Distinguish forward price and existing-contract value

Learning goals

• Calculate the existing long-forward value at month six.
• Explain why 105 applies to this case.
• Identify the case-specific assumption or failure mode before taking action.

Draft · approximately 55 minutes, excluding further revision.

Shared case and decision context

A non-dividend asset costs 100. A new one-year forward uses a 5% annual risk-free rate and frictionless borrowing. Six months later spot is 110, the old delivery price remains 105 and the remaining half-year discount rate is still 5% annually compounded.

Economic or professional mechanism

The delivery price makes a new forward have zero value at initiation under ideal assumptions. An existing forward keeps its contractual delivery price and acquires positive or negative market value as spot, rates and carry change. Pricing and valuation therefore answer different questions. Known income is subtracted in present value when determining the initial forward price.

Apply, challenge and communicate

Initial forward price is 105; the existing long is worth approximately 7.5305 at month six. Futures daily settlement changes cash timing and can produce differences from forwards when interest rates are stochastic. A positive economic mark does not remove collateral, liquidity or counterparty obligations.

Lock a future interest period

For a simple-compounded forward rate agreement the fixed rate is implied by discount factors for the start and end of the borrowing interval. For an interval fraction delta, F=(d_start/d_end−1)/delta. A borrower buying protection against rising rates receives a payment when the reference rate exceeds the contracted rate, subject to settlement conventions. A start-date-settled FRA discounts the end-period interest difference back over that interval. Exchange-traded short-rate futures can differ through daily settlement and convexity effects; do not automatically substitute a futures-implied rate for an OTC FRA rate.

Price a bond delivery after known coupon income

For a forward on a coupon bond, separate full price, accrued interest, coupons before delivery and the contract’s quotation convention. A full spot price102, known coupon3 with PV2.9 before a one-year delivery and a5% annual financing rate imply a simplified forward full delivery price(102−2.9)×1.05=104.055. A quoted clean forward can require subtracting delivery-date accrued interest. A bond futures additionally requires attention to conversion factors, deliverable baskets and cheapest-to-deliver options, so its quoted price is not automatically the same as this single-bond forward.

Value the fixed and floating swap legs consistently

At initiation a plain fixed-for-floating interest-rate swap has a par fixed rate that equates discounted fixed and floating cash flows under the specified curve framework. In a simplified single-curve annual example with d1=.96,d2=.91, par rate=(1−.91)/(.96+.91)=4.8128%. For an existing receive-fixed swap, value equals fixed-leg value minus floating-leg value using its old contractual fixed rate. Modern collateral and multi-curve conventions can require different projection and discount curves. Notional generally scales interest payments without being exchanged in a same-currency plain swap.

Convert both currency-swap legs into one numeraire

A currency swap exchanges cash flows in different currencies and may exchange principal at inception and maturity. Value each leg using the relevant currency, projection and discounting conventions, then convert one leg at current spot to obtain a value in a single reporting currency. If the domestic leg PV is105 and the foreign leg PV90 foreign units at1.20 domestic/foreign, receive-domestic/pay-foreign value is105−108=−3 domestic. Cross-currency basis and collateral terms matter; merely comparing nominal coupon percentages across currencies is insufficient.

Separate equity total return from the financing leg

An equity swap can exchange a reference asset’s price or total return for a fixed or floating financing payment. Total return includes dividends when the contract specifies them; price return alone does not. On100 notional, a6% total equity return and4% financing rate over a one-year period imply a2 payment to the equity-return receiver before other terms. Existing contract valuation depends on reset dates, accrued payments and future leg values, not simply today’s equity index level. Counterparty and collateral risks remain even when the equity exposure is economically replicated.

Formula and assumptions

Forward price F0=S0*(1+r)^T; existing long value=St−K/(1+r)^(T−t)

Case analysis with explicit assumptions

1. A non-dividend asset costs 100. A new one-year forward uses a 5% annual risk-free rate and frictionless borrowing. Six months later spot is 110, the old delivery price remains 105 and the remaining half-year discount rate is still 5% annually compounded.
2. Method: Forward price F0=S0*(1+r)^T; existing long value=St−K/(1+r)^(T−t)
3. Case result: 7.53. Initial forward price is 105; the existing long is worth approximately 7.5305 at month six. Futures daily settlement changes cash timing and can produce differences from forwards when interest rates are stochastic. A positive economic mark does not remove collateral, liquidity or counterparty obligations.

Errors to catch

• Do not replace the stated assumptions with an unstated shortcut. Reconcile units, timing and the claim being valued or duty being assessed.
• The fact that contracts have underlying assets is not a defensible conclusion for these case facts.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.cfainstitute.org