10Hiring and Compensation

A trader paid fifteen per cent of a twenty-million-dollar year and a trader paid nothing after a two-million-dollar loss on the next desk may have exactly the same skill. For a trader whose risk gives an annual P&L volatility of $10 million and whose true Sharpe ratio is the desk’s average of 0.8, the first year happens about one year in nine and the second one year in six. One year of P&L measures luck far more than ability: on the chapter’s desk, 87% of the differences in a year’s formulaic pay between traders are luck. A pay rule decides which of the two the firm is buying, and how long it takes to find out.

10.1 The pipeline and the interview

A trading firm hires from a funnel: applications, screens, tests, interviews, offers, acceptances. Two facts shape it. The base rate is low, so a test with a modest false-positive rate still fills the later stages with people who will not be hired; and every stage’s decision is a noisy measurement, so the order of stages matters: cheap, valid tests first, expensive ones last.

The research on selection is unusually settled on one point. Schmidt and Hunter’s review of 85 years of studies (1998) and its revision by Sackett, Zhang, Berry and Lievens (2022), which found that earlier estimates had been overstated by 0.10 to 0.20 through over-corrections, agree that structured interviews predict job performance better than unstructured ones; in the revision they are the top-ranked selection procedure. The interview questions of this series are written for that purpose: the same question, a known good answer, and what the interviewer is looking for. One Quant Book 18 applies the same format to new questions.

10.2 Pay structures: base, bonus and deferral

Pay in trading has three parts: base salary, fixed for the year; a bonus, decided after it; and, above some level, a deferred part that vests over later years. The balance between them is the firm’s choice where no rule limits it and a regulator’s where one does.

10.3 Sizing a bonus pool

A pool is sized top-down, then allocated. The common rules are a share of revenue (the compensation ratio of chapter 1, fixed in advance) or a share of net profit after costs and a charge for the capital used (chapter 7). The second pays only for value added: a desk that earns less than its cost of capital has no pool, whatever its revenue. The choice matters most in the years the firm least wants to pay: a revenue-based pool pays out in a year the desk destroyed value on its capital.

10.4 Formulaic against discretionary: paying for skill, not luck

A trader’s P&L in a year is skill plus luck. If skill across traders has a standard deviation $s$ (in P&L per year) and luck, the year’s noise, a standard deviation $n$, then after $T$ years the average P&L correlates with skill at $\sqrt{s^2/(s^2+n^2/T)}$.

On the chapter’s desk (illustrative: twenty traders, annual P&L volatility $10 million each, true Sharpe ratios spread with a standard deviation of 0.4, so $s=4$ and $n=10$), luck is 86% of the variance of one year’s P&L, and it takes 11.1 years of P&L for it to correlate with skill at 0.8. A formulaic payout of 15% of positive P&L inherits both: 87% of the variance of a year’s pay is luck, and its correlation with skill is 0.35 after one year, 0.64 after five and 0.80 after about twelve (Figure 10.1).

A discretionary rule can do better only if it uses information the P&L does not contain: the quality of the trader’s decisions, their risk-taking, their contribution to others’ P&L. Judgement applied to the P&L alone is at best a shrinkage estimate of skill (Listing 10.1), and on the chapter’s desk it correlates with skill at 0.37 after one year against the formulaic 0.35, and slightly less after five (0.61 against 0.64), because shrinkage is proportional and the pool it shares moves with the desk’s luck. A risk-adjusted payout, charging each trader’s capital, correlates at 0.34 and 0.63: it pays for value added, not for skill detection.

def shrunk_skill(pnl_history, sigma: float, prior_mean: float, prior_sd: float):
    """pnl_history (years, traders), annual P&L in units where each trader's annual noise has sd `sigma`.
    Posterior mean of each trader's expected annual P&L under a normal prior N(prior_mean, prior_sd^2)."""
    h = np.atleast_2d(np.asarray(pnl_history, float))
    n = h.shape[0]
    w = prior_sd ** 2 / (prior_sd ** 2 + sigma ** 2 / n)
    return prior_mean + w * (h.mean(0) - prior_mean)


def discretionary(pnl_history, pool: float, sigma: float, prior_mean: float, prior_sd: float):
    s = np.maximum(shrunk_skill(pnl_history, sigma, prior_mean, prior_sd), 0.0)
    tot = s.sum()
    return pool * s / tot if tot > 0 else np.zeros_like(s)

10.5 Deferral, clawback and retention

Deferral does three jobs. It exposes pay to the losses that appear after the year (through malus); it aligns pay with the firm’s longer-term results; and it builds a balance that the employee loses by leaving. The chapter’s plan pays 60% of each award in cash and vests the rest in four equal annual parts (Figure 10.3). A trader who receives the same award every year carries, at each year end, an unvested balance equal to one full year’s award: $0.4\times(1+\tfrac34+\tfrac12+\tfrac14)=1$.

@dataclass(frozen=True)
class DeferralPlan:
    cash_share: float = 0.6
    years: int = 4


def schedule(award: float, plan: DeferralPlan) -> np.ndarray:
    """Payments of one award: the cash share at once, the rest in equal parts in each of the next `years` years."""
    out = np.zeros(plan.years + 1)
    out[0] = plan.cash_share * award
    out[1:] = (1 - plan.cash_share) * award / plan.years
    return out


def unvested(awards_by_year, plan: DeferralPlan, now: int) -> float:
    """Unvested balance at the end of year `now` (after that year's vesting), awards_by_year[t] granted in year t."""
    bal = 0.0
    for t, a in enumerate(awards_by_year[: now + 1]):
        s = schedule(a, plan)
        bal += s[now - t + 1:].sum() if now - t + 1 <= plan.years else 0.0
    return bal

The balance is the retention device and the price of a move. A competitor that hires the trader must buy out a year’s award in deferred instruments of its own, and the trader carries the firm’s malus risk for the years the balance vests. Clawback reaches further than malus, to pay already received, and is harder to enforce: the US rule for listed companies’ executives, the EU banking rules and most private firms’ plans all rely mainly on malus, applied to what is still unvested.

10.6 Tutorial: twenty traders and three pay rules

What to change next. Double the skill spread and watch the years needed fall by four; give the discretionary rule a noisy observation of each trader’s decision quality alongside the P&L.

10.7 Build: the bonus pool

10.8 Exercises

10.9 Problem: Paid for Luck

10.10 Interview questions