The correlation between changes in price of a spot asset and futures asset is 99%.The standard deviation of changes in spot prices is $2,and that of futures prices is $3.What is the standard deviation of a position that is long 5 units of the spot asset and is optimally (i.e. ,minimum-variance)hedged by using futures?
A)1.41
B)1.99
C)2.52
D)3.11

Question

Quizplus · Accepted Answer

The optimal hedge ratio (h*) is calculated using the formula: h* = ρ(σ_S/σ_F), where ρ is the correlation between the spot and futures prices, σ_S is the standard deviation of the spot price, and σ_F is the standard deviation of the futures price. Substituting the given values: h* = 0.99 * (2/3) = 0.66. The variance of the hedged position (σ^2_hedged) is given by: σ^2_hedged = (σ_S^2 + (h*^2 * σ_F^2) - 2h*ρσ_Sσ_F). Substituting the values: σ^2_hedged = (2^2 + (0.66^2 * 3^2) - 2*0.66*0.99*2*3) = 2. The standard deviation of the hedged position is the square root of the variance, √2 ≈ 1.41.

The Correlation Between Changes in Price of a Spot Asset