CFA Level I Exam · Pricing and Valuation of Interest Rate and Other Swaps

How to Value an Equity Swap for CFA Level I

Updated 7 October 2026 · Fact-checked

An equity swap exchanges the return on a stock or index for a fixed or floating interest payment. At initiation its value is zero, and the fixed rate comes from discount factors: (1 − last factor) ÷ sum of factors. Later, value the equity leg from the index change and subtract the fixed leg's bond-like value.

Understand Equity Swaps Pricing and Valuation

An equity swap is a derivative in which one party pays the return on a stock, a basket or an index, and the other pays either a fixed rate or a floating rate such as a short-term reference rate. Both payments are based on the same notional principal. The notional is never exchanged. Only net payments change hands on each settlement date.

The equity leg pays the percentage return over the period, including dividends if it is a total return swap. If the index rises 5% over the period, the equity payer owes 5% of the notional. If the index falls, the payment reverses: the equity payer receives money from the other side. This is the big difference from an interest rate swap, where the floating rate for the current period is set in advance and is usually positive, although future floating rates are uncertain. In an equity swap the return is not known until the period ends, and it can be negative.

Pricing at initiation works like pricing any swap: no money changes hands, so the swap has zero value. For a fixed-versus-equity swap, the fixed leg is priced like a fixed-rate bond that must be worth par. The equity leg, like a floating-rate bond, is worth the notional at the start and just after each reset. So the fixed rate is the same swap rate you find for an interest rate swap, using discount factors.

After initiation, value changes for two reasons. First, the equity leg moves with the index: its value is the notional times the ratio of the current index level to the level at the last reset, which includes the payment due. Second, the fixed leg moves with interest rates, like a bond. The swap value to the equity receiver and fixed payer is the equity leg value minus the fixed leg value. The counterparty's value is the same number with the opposite sign.

If the equity leg is swapped against a floating rate, the floating leg is worth the notional (plus the accrued next payment) just after a reset. Then the swap is mostly an exposure to the index over the current period.

Key formulas to remember

Fixed swap rate per period: Fixed rate = (1 − Zₙ) ÷ (Z₁ + Z₂ + … + Zₙ); Zᵢ are discount factors for each settlement date. Multiply by the number of periods per year to annualize. This makes the swap value zero at initiation.
Fixed payment each period: Fixed payment = Notional × periodic fixed rate; Use the periodic rate (annual rate ÷ periods per year, or days ÷ 360 if the convention is given).
Equity payment each period: Equity payment = Notional × (Sₜ ÷ Sₜ₋₁ − 1); Add dividends if the swap is a total return swap. A negative result means the equity payer receives money.
Equity leg value between resets: Equity leg value = Notional × (Sₜ ÷ S last reset); This is the total value of the leg, including the payment due, not just the change. Just after a reset the ratio is 1, so it equals the notional.
Fixed leg value: Fixed leg = Σ (Notional × fixed rate × Zᵢ) + Notional × Zₙ; Value it like a fixed-rate bond using current discount factors for the remaining payments.
Swap value to equity receiver (fixed payer): V = Equity leg value − Fixed leg value; Reverse the sign for the equity payer. At initiation V = 0.

How to solve Equity Swaps Pricing and Valuation questions

Work out which leg you are valuing and from whose side, then treat each leg as a simple instrument.

1Identify who pays equity and who pays fixed (or floating). Write down the side the question asks about.
2Note the notional, settlement dates, and the date of the last reset.
3At initiation, if asked for the fixed rate, compute (1 − last discount factor) ÷ sum of discount factors. Annualize if needed.
4Value the equity leg as the notional times index level now ÷ index level at the last reset. This is the total leg value, including the payment due. Add dividends only if the swap is total return.
5Value the fixed leg as a bond: discount each remaining fixed payment and the notional at the end with current discount factors. If the leg is floating, it is worth about par just after a reset.
6Subtract: equity receiver value = equity leg − fixed leg. Flip the sign for the other party.
7Sanity check: a rising index with a stable rate should favour the equity receiver.

Quickest way: Leg-minus-leg shortcut

When to use it: Use for any valuation question after initiation with numbers given for index levels and discount factors.

Compute equity leg = notional × index ratio in one line.
Compute fixed leg = (notional × (1 + fixed rate)) × discount factor when one payment remains. For more payments, add each discounted payment.
Subtract and attach the sign for the side asked.
Eliminate the option that ignores discounting, or the option with the wrong sign.

Common mistakes in Equity Swaps Pricing and Valuation

Treating the equity leg like a known floating rate.
Interest rate swaps teach that the floating leg is always a positive rate.
Fix: Remember the equity payment can be negative. If the index falls, the equity payer receives money.
Valuing the equity leg as the full index level instead of the ratio.
Students forget the notional is a fixed amount and only the change since the last reset matters.
Fix: Use notional × (current level ÷ level at last reset).
Forgetting to discount the fixed leg and the notional.
The notional is not exchanged, so students leave it out, but the bond-style valuation needs it.
Fix: Include the notional with the final fixed payment and discount both.
Not annualizing the fixed rate, or annualizing a periodic rate incorrectly.
The discount-factor formula gives a rate per period.
Fix: Multiply by the periods per year, such as 4 for quarterly settlement.
Giving the answer from the wrong counterparty's side.
Questions switch between fixed payer and equity payer.
Fix: Write which side you are valuing before computing. Swap values for two parties are equal and opposite.
Assuming the swap has value at initiation.
Confusion with options, which carry a premium.
Fix: Swaps are set at zero value. Only the fixed rate is chosen to make it so.

Worked examples

Example 1

A three-year equity swap has annual settlement and a notional of €10 million. The discount factors for years 1, 2 and 3 are 0.97, 0.93 and 0.89. What is the fixed rate at initiation? With annual settlement, the periodic rate equals the annual rate. A. 3.45% B. 3.94% C. 4.42%

Show the solution

Sum of discount factors = 0.97 + 0.93 + 0.89 = 2.79.
Numerator = 1 − 0.89 = 0.11.
Periodic fixed rate = 0.11 ÷ 2.79 = 0.03943, about 3.94%.
Settlement is annual, so there is one period per year. The periodic rate equals the annual rate, and no further annualizing is needed.
Annual fixed payment = €10 million × 0.03943, about €394,300.

Answer: B. 3.94%

Example 2

A swap has a notional of $20 million and semiannual settlement. You receive the equity index return and pay a fixed rate of 4% per year, which is 2% per six-month period. The index was 4,000 at the last reset six months ago and is 4,200 now, with the next settlement in six months. The discount factor for six months is 0.9850. What is the swap's value to you? A. $0.60 million B. $0.91 million C. $1.00 million

Show the solution

Equity leg = $20 million × 4,200 ÷ 4,000 = $21.0 million.
Fixed leg: one payment remains, of notional plus the 2% periodic coupon = $20 million × 1.02 = $20.4 million.
Discount it: $20.4 million × 0.9850 = $20.094 million.
Value to equity receiver = 21.0 − 20.094 = $0.906 million, about $0.91 million.
Option A forgets discounting (21.0 − 20.4). Option C ignores the fixed coupon (21.0 − 20.0).

Answer: B. $0.91 million

Exam tips

Expect the equity-versus-interest-rate-swap contrast: the equity leg can be negative and uncertain, the fixed leg is known.
Read which side the question values. Many wrong options are the right size with the wrong sign, or the other counterparty's value.
Keep a calculator routine: to get a discount factor for half a year at 3%, on the TI BA II Plus press 1.03 y^x 0.5 = 1/x, which gives about 0.9853. Or just use the factors given.
Remember that the swap value is zero at initiation, and the equity leg resets to notional after each settlement.
If dividends are mentioned, check whether the swap is price return or total return before adding them.

Practice questions from Pricing and Valuation of Interest Rate and Other Swaps

Equity Swaps Pricing and Valuation in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Equity Swaps Pricing and Valuation: frequently asked questions

How is an equity swap different from an interest rate swap?

One leg pays the return on a stock or index, not an interest rate. That leg can be negative and is uncertain, so it is valued from the index change. The fixed leg is still valued like a bond.

How do I calculate the fixed rate on an equity swap?

Use the swap rate formula: (1 − last discount factor) ÷ sum of discount factors. This gives a periodic rate, so multiply by the number of periods per year. It sets the swap's initial value to zero.

What is the value of an equity swap at initiation?

It is zero, because the fixed rate is chosen to make the present values of both legs equal. No premium is paid. Value only changes as the index and interest rates move.

How do I value an equity swap after it starts?

Value the equity leg as the notional times the index ratio since the last reset. Value the fixed leg as a bond with the remaining payments. The equity receiver's value is the equity leg minus the fixed leg.