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P1.T2.711. Covariance and correlation (Miller, Ch.3)

Nicole Seaman

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Learning objectives: Calculate and interpret the covariance and correlation between two random variables. Calculate the mean and variance of sums of variables.


711.1. The following probability matrix displays joint probabilities for an inflation outcome, I = {2, 3, or 4}, and an unemployment outcome, U = {5, 7 or 9}. Also shown are the expected values and variances for each random variable (e.g., the variance of the inflation random variable is 0.5690) and the expected value of their product, E(I*U) = 20.590.

Which of the following is nearest to the correlation coefficient, ρ(I,U)?

a. -0.494
b. -0.137
c. Zero
d. +0.258

711.2. A discrete random variable can assume a value of {1, 2, 3, 4 or 5} with the following probabilities, where the sum of f(x)*X and and f(x)*X^2 is also shown:

If Y = 3*X + 5, then what is the variance of Y, σ^2(Y)?

a. 1.29
b. 5.51
c. 11.61
d. 16.61

711.3. Consider a $100.00 position in Security A which has an expected return of 11.0% and volatility of 30.0%:

Security B has an expected return of 8.0%, volatility of 20.0% and its correlation to Security A, ρ(A,B) = +0.50. If we can only hedge this position by adding a position in Security B, then what trade will minimize the variance of the net portfolio? (note: This question applies Miller's Application: Portfolio Variance and Hedging in Chapter 3)

a. Zero (no additional position in Security B ensures the lowest portfolio volatility)
b. Long $33.0 in Security B
c. Short $75.0 in Security B
d. Short $167.0 in Security B

Answers here: