Answer-first summary for fast verification
Answer: 0.0144
Here the hedged basis is \(S-hF\), so its variance is \[ \mathrm{Var}(S-hF)=\sigma_S^2+h^2\sigma_F^2-2h\rho\sigma_S\sigma_F \] Using \(\sigma_S=0.20\), \(\sigma_F=0.32\), \(\rho=0.80\), and \(h=0.50\): \[ 0.20^2 + (0.50)^2(0.32^2) - 2(0.50)(0.80)(0.20)(0.32) \] \[ = 0.04 + 0.25(0.1024) - 0.0512 = 0.04 + 0.0256 - 0.0512 = 0.0144 \] So the variance of the basis is **0.0144**.
Author: Manit Arora
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Q-153.3. If our hedge employs the minimum variance hedge ratio from the previous P1.T3. (P1.T3.153.2), such that we hedge each barrel of spot oil (S) with an (h) fraction of barrel under the futures contract (hF), what is the variance of the basis; i.e., instead of a basis of (S−F), our basis is (S − hF)?
A
0.010
B
0.0144
C
0.0225
D
0.040
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