CFA Level II Exam · Pricing and Valuation of Forward Commitments

How to Value an Equity Swap at CFA Level II

Updated 7 October 2026

An equity swap exchanges the return on a stock or index for a fixed or floating payment. To value it, treat the equity leg as worth the current equity value scaled to the notional, and treat the other leg as a bond. The value to the equity receiver is the equity leg minus the bond leg.

Understand Pricing and Valuation of Equity Swaps

An equity swap is a contract where one party pays the return on a stock, a basket or an index, and the other pays a fixed rate, a floating rate, or the return on a different equity. The payments are based on a notional principal. The notional is never exchanged. Only the net difference changes hands on each settlement date.

The key idea is that each leg looks like something you can already price. The fixed leg is a fixed-rate bond with the notional repaid at the end. The floating leg is a floating-rate bond, which is worth the notional on each reset date. The equity leg behaves like the underlying equity position. Its value at any time equals the notional scaled by how much the equity has moved since the last reset.

At initiation, a swap has zero value. The equity leg is worth the notional, so the fixed rate is set so the fixed bond is also worth the notional. That gives the swap fixed rate formula below. After initiation, the equity leg value moves with the equity. The bond leg moves with interest rates. The difference is the swap value.

The payoff on a settlement date is simple. The equity receiver gets notional × the equity return over the period, and pays the fixed or floating amount. If the equity return is negative, the equity receiver also pays that loss to the counterparty. This is a major difference from an interest rate swap, where the floating payment is set at the start of the period and is known in advance. The equity return can be negative.

Compared with an interest rate swap, the equity leg payment is not known in advance. Interest rate swap values change only through interest rates. Equity swap values change through the equity price and interest rates. The equity leg's return can be negative and is generally more volatile than a floating rate.

Key formulas to remember

Swap fixed rate at initiation (per period): Fixed rate = (1 − Z_n) ÷ Σ Z_i; Z_i is the discount factor for payment date i. Z_n is the last one. Multiply by the number of periods per year to annualise.
Fixed leg value (as a bond): V_fixed = NP × [c × Σ Z_i + Z_n]; c is the periodic fixed rate. NP is the notional. Use current discount factors for the remaining payment dates.
Equity leg value: V_equity = NP × S_t ÷ S_last reset; S_last reset is the equity level at the last reset date. For a swap just after initiation, S_last reset is the starting level.
Floating leg value between resets: V_float = NP × (1 + r_last × days in period ÷ 360) ÷ (1 + r_now × days remaining ÷ 360); r_last is the rate set at the last reset. The numerator uses the full length of the period (for example 90 days), not the days elapsed. r_now is the current rate for the days remaining to the next payment. The day count shown is 360.
Value to the equity receiver: V_swap = V_equity − V_bond leg; The bond leg is fixed or floating. The equity payer's value is the negative of this.
Net settlement for the equity receiver: Net = NP × equity return − NP × periodic fixed or floating rate; A negative equity return makes the equity receiver pay more.

How to solve Pricing and Valuation of Equity Swaps questions

Use the same sequence for any equity swap question. Read the vignette first and mark who pays equity and who pays fixed or floating.

1Identify the direction. Find who receives the equity return and who pays fixed or floating. Decide whose value you are asked for.
2Pull the data: notional, settlement frequency, equity level at the last reset and now, and current discount factors or rates.
3Value the equity leg as NP × S_t ÷ S_last reset. If total return or dividends are mentioned, use the return the contract specifies.
4Value the other leg as a bond. For fixed, discount the fixed payments plus the notional using current discount factors. For floating, use the notional on a reset date, or the floating formula between resets.
5Subtract the bond leg from the equity leg to get the value to the equity receiver.
6Remember that the equity receiver is the fixed (or floating) payer. Flip the sign only when the question asks for the equity payer.
7For a settlement question, compute the equity return over the period, multiply by notional, and net it against the fixed or floating payment.
8Check the sign. If the equity has risen more than the bond leg has accrued, the equity receiver should be in the money.

Quickest way: Equity leg minus bond leg

When to use it: Use it when the vignette gives current discount factors or a current rate and asks for swap value or settlement. It avoids rebuilding the swap from scratch.

Write the equity leg in one line: NP × (S_now ÷ S_last reset).
Write the bond leg in one line: NP × (c × ΣZ + Z_n) for fixed, or NP on a reset date for floating.
Subtract and attach the sign for the equity receiver.
If asked for a new fixed rate for a fresh swap, use (1 − Z_n) ÷ ΣZ and skip the rest.

Common mistakes in Pricing and Valuation of Equity Swaps

Valuing the equity leg as zero or as NP after the equity has moved
Students remember that a floating leg resets to par and apply the same idea to the equity leg.
Fix: The equity leg is worth NP × S_now ÷ S_last reset. It only equals NP just after a reset.
Forgetting to include the notional in the fixed leg value
The notional is not exchanged in the swap, so students leave it out of the bond.
Fix: Value the fixed leg as a bond. The notional is added at the end for valuation purposes, using the last discount factor.
Using original discount factors after initiation
The initial curve is given first in the vignette and is easy to grab.
Fix: Use the discount factors for the remaining payment dates as of the valuation date.
Reporting the wrong party's sign
Vignettes may name the parties in different ways, or ask for the counterparty's value, and students attach the sign of the wrong party.
Fix: Write the party at the top: equity receiver = fixed (or floating) payer. The value to that party is equity leg minus bond leg. Flip the sign only when the question asks for the equity payer.
Treating a negative equity return as zero in settlement
Students think of the equity leg like an option or a floating rate that cannot be negative.
Fix: A negative return means the equity receiver pays the loss and also pays the fixed or floating amount.
Applying the floating formula on a reset date
Students use the long formula in every question.
Fix: Just after a reset, the floating leg is worth NP. Use the long formula only between resets.

Worked examples

Example 1

A 2-year swap has annual settlement and a notional of USD 20,000,000. Party A receives the return on an equity index and pays a fixed rate. At initiation the index is 4,000 and the discount factors are Z1 = 0.9615 and Z2 = 0.9246. (a) Calculate the fixed rate at initiation. (b) Six months after initiation the index is 4,300 and the discount factors for the remaining payments, which are 0.5 and 1.5 years away, are 0.9800 and 0.9450. Use the fixed rate from (a), rounded to 3.998%. Calculate the swap value to Party A. (c) Separately, consider the first settlement date, one year after initiation, which is the 0.5-year payment date in (b). On that date the index is 4,200 (this replaces the 4,300 in (b)), compared with 4,000 at initiation. Calculate Party A's net payment at that settlement, using the 3.998% fixed rate and price return only.

Show the solution

(a) Fixed rate = (1 − 0.9246) ÷ (0.9615 + 0.9246) = 0.0754 ÷ 1.8861 = 3.998% (rounded to three decimals; this is slightly below 4.00%).
(b) The last reset was at initiation, so the equity leg is the current index ratio times the notional = 20,000,000 × 4,300 ÷ 4,000 = USD 21,500,000.
(b) Fixed payment each year = 0.03998 × 20,000,000 = USD 799,600. The first payment falls 0.5 years from the valuation date and is discounted with Z = 0.9800. The second falls 1.5 years away and uses Z = 0.9450.
(b) Fixed leg = 799,600 × (0.9800 + 0.9450) + 20,000,000 × 0.9450 = 799,600 × 1.9250 + 18,900,000 = 1,539,230 + 18,900,000 = USD 20,439,230.
(b) Swap value to Party A (equity receiver) = 21,500,000 − 20,439,230 = USD 1,060,770.
(c) The settlement period runs from the initiation level of 4,000 to 4,200. Equity return = 4,200 ÷ 4,000 − 1 = 5%.
(c) Equity payment = 0.05 × 20,000,000 = USD 1,000,000 received by Party A.
(c) Party A pays the fixed amount of USD 799,600. Net = 1,000,000 − 799,600 = USD 200,400 received.

Answer: (a) About 3.998%. (b) USD 1,060,770 positive to Party A. (c) Party A receives a net USD 200,400.

Example 2

A quarterly-settlement swap has a notional of USD 10,000,000. Party B pays the return on an equity index and receives a floating rate. The index was 2,500 at the last reset and is 2,550 now. The floating rate set at the last reset was 1.60% annualised. The period is 90 days, 30 days have passed, and the current rate for the remaining 60 days is 2.10%. Use a 360-day year. (a) Calculate the value of the floating leg. (b) Calculate the swap value to Party B. (c) What is the value of the swap to Party B just after the next reset if both legs reset on the same date?

Show the solution

(a) Next floating payment factor, using the full 90-day period = 1 + 0.016 × 90 ÷ 360 = 1.004.
(a) Accrual/discount divisor for the remaining 60 days = 1 + 0.021 × 60 ÷ 360 = 1.0035. This is a divisor, not a discount factor.
(a) Floating leg = 10,000,000 × 1.004 ÷ 1.0035 = about USD 10,004,983.
(b) Equity leg = 10,000,000 × 2,550 ÷ 2,500 = USD 10,200,000.
(b) Party B pays equity and receives floating, so value = floating leg − equity leg = 10,004,983 − 10,200,000 = −USD 195,017.
(c) After a reset both legs are worth the notional, so the net value is zero.

Answer: (a) About USD 10,004,983. (b) About −USD 195,017 for Party B, so the swap is a liability to Party B. (c) Zero.

Exam tips

Mark the direction first. Many wrong answers come from mixing up equity receiver and equity payer.
Remember that the equity leg is worth NP × S_now ÷ S_last reset, not NP. It only equals NP right after a reset.
Look for the last discount factor in the vignette and use it for the notional in the fixed leg.
If the question asks for the fixed rate at initiation, use (1 − Z_n) ÷ ΣZ. Do not build a bond value.
Do a quick sign check. If the equity has gone up and rates are stable, the equity receiver's value should be positive. Cross out any option that contradicts this.

Pricing and Valuation of Equity Swaps: frequently asked questions

How do I value an equity swap where I pay fixed and receive equity?

Value the equity leg as NP × S_now ÷ S_last reset. Value the fixed leg as a fixed-rate bond with the notional repaid at the end, using current discount factors. Your swap value is equity leg minus fixed leg.

What is the difference between an equity swap and an interest rate swap?

In an interest rate swap one leg is fixed and the other floats with an interest rate, so the swap's value changes only through interest rates. In an equity swap one leg depends on an equity return, which can be negative and is generally more volatile than a floating rate. That is why the equity receiver may owe both legs in a bad period.

Why is an equity swap worth zero at initiation?

The equity leg is worth the notional at the start. The swap fixed rate is chosen so the fixed leg bond is also worth the notional. Both legs are equal, so the net value is zero.

How is the floating leg valued between resets?

Use NP × (1 + r_last × days in period ÷ 360) ÷ (1 + r_now × days remaining ÷ 360). The numerator uses the full period length, not the days elapsed. On a reset date, the floating leg is simply worth the notional.