrict sale and set a price on leaving. [Carried interest](#def-in-how-pay-works-carry) is a performance fee’s share paid to the people who manage the fund (Book 1, chapter 3, defines the fee and the high-water mark).

**As of April 2026 — Carried interest tax.**

**UK**: from 6 April 2026, [carried interest](#def-in-how-pay-works-carry) is taxed wholly within income tax, “treated as trading profits and subject to Income Tax and Class 4 National Insurance contributions”; for qualifying [carried interest](#def-in-how-pay-works-carry) “the amount to be treated as trading profits is 72.5% of the qualifying profits”. **US**: gains on an applicable partnership interest are long-term only after three years’ holding rather than one (26 U.S.C. 1061).

## 13.6 Structure by firm type

The same parts combine differently by kind of employer, for reasons that the earlier chapters give.

- **Banks.** Variable pay above rule thresholds is deferred and partly in shares, under the rules of the dated box for the staff they cover; a US bank’s own RSUs vest over three years. Deferral retains, and a buyout is part of the cost of hiring an experienced banker (chapter 7’s divisions, chapter 18’s roles).
- **Market makers and proprietary firms.** Private firms publish no pay rules; an offer is typically a base and a discretionary award from a pool that follows the firm’s revenue, which chapter 12 found moves with volatility more than any other kind of firm’s. Any deferral is contractual, not regulatory, outside the entities that the rules cover.
- **Platforms.** A portfolio manager’s pay is a payout rate of the book’s profit (chapter 5); an analyst’s, in the illustrative offer of this chapter, is a base and a small share of the book’s result; the book can be closed by a loss limit. Sign-ons and guarantees buy people out of their previous firm.
- **Asset managers and funds.** Base and bonus, which may be partly deferred into the firm’s funds or shares; senior people may share in performance fees or [carried interest](#def-in-how-pay-works-carry) (chapter 8).
- **Exchanges, vendors and regulators.** Listed exchanges and vendors pay base and bonus like other listed companies; a regulator pays on a published scale (chapter 9).
- **Crypto firms.** Tokens and [token warrants](https://one-course.com/books/quant/17/en/chapter/10-crypto-native-firms#def-in-crypto-native-firms-tokens) add a volatile, often locked-up component (chapter 10).

## 13.7 Tutorial: three offers, one choice

**Goal.** Value three stylised offers from the employee’s side and compare them at two levels of risk aversion. **End state:** Figures [13.2](#fig-in-how-pay-works-offers) and [13.3](#fig-in-how-pay-works-ce) and the table below.

1. **The offers** (every number illustrative, in US dollars): a *bank* role with base 250 000 and a discretionary award of median 200 000 (log standard deviation 0.5), 40% deferred into stock (volatility 30%) over four years, forfeited on leaving; a *market-maker* role with base 200 000 and an award of median 250 000 (log standard deviation 0.8), paid in cash; a *platform analyst* with base 175 000, a payout of 2% of the book’s profit (mean 15 million, standard deviation 20 million a year), the book closed after a year losing more than 10 million, a sign-on of 100 000 repayable within a year, and a first-year guarantee of 150 000.
2. **The career.** Five years, a 10% chance a year of leaving voluntarily, a 5% discount rate; `firm.payoffer.simulate` draws 20 000 careers per offer ([Listing 13.1](#lst-in-how-pay-works-sim)). `for t in range (1 , years + 1 ): working = leave >= t paid_award = working & ~((leave == t) & cut) pv += np.where(working, pkg.base * disc[t - 1 ], 0.0 ) a = np.where(paid_award, aw[:, t - 1 ], 0.0 ) pv += (1.0 - pkg.deferral) * a * disc[t - 1 ] if pkg.deferral and pkg.vest_years: tranche = pkg.deferral * a / pkg.vest_years for k in range (1 , pkg.vest_years + 1 ): s = t + k # vests at the end of year s ret = np.exp(pkg.inst_vol * np.sqrt(k) * rng.standard_normal(n) - 0.5 * pkg.inst_vol ** 2 * k) value = tranche * ret kept = (leave >= s) | (pkg.good_leaver & ~cut) | (leave == years + 1 ) pv += np.where(kept, value * ddisc[s - 1 ], 0.0 ) forfeited += np.where(kept, 0.0 , value * ddisc[s - 1 ]) for e in range (t, min (s, years + 1 )): unvested[:, e - 1 ] += tranche # at grant value, still unvested at the end of year e` **Listing 13.1.** Each year: base while working, the award’s upfront part, and each deferred tranche delivered if still employed or a good leaver, forfeited otherwise. code/firm/payoffer/firm_payoffer.py
3. **Value.** `summary` gives the mean and percentiles of the present value received; `certainty_equivalent(pv, rra, 500_000)` gives the certainty equivalent with 500 000 of other wealth.

| offer (illustrative) | mean PV | 10th pct | 90th pct | CE, RRA 1 | CE, RRA 3 |
| --- | --- | --- | --- | --- | --- |
| bank | 1 618 | 597 | 2 230 | 1 500 | 1 186 |
| market maker | 1 949 | 686 | 2 956 | 1 779 | 1 365 |
| platform analyst | 1 703 | 171 | 3 010 | 1 439 | 904 |

*Present value of five years’ pay, $ thousand; CE is the certainty equivalent.*

![Five years of pay under three illustrative offers: boxes span the 25th to 75th percentiles of the present value received, whiskers the 10th to 90th, the bar is the median and the diamond the mean. The platform analyst’s spread is the widest: a closed book ends the job and the payout together. Parameters are illustrative; data: in_pay.table.](https://one-course.com/images/onecourse/chapters/quant-17/in-how-pay-works/fig-41d186ad6352.svg)

***Figure 13.2.** Five years of pay under three illustrative offers: boxes span the 25th to 75th percentiles of the present value received, whiskers the 10th to 90th, the bar is the median and the diamond the mean. The platform analyst’s spread is the widest: a closed book ends the job and the payout together. Parameters are illustrative; data: `in_pay.table`.*

![Certainty equivalents of the three illustrative offers against relative risk aversion, with 500 000 of other wealth. The platform package loses most as risk aversion rises: at low aversion it is worth about as much as the bank offer, at high aversion much less. Data: in_pay.ce_curve.](https://one-course.com/images/onecourse/chapters/quant-17/in-how-pay-works/fig-45c9636080cd.svg)

***Figure 13.3.** Certainty equivalents of the three illustrative offers against relative risk aversion, with 500 000 of other wealth. The platform package loses most as risk aversion rises: at low aversion it is worth about as much as the bank offer, at high aversion much less. Data: `in_pay.ce_curve`.*

The market-maker offer is worth most at every level of risk aversion here, because its parameters give it the highest median award; that is a property of the illustrative numbers, not of market makers. The lesson is in the shapes. The platform package’s mean is above the bank’s, but its 10th percentile is $171 000, because a book closed after a bad year ends the pay; in 35.4% of simulated careers the book is closed within five years. Its certainty equivalent falls from $1 439 000 at relative risk aversion 1 to $904 000 at 3, while the bank’s falls from $1 500 000 to $1 186 000. A candidate who cannot bear the platform’s lower tail should value it well below its mean.

**What to change next.** Give the bank offer a [good-leaver provision](#def-in-how-pay-works-rsu) and see how much of the [forfeiture](#def-in-how-pay-works-rsu) it removes for a planned move; raise the platform’s loss limit and trace the certainty equivalent.

## 13.8 Build: the offer valuer

**Purpose.** Value a pay package from the employee’s side, for this chapter and for chapters 22, 28 and 30 (and for Book 18’s chapter on offers).

**Interface.** `firm.payoffer`: `Package(name, base, median, sigma, deferral, vest_years, inst_vol, good_leaver, sign_on, sign_on_years, guarantee, share, pnl_mean, pnl_sd, cut)`; `simulate(pkg, years, hazard, rate, n, rng, leave_year)`; `summary(sim)`; `certainty_equivalent(pv, rra, wealth)`; `buyout(pkg, year, n, rng, rate)`.

**Rules.** Awards are paid at the end of the year worked; deferred tranches vest in equal parts after the award and are delivered only to those still employed or covered as good leavers; a sign-on is repaid in full within its period; a guarantee floors the first award; a closed book pays nothing for its last year; every parameter is the caller’s.

**Acceptance tests.** `code/firm/payoffer/tests/`: a base-only package is an annuity; deferral without risk matches hand arithmetic; a leaver forfeits exactly the unvested tranches and a good leaver none; a sign-on is repaid on an early exit; the buyout equals the unvested balance; the certainty equivalent of a sure amount is that amount and falls with risk aversion; the mean with stock risk matches the closed form within 1%.

**Stretch.** Malus and clawback as events with a probability; taxes by location (chapter 15); correlated awards across years; a leaving hazard that depends on the year’s award.

Sources and further reading

- Office of the New York State Comptroller, securities industry bonus releases, March 2022, 2024, 2025 and 2026.
- Directive 2013/36/EU, Article 94, and Directive (EU) 2019/878; Bank of England, PS21/25 – Remuneration Reform.
- The Goldman Sachs Group, Inc., Form 10-K for 2025, Note 29.
- US Internal Revenue Service, Publication 525; 26 U.S.C. 1061.
- HM Treasury and HMRC, Reform of the tax treatment of carried interest: revised tax regime (2025).

## 13.9 Exercises

**Exercise 13.1 ★.**

By how much did New York City’s average securities bonus change from 2021 to 2022 and from 2023 to 2024?

**Solution of Exercise 13.1.**

From $257 500 to $180 000, $-30.1\%$; from $176 500 to $244 700, $+38.6\%$ on the first estimates. The 2025 release reports $+31.5\%$, because it compares with a revised 2023 figure: estimates are revised, so compare a release with its own previous-year figure.

**Exercise 13.2 ★.**

Under the UK rules in force for performance years after October 2025, how much of a £1 000 000 bonus must be deferred?

**Solution of Exercise 13.2.**

40% of the first £660 000 is £264 000 and 60% of the remaining £340 000 is £204 000: £468 000, 46.8% of the bonus.

**Exercise 13.3 ★.**

At a 5% discount rate, what is a tranche vesting in four years worth per unit of award, before any risk?

**Solution of Exercise 13.3.**

$1.05^{-4}=0.82$ per unit of award.

**Exercise 13.4 ★★.**

In the bank offer, list the tranches still unvested at the end of year two and compute their grant value, using an expected award of $200\,000\,e^{0.5^2/2}$.

**Solution of Exercise 13.4.**

The year-1 award vests at the ends of years 2 to 5, so three tranches remain; the year-2 award’s four tranches all remain. Each tranche is $0.4\times200\,000\,e^{0.125}/4=\$22\,663$; seven tranches are $158 641, which the simulation reports as about $158 000.

**Exercise 13.5 ★★.**

Why is a payout of a share of positive profit an option, and what does that do to its certainty equivalent?

**Solution of Exercise 13.5.**

It pays $\max(\text{share}\times\text{P\&L},0)$: a call on the book’s result struck at zero. Its payoff is convex, with a mass at zero and a long right tail; a concave utility weights the zeros heavily, so the certainty equivalent falls further below the mean as risk aversion rises, as the platform curve shows.

**Exercise 13.6 ★★.**

A candidate is offered a sign-on of $100 000 repayable in full if she leaves within a year. She thinks there is a 15% chance she will. What is the sign-on worth to her in expectation, ignoring discounting?

**Solution of Exercise 13.6.**

She keeps it with probability 0.85: $0.85\times100\,000=\$85\,000$ in expectation, before discounting and before the cost of feeling bound to stay.

**Exercise 13.7 ★★★.**

*Coding.* Give the bank offer a [good-leaver provision](#def-in-how-pay-works-rsu) covering voluntary moves. How much does the expected [forfeiture](#def-in-how-pay-works-rsu) fall, and how much does the mean present value rise?

**Solution of Exercise 13.7.**

With the same simulated careers, the expected [forfeiture](#def-in-how-pay-works-rsu) falls from $55 022 to zero and the mean present value rises by the same amount, from $1 617 971 to $1 672 994: a [good-leaver provision](#def-in-how-pay-works-rsu) is worth exactly what the leavers would otherwise have forfeited.

**Exercise 13.8 ★★★.**

*Find the flaw.* “The average Wall Street bonus was $246 900 in 2025, so a trader joining a bank in New York should expect about that.”

**Solution of Exercise 13.8.**

The average covers every securities employee in the city, from operations to senior traders, so it describes no role; it is a mean over a skewed distribution; and the next year’s figure moved by about 30% in either direction in 2022 and 2024. Chapter 14 gives role and seniority ranges.

## 13.10 Problem: Three Offers, One Choice

**Problem 13.1.**

Weekend problem — three offers, one choice

A quant with 500 000 of savings holds three offers: a bank, a market maker and a platform. She wants to know what each is worth to her, and what the bank would cost her to leave in two years.

**Part I — The parts.**

1. Define [base salary](#def-in-how-pay-works-base) and [total compensation](#def-in-how-pay-works-base) . Why do offers compare on [total compensation](#def-in-how-pay-works-base) , and what does it omit?
2. Give New York City’s average securities bonus for 2021–2025 and the share of wages bonuses made up in 2024.
3. Why does pay in trading have two parts?
4. Contrast formulaic and discretionary pay in shape, whose risk, and what ends it.
5. Define the certainty equivalent and say what it depends on besides the package.

**Part II — Deferral.**

6. Define an RSU, [forfeiture](#def-in-how-pay-works-rsu) and a [good-leaver provision](#def-in-how-pay-works-rsu) .
7. State the EU and UK deferral rules and one US bank’s RSU vesting.
8. Name four things that set a deferred award’s value to the employee.
9. When is a US employee’s RSU taxed, and on what value?
10. Give the bank offer’s unvested balance at the end of each year and the value forfeited by leaving after year two.

**Part III — The offers.**

11. Define a sign-on and a [guaranteed bonus](#def-in-how-pay-works-signon) , and say what each solves for the firm.
12. State the three offers’ parameters and the career assumptions.
13. Give each offer’s mean present value and 10th and 90th percentiles.
14. In what share of careers is the platform book closed within five years?
15. Define [carried interest](#def-in-how-pay-works-carry) and a [partnership share](#def-in-how-pay-works-carry) , and state the UK and US carried-interest tax rules.

**Part IV — The verdict.**

16. State the *named result* : each offer’s certainty equivalent at relative risk aversion 1 and 3, and the deferral buyout that makes moving from the bank in year two neutral.
17. Why does the platform offer lose most as risk aversion rises?
18. What should she ask about a buyout besides its size?
19. Which result depends on the illustrative parameters, and which on the structure?
20. In two sentences, how should she choose?

**Solution of Problem 13.1.**

1. Fixed contractual pay; base plus the year’s variable award at award value. It omits [forfeiture](#def-in-how-pay-works-rsu) risk, the instrument’s risk, timing and taxes.
2. $257 500, $180 000, $176 500, $244 700, $246 900; about 42% of wages in 2024.
3. The firm has a fixed cost base and a result that swings with markets; variable pay shares the swing.
4. Formulaic is convex with a mass at zero, bears the book’s risk and ends with the book; discretionary is smoother, bears the pool’s risk and the manager’s judgement, and can go to zero without the job ending.
5. The sure amount with the same expected utility; it depends on risk aversion and other wealth.
6. A promise of a share on vesting; loss of unvested awards on leaving; a term letting some leavers keep them.
7. EU: at least 40% deferred over four to five years, pro rata, 60% for large amounts, half in instruments, variable at most 100% (200%) of fixed. UK: four-year minimum deferral, 40% on the first £660 000 and 60% above. One US bank: RSUs delivered over three years.
8. Time, the instrument’s risk, the probability of leaving (and good-leaver terms), malus and clawback.
9. When it vests, on its market value then.
10. About $90 000, $158 000, $203 000, $226 000, $226 000; leaving after year two forfeits a present value of about $129 000.
11. A joining payment, repayable if leaving early, which pays for what the candidate gives up and retains her; a fixed minimum award, which removes the first year’s risk.
12. As in the tutorial: bank base 250 000, median award 200 000, 40% deferred into stock over four years; market maker base 200 000, median award 250 000 in cash; platform base 175 000, 2% of the book’s profit, closed after a loss beyond 10 million, sign-on 100 000 and guarantee 150 000. Five years, 10% leaving hazard, 5% discount rate, 500 000 of wealth.
13. Bank $1 618 thousand (597 to 2 230); market maker $1 949 thousand (686 to 2 956); platform $1 703 thousand (171 to 3 010).
14. 35.4%.
15. A share of a fund’s profits paid to its managers through the general partner; a member’s profit entitlement in a partnership. UK: income tax on 72.5% of qualifying [carried interest](#def-in-how-pay-works-carry) from 6 April 2026; US: a three-year holding period.
16. At relative risk aversion 1: bank $1 500 thousand, market maker $1 779 thousand, platform $1 439 thousand; at 3: $1 186, $1 365 and $904 thousand. The buyout for a move from the bank at the end of year two is about $158 000 of new awards on the old vesting dates.
17. Its outcomes are the most spread, with a heavy lower tail from closed books; concave utility penalises that most.
18. Its vesting dates, whether it is itself deferred and forfeitable, repayment terms, and good-leaver treatment.
19. The ranking by level depends on the illustrative medians; the shapes (the platform’s tail, the bank’s handcuff) come from the structures.
20. Value each offer with her own risk aversion and the real terms, not the headline; if she cannot bear a year of no pay, the platform is worth well below its mean, and the bank’s deferral is a cost to price if she may move.

## 13.11 Interview questions

**Interview question 13.1 ★ trader, researcher.**

Your bonus is 2% of your book’s positive P&L. What option is that, and on what?

**Solution of Interview question 13.1.**

A call option on the book’s annual P&L struck at zero, with notional 2%; it is also a short put on her job if a loss closes the book.

*What the interviewer is looking for: convexity and the hidden short option of the loss limit.*

**Interview question 13.2 ★ bank.**

Why do bank regulators require part of variable pay to be deferred and paid in shares?

**Solution of Interview question 13.2.**

To align pay with the risk taken: deferred pay can be reduced if losses appear later, and shares tie the payee to the firm’s long-run value rather than a single year’s result.

*What the interviewer is looking for: time-alignment of risk and reward; malus.*

**Interview question 13.3 ★★ researcher, risk.**

Compute the certainty equivalent, with log utility and wealth 100, of a coin flip paying 0 or 200.

**Solution of Interview question 13.3.**

$\sqrt{100\times300}-100=73.2$, against a mean of 100.

*What the interviewer is looking for: the geometric mean of wealth, minus wealth.*

**Interview question 13.4 ★★ developer.**

Design the data model for an employee’s awards so that the unvested balance on any date, and the [forfeiture](#def-in-how-pay-works-rsu) on any leaving date, can be computed.

**Solution of Interview question 13.4.**

One row per tranche: award id, grant date, vest date, units or amount, instrument, conditions (service, performance, good-leaver classes), status. The unvested balance on a date sums tranches with vest date after it; [forfeiture](#def-in-how-pay-works-rsu) on a leaving date applies the conditions to those tranches.

*What the interviewer is looking for: tranche granularity and conditions as data.*

**Interview question 13.5 ★★ bank, risk.**

What is the difference between malus and clawback, and which is harder to enforce?

**Solution of Interview question 13.5.**

Malus reduces an award before it vests; clawback recovers pay already delivered. Clawback is harder, because it must recover money from a person, possibly a former employee, rather than cancel a book entry.

*What the interviewer is looking for: before against after vesting, and enforceability.*

**Interview question 13.6 ★★★ researcher.**

A firm defers 40% of pay over four years. Estimate how much that saves it in turnover, and what data you would need.

**Solution of Interview question 13.6.**

Compare leaving rates of otherwise similar employees with and without unvested balances, or around vesting dates (a jump in leaving just after vesting is the signature). Data: individual award schedules and leaving dates, with controls for performance and market conditions.

*What the interviewer is looking for: an identification strategy, not an assertion.*