How Level I tests no-arbitrage logic, replication, cost of carry, and forward contract pricing and valuation.
Once you know what contract family you are looking at, Derivatives becomes a no-arbitrage topic. Level I wants you to understand that derivative prices are anchored by replicating portfolios and the economics of carrying the underlying through time.
Candidates often miss these questions because they:
The stronger reader asks which portfolio replicates the derivative payoff.
| Concept | What it means | Why it matters |
|---|---|---|
| Arbitrage | Riskless profit with no net investment | If arbitrage exists, prices will not remain at that level |
| Replication | Building the same payoff using other assets | Equivalent payoffs should have equivalent values under no-arbitrage |
The exam often tests this in words before it tests it in formulas.
Forward price is not just a guess about where spot price will be later. It reflects the economics of holding the underlying until expiration:
That is why the no-arbitrage forward price can differ from the market’s expected future spot price.
For a basic one-period setup:
$$ F_0(T) = S_0(1 + r)^T $$
where (S_0) is spot price and (r) is the financing rate over the contract horizon.
The point is not just the algebra. If the forward price is too high or too low relative to this carry relationship, a cash-and-carry or reverse cash-and-carry arbitrage may exist.
| Price concept | What it represents | Common trap |
|---|---|---|
| Spot price | Current cash-market price of the underlying | Treating it as if it already includes all carry through expiration |
| Forward price | Contract price set today for future delivery | Confusing it with the contract’s value after initiation |
| Expected future spot price | Market expectation of future cash-market price | Assuming it must equal the no-arbitrage forward price |
Level I likes testing this distinction because many wrong answers sound intuitive but mix economic roles.
At initiation, the forward contract price is set so that contract value is zero. Later, if market conditions change, the original contract can gain or lose value.
For a long forward on a non-income asset, a simple discrete-time expression is:
$$ V_t(T) = S_t - \frac{F_0(T)}{(1+r)^{T-t}} $$
If the market-implied forward price rises above the delivery price locked into your contract, the long position gains value.
A standard forward-rate link is:
$$ (1+s_2)^2 = (1+s_1)(1+f_{1,1}) $$
The point is that two investment paths across time should be consistent. Level I may ask you to interpret the implied forward rate rather than treat it as a guaranteed future realized rate.
A candidate sees that the quoted forward price on a non-income asset is above the spot price and concludes the contract must be overvalued. That is too fast. A stronger answer asks whether the price difference is just the normal financing carry or a true no-arbitrage violation.
That is classic Level I design: the relationship matters more than the raw direction.
What is the strongest reason a forward price on a non-income asset can exceed the current spot price without implying mispricing?
Best answer: The forward price can reflect the cost of financing the underlying until expiration, so a price above spot may simply reflect normal carry.
Why: Level I is testing whether you understand no-arbitrage pricing rather than naive price comparison.