24 — FX Forwards, Carry, and Commodity Roll Yield¶

Free learning pack¶

1. reference/fx/spot_and_forward.md, cross_currency_basis.md, fx_carry.md
2. reference/commodities/roll_yield.md

Do not search for more material until these are insufficient.

PREDICT¶

USD rates are 5%, EUR rates are 3%, spot is 1.10 USD/EUR. Without calculating, does EUR trade forward stronger (more USD per EUR) or weaker than spot? Which currency's rate advantage does that reflect?

Formula (covered interest parity)¶

F = S * (1 + r_domestic*T) / (1 + r_foreign*T)

In [ ]:

spot = 1.10       # USD per EUR
r_usd = 0.05
r_eur = 0.03
years = 1.0

# MANUAL FIRST:
# compute the 1-year CIP forward rate.
forward = None
print(forward)

spot = 1.10 # USD per EUR r_usd = 0.05 r_eur = 0.03 years = 1.0 # MANUAL FIRST: # compute the 1-year CIP forward rate. forward = None print(forward)

PREDICT (basis)¶

The market forward is actually quoted at 1.1250, slightly above the CIP value you just computed. Is the implied cross-currency basis positive or negative? What might cause it (a fundamental view, or a funding technical)?

In [ ]:

market_forward = 1.1250

# MANUAL FIRST:
# solve for the implied foreign rate that would make CIP reproduce
# market_forward, then compute the basis (implied_rate - r_eur).
basis = None
print(basis)

market_forward = 1.1250 # MANUAL FIRST: # solve for the implied foreign rate that would make CIP reproduce # market_forward, then compute the basis (implied_rate - r_eur). basis = None print(basis)

FX carry¶

carry = r_foreign - r_domestic

In [ ]:

# MANUAL FIRST:
# a PM is long a currency yielding 7%, funded in one yielding 2%.
# compute the unhedged carry.
carry = None
print(carry)

# MANUAL FIRST: # a PM is long a currency yielding 7%, funded in one yielding 2%. # compute the unhedged carry. carry = None print(carry)

PREDICT (commodities)¶

Crude oil's near-month future trades at $80, the 12-month-out contract at $74 (backwardation). If spot doesn't move at all over the year, does a long position that keeps rolling from near to far month make or lose money purely from rolling?

Formula¶

roll_yield = (near_price - far_price) / far_price

In [ ]:

near_price, far_price = 80.0, 74.0

# MANUAL FIRST:
# compute the roll yield and state whether the curve is in contango or
# backwardation.
yield_from_roll = None
print(yield_from_roll)

near_price, far_price = 80.0, 74.0 # MANUAL FIRST: # compute the roll yield and state whether the curve is in contango or # backwardation. yield_from_roll = None print(yield_from_roll)

Experiment¶

Flip the commodity example into contango (near=$74, far=$80) and recompute roll yield. Then check: does the sign match your intuition from the PREDICT question?

Reference¶

reference/fx/spot_and_forward.md
reference/fx/cross_currency_basis.md
reference/fx/fx_carry.md
reference/commodities/roll_yield.md

Promote¶

Use src/pm/fx.py (fx_forward_rate, cross_currency_basis, fx_carry) and src/pm/commodities.py (roll_yield, commodity_curve_state) only after your own implementation.

Test¶

pytest tests/test_fx.py tests/test_commodities.py

ORAL CHECK¶

Explain to a PM why a persistently nonzero cross-currency basis is the FX market's version of the CDS-bond basis, and why a commodity's roll yield matters even when its spot price doesn't move.

Try /tutor concept fx carry for an adaptive walkthrough.