5The Bank Markets Division

A large US bank’s annual report for 2025 allocates $149.5 billion of its common equity to its commercial and investment bank and reports that the business earned 18% on it. The same report explains how the number was chosen: the allocation “incorporates Basel III Standardized risk-weighted assets and the global systemically important banks surcharge … as well as a simulation of capital depletion in a severe stress environment”. Every desk inside that business answers for its share of the equity, and its share depends on which of those rules binds for it. A repo desk that looks nearly free by one rule is the most expensive desk in the building by another.

5.1 What a markets division sells: flow, financing and structuring

A bank’s markets division (One Quant Book 1, chapter 2) earns its revenue in three ways. Flow desks make markets for clients in rates, FX, credit, equities and commodities and earn the spread and the franchise (Book 1, chapter 2; Book 9, chapter 24). Financing desks lend cash and securities to clients, in repo, securities lending and prime services, and earn a spread on the balance sheet they lend. Structuring desks sell tailored derivatives and structured products and earn a margin that pays for the risk they warehouse (One Quant Book 5, chapter 19).

The three lines use the bank’s resources in very different proportions. A flow desk turns its inventory over and uses risk capital for the market risk it holds; a financing desk holds large, low-risk assets on the balance sheet for a thin spread; a structuring desk holds long-dated, complex risk that is capital-intensive per dollar of notional. What the division sells, therefore, is priced not in revenue but in revenue per unit of the constraint each business consumes.

5.2 The capital stack: common equity, leverage and stress buffers

The stack sets two requirements that bind in different places (Figure 5.2). For the bank of the dated box, the risk-based rules require Tier 1 capital of 13.0% of RWA, $257.6 billion; the leverage rule requires 5.0% of its leverage exposure, $265.1 billion. At the level of the whole bank the leverage rule binds, by a small margin; its leverage exposure is 2.7 times its RWA. A markets division whose financing business makes its leverage exposure four times its RWA faces a leverage rule that binds by a wide one.

5.3 Return on capital by desk

A desk’s return on allocated equity is its after-tax profit over its allocated equity, the desk-level version of the return on equity of chapter 1, and it is compared with the bank’s hurdle rate (One Quant Book 6, chapter 19). The division of the chapter (illustrative) has six desks. With equity of 13% of risk-weighted assets, 5% of leverage exposure, or the desk’s stress loss, a tax rate of 25% and the desks’ figures in the module (fm_bank.DESKS), their returns are:

The repo desk is the division’s best business by risk-weighted assets and its worst by leverage. Its assets are short-term secured loans with low risk weights, and they fill the balance sheet: $400 billion of leverage exposure for $15 billion of RWA. Equity derivatives and credit are the opposite: risk-heavy and balance-sheet-light, they are bound by RWA.

The chapter’s desks need $35.1 billion of equity by RWA and $55.5 billion by leverage; the group holds $55.5 billion, but the desks’ own maxima add up to $62.1 billion. Charged each by its own binding constraint, the division would report a return of 11.4% on equity it does not have. A consistent allocation scales one key to the group’s binding constraint, or blends the keys with weights that add to the group’s equity, as the bank of the dated box does when it combines RWA, its GSIB surcharge and a stress simulation.

5.4 The balance sheet as a scarce input

At 0.6% a year the repo desk’s $400 billion of leverage exposure costs $2.4 billion, and its after-tax profit of $1.05 billion becomes a loss of $0.75 billion. It breaks even at a charge of 0.35% (35 basis points) a year. The prime services desk earns $0.45 billion after the charge and equity derivatives $1.11 billion. The charge does not say that repo should close; it says that every dollar of balance sheet it uses must be priced at 60 basis points a year, and that the business is viable only at a spread above that.

def allocate(desks, keys: Keys) -> dict:
    rwa = np.array([d.rwa for d in desks]) * keys.k_rwa
    lev = np.array([d.le for d in desks]) * keys.k_le
    st = np.array([d.stress for d in desks])
    return {"rwa": rwa, "leverage": lev, "stress": st, "binding": np.maximum.reduce([rwa, lev, st])}


def roae(desks, equity, tax: float) -> np.ndarray:
    return np.array([d.profit(tax) for d in desks]) / np.asarray(equity, float)


def binding(desk: Desk, keys: Keys) -> str:
    parts = {"rwa": keys.k_rwa * desk.rwa, "leverage": keys.k_le * desk.le, "stress": desk.stress}
    return max(parts, key=parts.get)


def balance_sheet_charge(desk: Desk, rate_per_le: float, tax: float) -> float:
    """After-tax profit after a charge of rate_per_le per unit of leverage exposure (the charge is deductible)."""
    return (desk.revenue - desk.cost - rate_per_le * desk.le) * (1 - tax)


def breakeven_charge(desk: Desk) -> float:
    """The charge per unit of leverage exposure that takes the desk's profit to zero."""
    return (desk.revenue - desk.cost) / desk.le


def optimal_mix(desks, equity: float, keys: Keys, x_max: float = 1.5) -> np.ndarray:
    """Scale x_i in [0, x_max] of each desk (x = 1 today) maximising after-tax profit, subject to the group's
    equity covering the RWA-based and the leverage-based requirements of the whole mix."""
    c = -np.array([d.profit(keys.tax) for d in desks])
    A = np.array([[keys.k_rwa * d.rwa for d in desks], [keys.k_le * d.le for d in desks]])
    res = linprog(c, A_ub=A, b_ub=[equity, equity], bounds=[(0.0, x_max)] * len(desks), method="highs")
    if not res.success:
        raise RuntimeError(res.message)
    return res.x

With the group’s equity fixed at the $55.5 billion its leverage requirement holds today, the desk mix that maximises the division’s after-tax profit (a linear programme, firm.bankdesk.optimal_mix, each desk scaled between zero and 1.5 times its size) shrinks repo to about a tenth of its size and grows every other desk to the cap (Figure 5.4): profit rises from $7.05 billion to $9.12 billion. The programme assumes each desk can grow without lowering its margins and that the desks are independent. The second assumption is the one a franchise breaks.

5.5 The client franchise

A client who finances its positions with a bank also clears, borrows and trades with it. The flow desks’ franchise (One Quant Book 1, chapter 2) is built partly on the financing desks’ balance sheet: prime services clients choose the bank that lends to them, and trade with it; the central risk book (One Quant Book 9, chapter 25) nets the flows of all of them. A desk that looks value-destroying alone may be what keeps clients in the building.

5.6 Tutorial: six desks and three keys

What to change next. Raise the leverage requirement by the new eSLR buffer and redo the allocation; add a constraint that prime services cannot exceed repo’s size, a crude franchise link, and rerun the programme.

5.7 Build: the division’s capital model

5.8 Exercises

5.9 Problem: The Desk That Uses No Capital

5.10 Interview questions