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Q-153.1. Assume the volatility (standard deviation) of the change in prices for the spot price of oil and the futures price, respectively, are 20% and 32%. The (coefficient of) correlation between changes in the two prices is 0.80. What is the variance of the basis? | Financial Risk Manager Part 1 Quiz - LeetQuiz

Explanation:

The basis is the difference between the spot and futures prices: $B = S - F$ . Its variance is

\mathrm{Var}(B)=\mathrm{Var}(S-F)=\sigma_S^2+\sigma_F^2-2\rho\sigma_S\sigma_F

Given:

$\sigma_S = 0.20$
$\sigma_F = 0.32$
$\rho = 0.80$

So:

\mathrm{Var}(B)=0.20^2+0.32^2-2(0.8)(0.20)(0.32)

=0.04+0.1024-0.1024=0.04

Therefore, the variance of the basis is 0.04.

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Q-153.1. Assume the volatility (standard deviation) of the change in prices for the spot price of oil and the futures price, respectively, are 20% and 32%. The (coefficient of) correlation between changes in the two prices is 0.80. What is the variance of the basis?

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