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CFA Level I Exam · Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Forward Pricing for Assets with No Cash Flows

Updated 7 October 2026 · Fact-checked

The forward price of an asset with no income or storage costs is the spot price compounded at the risk-free rate to the contract's expiry: F0 = S0(1+r)^T with discrete compounding, or F0 = S0 × e^(rT) with continuous compounding. It is set so the contract has zero value at initiation and no arbitrage exists.

Understand Forward Pricing for Assets with No Cash Flows

A forward contract is an agreement to buy or sell an asset at a fixed price on a future date. The fixed price is the forward price. Nobody pays anything at initiation, so the contract must start with a value of zero.

For an asset with no cash flows, such as a non-dividend-paying stock, there is no income to collect and no storage cost while you hold it. Now compare two ways to own the asset at time T. You can buy it today at S0 and hold it. Or you can enter a forward and pay the forward price at T.

If you buy today, you tie up S0 of money. That money could have earned the risk-free rate. So holding the asset has an opportunity cost, and the forward price must reflect it. The forward price is the spot price grown at the risk-free rate over the life of the contract.

No-arbitrage enforces this. If the forward price is too high, you borrow at the risk-free rate, buy the asset, and sell it forward. You lock in a risk-free profit. If it is too low, you short the asset, invest the proceeds at the risk-free rate, and buy it forward. Either way the profit disappears only at the no-arbitrage price.

Note that the forward price is not a forecast of the future spot price. It depends on today's spot price, the risk-free rate and time. Your view on the asset does not enter the formula.

Key formulas to remember

Forward price, discrete compounding
F0(T) = S0 × (1 + r)^T
r is the annual risk-free rate and T is in years. Use this when the question gives an effective annual rate.
Forward price, continuous compounding
F0(T) = S0 × e^(rT)
Use when the rate is stated as continuously compounded. On the BA II Plus, e^x is 2ND then LN.
Spot price from forward price
S0 = F0(T) ÷ (1 + r)^T
Rearrange to find the spot or the implied rate. This is the present value of the forward price.
Implied risk-free rate
r = (F0 ÷ S0)^(1/T) − 1
Discrete form. For continuous compounding, r = ln(F0 ÷ S0) ÷ T.

How to solve Forward Pricing for Assets with No Cash Flows questions

Use this method for any forward pricing question on an asset with no income or storage costs.

  1. 1Confirm the asset has no cash flows. If it pays dividends or has storage costs, a different formula applies.
  2. 2Identify S0, the risk-free rate r and the time T. Convert months to years, for example 6 months = 0.5.
  3. 3Check how the rate is compounded. Annual or effective rates use (1 + r)^T. Continuous rates use e^(rT).
  4. 4Match the rate and time units. If T is in years, r must be annual.
  5. 5Compute the growth factor first, then multiply by S0.
  6. 6Check the answer. F0 should be above S0 when r is positive and T is positive.
  7. 7Choose the option closest to your result. Options run from smallest to largest, so a quick order-of-magnitude check removes one or two.

Quickest way: Growth factor shortcut

When to use it: Use when you need a fast answer and the numbers are simple, or when you only need to eliminate two options. It works only when r and T are small.

  1. Estimate the growth: for small r and T, the factor is about 1 + rT.
  2. Multiply S0 by this factor to get a rough forward price.
  3. For small r and T, discrete and continuous answers differ only slightly. This does not hold for large rates or long times, so do not rely on it there. Eliminate options that are far from the estimate.
  4. Do the exact calculation only if two options remain close.
  5. On the BA II Plus, use S0 × (1 + r)^T with the yx key, or S0 × e^x with 2ND then LN for continuous.

Common mistakes in Forward Pricing for Assets with No Cash Flows

  • Using the expected future spot price instead of the spot price today.

    Students think a forward is a prediction of the future price.

    Fix: Always start from today's S0. The forward price depends only on S0, r and T.

  • Using (1 + r)^T when the rate is continuously compounded, or e^(rT) when it is annual.

    The two formulas look similar and the question wording about compounding is easy to skip.

    Fix: Read the rate description before choosing the formula. 'Continuously compounded' means e^(rT).

  • Leaving T in months.

    The question says 9 months and the rate is annual.

    Fix: Convert T to years before calculating, for example 9 months = 0.75 years.

  • Discounting instead of compounding.

    Students confuse forward pricing with present value.

    Fix: Forward price is above spot for a positive rate. Only go backward, dividing by the growth factor, if you are asked for the spot price.

  • Adding dividends or costs to an asset that has none, or ignoring them when they are given.

    Students memorise one formula for all underlyings.

    Fix: Check the wording. This formula applies only when there are no cash flows on the asset.

Worked examples

Example 1

A non-dividend-paying stock trades at $80. The annual risk-free rate is 4% (effective annual). What is the price of a forward contract expiring in 6 months?

Show the solution
  1. No cash flows, so F0 = S0 × (1 + r)^T.
  2. T = 0.5 years.
  3. (1.04)^0.5 = 1.019804.
  4. F0 = 80 × 1.019804 = 81.584.

Answer: About $81.58. Order of the options would be smallest to largest, so choose the option closest to 81.58.

Example 2

A stock with no dividends has a spot price of €50. The continuously compounded risk-free rate is 5%. What is the 9-month forward price?

Show the solution
  1. Continuous compounding, so F0 = S0 × e^(rT).
  2. T = 9 ÷ 12 = 0.75 years.
  3. rT = 0.05 × 0.75 = 0.0375.
  4. e^0.0375 = 1.038212.
  5. F0 = 50 × 1.038212 = 51.9106.

Answer: About €51.91. Discrete compounding at 5% would give about €51.86, so check which compounding the question states.

Exam tips

  • Look for the words 'continuously compounded' in the stem. They decide which formula you use.
  • Convert months to years first. This is the most frequent error in time-pressured questions.
  • With three options, a sense check (F0 above S0 by roughly rT) often removes two of them.
  • Know the reverse question: given F0 and S0, find the implied rate or the spot price.
  • Expect the same logic to carry into the next topics on assets with income or carry costs, where you adjust the spot price.

Practice questions from Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Forward Pricing for Assets with No Cash Flows: frequently asked questions

What is the forward price formula for a stock with no dividends?

With discrete compounding, F0 = S0(1 + r)^T. With continuous compounding, F0 = S0 × e^(rT). Here r is the risk-free rate and T is time in years.

Why is the forward price not equal to the expected future spot price?

The forward price is set by no-arbitrage using today's spot price and the risk-free rate. It does not depend on what investors expect the price to be. Expectations affect the future spot price, not the forward price.

Is the forward contract worth anything at initiation?

No. The forward price is set so the contract has zero value to both parties when it starts. Value changes later as the spot price and time move.

How do I calculate e^(rT) on the BA II Plus?

Enter the value of rT, then press 2ND and LN to get e^x. Multiply the result by S0. Keep rT as a decimal, for example 0.0375.