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You estimate that a passive portfolio, that is, one invested in a risky portfolio that mimics the S&P 500 stock index, yields an expected rate of return of 12% with a standard deviation of 25%. You manage an active portfolio with an expected return of 19% and a standard deviation of 32%. The risk-free rate is 7%. Your client's degree of risk aversion is A = 3.3.

If he chose to invest in the passive portfolio, what proportion, y, would he select?
Proportion of y ____%??

User Adebayo
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Final answer:

To find the proportion of the portfolio a client should invest in, known as 'y', one would need to consider their risk aversion and how it relates to the expected return and risk (standard deviation) of the passive portfolio. Without sufficient data or a complete model, we cannot calculate the exact value for 'y'.

Step-by-step explanation:

To determine what proportion, y, of the portfolio a client with a degree of risk aversion of A = 3.3 would invest in a passive portfolio, we can use the concept of the Indifference Curve and the Capital Allocation Line. The Indifference Curve represents the combinations of portfolios that give the client the same level of utility based on the expected return and standard deviation, while the Capital Allocation Line represents the opportunity set of risky and risk-free assets.

An investor's optimal choice of y is where their Indifference Curve is tangent to the Capital Allocation Line. Although we haven't been provided the full equation for the Indifference Curve and Capital Allocation Line, the basic idea is to find a point on the Capital Allocation Line that satisfies the investor's level of risk aversion given his utility function U = E(R) - 0.5 * A * σ^2, where E(R) is the expected return and σ^2 is the variance of the portfolio's return.

Without more specific data or a complete model, we cannot calculate the exact proportion y. In real-world scenarios, this calculation would typically involve solving an optimization problem to balance the expected return and the investor's tolerance for risk.

User Endri
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