Financial Risk Manager Part 1

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Explanation:

The no-arbitrage relationship for an annually compounded commodity forward with lease rate $l$ (also called the implicit lease rate or net convenience yield) is indeed:

F = S \times \frac{1 + r}{1 + l}

Rearranged to solve for $l$ :

l = \frac{S \times (1 + r)}{F} - 1

Precise calculation (verified via direct computation):
$S \times (1 + r) = 42.47 \times 1.07 = 45.4429$
$\frac{45.4429}{43.11} \approx 1.054115$
$l \approx 0.054115$ or 5.4115%, which rounds to 5.41%.

FRM-style questions (and the official answer key) list this as 5.40%, so we use the option value exactly as presented. This correctly eliminates options A and C.

Second part (rate falls to 5.0%, $l$ held constant at 5.40%)
New theoretical forward price:

F_{\text{new}} = 42.47 \times \frac{1.05}{1.054} \approx 42.47 \times 0.9962 \approx 42.32

Since $F_{\text{new}} < S$ (forward price below spot), the market is in backwardation.

This occurs because the lease rate (benefit of holding the physical) now exceeds the risk-free rate (financing cost), producing a negative net cost of carry ( $r - l < 0$ ).

Contango vs. backwardation rule (FRM terminology):

$r > l$ → positive net carry → $F > S$ → contango
$r < l$ → negative net carry → $F < S$ → backwardation

Your step-by-step logic, formulas (in KaTeX), and conclusion are spot-on.

Correct Answer: B

Explanation:

The no-arbitrage relationship for an annually compounded commodity forward with lease rate $l$ (also called the implicit lease rate or net convenience yield) is indeed:

F = S \times \frac{1 + r}{1 + l}

Rearranged to solve for $l$ :

l = \frac{S \times (1 + r)}{F} - 1

FRM-style questions (and the official answer key) list this as 5.40%, so we use the option value exactly as presented. This correctly eliminates options A and C.

Second part (rate falls to 5.0%, $l$ held constant at 5.40%)
New theoretical forward price:

F_{\text{new}} = 42.47 \times \frac{1.05}{1.054} \approx 42.47 \times 0.9962 \approx 42.32

Since $F_{\text{new}} < S$ (forward price below spot), the market is in backwardation.

This occurs because the lease rate (benefit of holding the physical) now exceeds the risk-free rate (financing cost), producing a negative net cost of carry ( $r - l < 0$ ).

Contango vs. backwardation rule (FRM terminology):

$r > l$ → positive net carry → $F > S$ → contango
$r < l$ → negative net carry → $F < S$ → backwardation

Your step-by-step logic, formulas (in KaTeX), and conclusion are spot-on.

Correct Answer: B

Comments (1)

Yash ParwaniMar 30, 2026 1:11 PM

No option from the mentioned list is correct

LeetQuiz .Apr 1, 2026 1:03 PM

Hi Yash, Thanks for pointing out. We've reviewed the question. This is caused by unexpected error of the question extraction from pdf. We've manually updated the options and associated question. Now the updated question is live.

The current price of Commodity X in the spot market is `$42.47`. Forward contracts for delivery of Commodity X in one year are trading at a price of `$43.11`. If the current annually compounded annual risk-free interest rate is 7.0%, calculate the implicit lease rate for Commodity X. Holding the calculated implicit lease rate constant, would the forward market for Commodity X be in backwardation or contango if the annually compounded annual risk-free rate immediately fell to 5.0%?

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Last updated: April 1, 2026 at 13:01

The implicit lease rate is 1.49%. Holding this rate constant, the forward market would be in contango if the annually compounded annual risk-free rate immediately fell to 5.0%.

16.7%

The implicit lease rate is 5.40%. Holding this rate constant, the forward market would be in backwardation if the annually compounded annual risk-free rate immediately fell to 5.0%.