Free lesson · Crypto derivatives

Basis annualization and its limits

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Annualization rescales a price difference to compare maturities. It does not promise you can repeat the trade at that rate for a year.

Use calendar days to the actual settlement date and state a simple or compounded convention. The simple annualized basis ignores financing and costs; a net carry comparison needs an additional ledger.

Basis can be negative. As maturity approaches, a small pricing or timing error creates a large annualized percentage. Compare dollar economics and liquidity, not just annualized rankings.

Apply it in a strategy

• Compare dated maturities while retaining net dollars, funding assumptions and remaining calendar time.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: Annualized gross basis is not net return on collateral and is not repeatable by definition.

Research deliverable

Build and explain a basis annualization and its limits worksheet. Compare dated maturities while retaining net dollars, funding assumptions and remaining calendar time.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def annual_basis(spot,future,days):
    if min(spot,future,days)<=0: raise ValueError("Positive prices and maturity required")
    return (future/spot-1)*365/days

print(annual_basis(50000,51000,73))