Equity Derivatives

Equity Swap

Also known as: Price return swap

Trade the return of a stock or index against an interest rate — exposure without ownership.

Asset class
Equity derivatives
Instrument type
Swap (linear)
Traded
OTC, bilateral
Typical users
Hedge funds, banks, asset managers
BeginnerWhat is it, really?

An equity swap is an agreement to exchange two streams of payments: one side pays the return of a stock or index, the other pays an interest rate (usually a floating money-market rate plus a spread) on the same notional amount.

Receive the equity leg and you profit when the stock rises and pay when it falls — exactly as if you owned it, though you never touch a share. The other side, typically a bank, holds the actual shares as its hedge and effectively lends you the exposure.

Why bother? Ownership can be expensive or impossible: foreign-investor restrictions, tax frictions, disclosure thresholds, or simply not wanting to tie up cash. A swap converts all of that into a clean financing arrangement.

Key intuition: an equity swap is buying stock with borrowed money, rebuilt as a contract — the interest leg is the loan, the equity leg is the stock.
IntermediateHow it works in practice

Anatomy of a trade

  • Notional: e.g. €10M of an index. Often "resetting" — the notional is marked to the index each period.
  • Equity leg: price return (capital gains only) or total return (including dividends — see Total Return Swap).
  • Financing leg: floating rate (€STR, SOFR) ± spread. The spread is the bank's charge for balance sheet, hedging costs and stock borrow.
  • Resets: at each period-end, the equity performance is cash-settled and the clock restarts.

Who pays whom

If the index returned +3% this quarter and financing is 1% for the period, the equity receiver nets +2% × notional. If the index fell 4%, they pay 5% × notional (4% loss plus 1% financing).

Common motivations

  • Synthetic prime brokerage: hedge funds run long/short books largely via swaps ("delta one").
  • Market access: exposure to markets where direct custody is impractical.
  • Dividend and tax positioning — heavily regulated; the era of cross-border dividend-tax swaps has driven major rule changes.
Worked example: €10M notional, quarterly resets. Index +5.0%, €STR+0.35% financing ≈ 0.85% for the quarter. Equity receiver gets €500k − €85k = €415k.
AdvancedPricing & valuation

Valuation

A resetting equity swap is worth zero at each reset with a fair financing spread; between resets, its value is the accrued equity performance minus accrued financing, discounted:

$$ V_t \;=\; N\left(\frac{S_t}{S_{t_0}} - 1\right) - N\,(r+s)\,\tau \quad\text{(current period, undiscounted approximation)} $$

The full swap is a strip of forward-starting periods, each valued off the equity forward curve \(F(T)\) and the discount curve. Because each period's exposure resets, duration is short and the trade is dominated by the spread \(s\).

What sets the spread

$$ s \;\approx\; \underbrace{c_{\text{balance sheet}}}_{\text{capital, leverage ratio}} \;+\; \underbrace{b_{\text{borrow}}}_{\text{for shorts: stock loan fee}} \;+\; \underbrace{\delta_{\text{div risk}}}_{\text{dividend uncertainty}} \;-\; \underbrace{\pi_{\text{netting}}}_{\text{portfolio offsets}} $$

Long exposure a bank can hedge with easily-funded index futures commands tight spreads; hard-to-borrow single names on the short side can cost hundreds of basis points.

Risk management view

Delta is ~1 by construction; residual risks are dividends (if price-return), rate resets, correlation between client default and equity level (wrong-way risk), and gap risk on resets. Since 2021's family-office blowups, swap desks stress concentrated single-name books far harder.

Practitioner note: quote = funding + borrow + capital. When a swap looks "cheap", one of those three is being given away — find out which and why.