Correct Answer: C: Basis strengthens by +$0.20

Step-by-step explanation:

In the FRM Part I curriculum (Foundations of Risk Management and Financial Markets and Products), the basis for a commodity is defined as:

Basis = Spot price (S) − Futures price (F)

This is the standard convention used in GARP materials.

1. Initial basis (May 2011):
   S₁ = $7.00
   F₁ = $9.00 (December 2011 futures)
   Basis₁ = 7.00 − 9.00 = −$2.00

2. Basis three months later (August 2011):
   S₂ = $7.30
   F₂ = $9.10
   Basis₂ = 7.30 − 9.10 = −$1.80

3. Change in basis:
   Change = Basis₂ − Basis₁ = (−1.80) − (−2.00) = +$0.20

4. Interpretation of the change:

   • The basis moved from −$2.00 to −$1.80 (i.e., it became less negative).
   • In futures terminology, when the basis increases algebraically (moves toward zero or becomes more positive), the basis is said to strengthen.
   • Here the basis strengthened by exactly +$0.20.

Why the other choices are incorrect:

• A & B: Both use +$0.10, which is the actual change in the futures price only. They ignore the larger spot-price increase ($0.30).
• D: This option would be correct only if the basis were incorrectly defined as Futures − Spot (which is not the FRM convention). Even then, the sign wording would not match standard strengthening/weakening language.

Key takeaway for the exam:
Always calculate Basis = S − F.
A positive change in basis (Basis₂ > Basis₁) = basis strengthens.
A negative change in basis (Basis₂ < Basis₁) = basis weakens.

This concept appears frequently in hedging-risk questions (e.g., basis risk for a short or long hedge).