9. Determine the correlation between price movements ofstock A and B using the f
ID: 2792231 • Letter: 9
Question
9. Determine the correlation between price movements ofstock A and B using the forecasts of their rate of return and the assessments of the possible states of the world in the following table. The s tandard deviations for stock A and stock B are 0.065 and0.1392, respectively. Before doing the calculation, form an expectation of whether that correlation will be closer to 1 or -1 by merely inspecting the numbers State of the Economy Moderate recession Slight recession 2% growth 3% growth Probabilitv .05 15 .60 .20 Stock A: Rate of Return .02 .01 Stock B Rate of Return -.20 -.10 15 .30 15Explanation / Answer
Expected Return for Stock-A =0.05x-0.02 + 0.15x-0.01 + 0.60x0.15 + 0.20x0.15
=-0.0010 -0.0015 + 0.0900 + 0.0300
= 0.1175
Expected Return for Stock-B =0.05x-0.20 + 0.15x-0.10 + 0.60x0.15 + 0.20x0.30
=-0.0100 -0.0150 + 0.0900 + 0.0600
= 0.1250
Sum of Product of Deviations = 0.05x(-0.02-0.1175)x(-0.20-0.1250) + 0.15x(-0.01-0.1175)x(-0.10-0.1250) + 0.60x(0.15-0.1175)x(0.15x0.1250) + 0.20x(0.15-0.1175)x(0.30-0.1250)
= 0.0022 + 0.0043 + 0.00048 + 0.0011
= 0.0081625
Correlation Coefficient =Sum of Product of Deviations / (Std Dev of A x Std Dev of B)
= 0.0081625 / (0.065 x 0.1392)
= 0.9021
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