Expectancy model
Also written Expectancy model of futures pricing
The view that a futures price is simply the market's expected spot price at expiry, so futures can trade at a premium or discount to spot and signal the expected direction of prices.
In plain language
There are two ways to explain where a futures price comes from.
The first is cash and carry: buy the bond today, finance it, collect its income, and the futures price must equal cash price + financing cost − income on the cash position, or someone can arbitrage. That model rests on assumptions the workbook lists: the underlying is available in abundance, it is easy to hold, it can be sold short, and there are no transaction costs, taxes or margins.
When those assumptions fail, the second explanation takes over. The workbook: according to the expectancy model, it is not the relationship between spot and futures prices but that of expected spot and futures prices which moves the market, especially in cases when the asset cannot be sold short or cannot be stored. It argues that the futures price is nothing but the expected spot price of an asset in the future, and participants price futures on their own estimates of that future spot price.
Two consequences follow: futures can trade at a premium or a discount to spot, and futures prices indicate the expected direction of the spot price.
How it works
Reading a bond futures price under the model.
| Futures vs spot | What participants may expect |
|---|---|
| Futures above spot | Interest rates to fall, yields to fall, the bond price to rise |
| Futures below spot | Interest rates to rise, yields to rise, the bond price to fall |
The price is a forecast for one moment. In section 3.7.4 the workbook takes the October 2021 contract on 6.10% GOI 2031 trading at Rs 98.50 in September 2021. It means the market expects the bond to settle at Rs 98.50 at the close on the last Thursday of October 2021 — 28 October, the contract's last trading day. Every participant is predicting the price at that single point in time.
Convergence. Because the futures price is the expected spot price at maturity, futures and spot prices converge at maturity; at that moment there cannot be a difference. That is why all futures contracts settle at the underlying cash market price on expiry.
Basis, as the workbook defines it. When the futures price is greater than spot, basis is negative (seen in contango); when futures are below spot, basis is positive (backwardation). In bond futures the workbook observes that basis is positive most of the time, because income on the bond exceeds the financing cost.
The workbook's caution on the carry model. Borrowing costs and returns differ between participants, so there can be as many fair values as participants, and no generalised statement can be made about using the cash and carry model for every asset.
A worked example
Start from the workbook's carry calculation on a 5.75% GOI bond (trade date 3 August):
| Item | Rs |
|---|---|
| Clean price | 101.5000 |
| Dirty (cash) price (A) | 103.0174 |
| Cost of borrowing at 4% to 27 August (B) | 0.2597 |
| Accrued interest to 27 August (C) | 1.8847 |
| Theoretical futures clean price = A + B − C | 101.3924 |
Carry says the futures should trade below the Rs 101.50 spot, because the bond earns more than it costs to finance.
Now suppose (illustrative) the futures actually trade at Rs 101.80.
- Basis = spot − futures = 101.50 − 101.80 = −0.30, a negative basis.
- Gap to the carry price = 101.80 − 101.3924 = 0.4076 per bond, or 0.4076 × 2,000 = Rs 815.20 per lot.
The expectancy reading: participants are paying up for the bond forward because they expect interest rates to fall and the bond price to rise by expiry. Under cash and carry the same gap is an arbitrage signal; the workbook notes that in India short selling of GOI securities is allowed only in certain securities and for certain entities, which is exactly the kind of limit under which the expectancy model says expectations, not carry, set the price.
Why NISM asks about it
Chapter 3 (Exchange Traded Interest Rate Futures) sets out the cash and carry computation and its assumptions in section 3.7.2, the expectancy model in section 3.7.3 and price discovery and convergence in section 3.7.4; section 3.7.1.4 defines basis. Expect a direct question on what the expectancy model says the futures price represents, when it is more relevant than cash and carry, and what a futures premium to spot implies for expected interest rates.
Common exam traps
- Expectancy model: futures price = expected future spot price. Cash and carry: spot + financing cost − income.
- It matters most when the asset cannot be stored or sold short.
- Futures above spot on a bond implies expected rates falling (prices rising), not rising.
- Futures can trade at a premium or a discount under this model; neither is an error.
- Basis = spot − futures in this workbook: futures above spot gives a negative basis.
- Both explanations agree on convergence at expiry.
- The expected price refers to the close of the last trading day of the contract, not to an average over the month.
Where this is taught
Free preparation for NISM Series IVRelated terms
- ConvergenceThe certainty that a futures price and the spot price of its underlying meet at expiry — because on the last trading day the contract settles at the cash market price, leaving no room for a difference.
- BasisThe difference between the spot price and the futures price of an asset — positive when spot exceeds futures, negative when futures exceeds spot, and zero at expiry.
- Cash and carry pricingThe no-arbitrage model for bond futures: theoretical futures price = cash (dirty) price + financing cost − income on the cash position, which is accrued interest to the futures settlement date.
- Futures contractA standardised forward traded on an exchange, where the exchange fixes every term except the price and the clearing corporation guarantees settlement, so neither side carries the other's default risk.
- Price discoveryThe process by which the free interaction of buyers and sellers produces a price that reflects every participant's expectation of what the underlying will be worth at a future date.
- Interest Rate FuturesA standardised exchange-traded contract to buy or sell a notional government security, or an interest rate itself, at a price agreed today for settlement on a future date.
- Regular arbitrageBuying a bond in the underlying market and selling futures on the same bond when futures trade above their theoretical price — locking in a pay-off that is the same whether the bond price rises or falls.
- BackwardationA market in which the futures price sits below the spot price — the cost of carry says futures should be dearer, and something is overriding it.
- ContangoA market in which the futures price sits above the spot price, normally because the futures buyer is paying for the cost of carrying the commodity through to delivery.
- Forward rateThe interest rate for a period that starts in the future, implied today by two spot rates — because rolling a short investment must return the same as locking in a long one, or arbitrage follows.
- ArbitragerA participant who locks a profit by entering opposite transactions in two markets at once — carrying no exposure and taking no view, and in the process pulling the two prices back together.