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You have identified an active portfolio with an alpha of 1.5%, a beta of 0.7, and...

You have identified an active portfolio with an alpha of 1.5%, a beta of 0.7, and a residual variance of 0.02. The excess return on the S&P500 is 6% and its variance is 0.013. Use the Index Model and form the optimal risky portfolio. How much should be passively managed? Note: Answer in decimal form, report four decimal places.

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Answer #1

First, we calculate the initial weight of active portfolio -

Initial Weight (WA) = (Alpha / residual variance) / (Excess return on market / Variance of market)

or, WA = (0.015 / 0.02) / (0.06 / 0.013) = 0.0352083333

Now, we compute the final weights by adjusting for Beta -

Final weight or weight of optimally risky portfolio (WA*) = WA / (1 + (1 - beta) * WA ) = 0.0352083333 / ( 1 + (1 - 0.7) * 0.0352083333 ) = 0.03484033232 or 0.0348

Weight of the passive portfolio = 1 - WA* = 1 - 0.03484033232 = 0.96515967 or 0.9652

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