# Portfolio Risk

Q- Two investors have utility functions that differ only with regard to the coefficient of risk aversion. Relative to the investor with a higher coefficient of risk aversion, the optimal portfolio for the investor with a lower coefficient of risk aversion will most likely have:

1. a lower level of risk and return.
2. a higher level of risk and return.
3. the same level of risk and return.

Solution

B is correct. A less risk-averse investor’s highest utility curve, given the lower coefficient of risk aversion, is likely to touch the capital allocation line at a point that would represent a portfolio with higher risk and more expected return.

A is incorrect because for a high coefficient of risk aversion, the investor will seek a lot of return for a bit of extra risk and will have an optimal portfolio that is tangential to the capital allocation line at a lower level of risk and return relative to the investor with a lower coefficient of risk aversion.

C is incorrect because only investors with identical coefficients of risk aversion would select the same optimal portfolio.

Why so? I thought more risk averse the investor is, higher the return he expects.. Then why a less risk-averse investor represent a portfolio with higher risk and more expected return? Please help me out

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Q- Two investors have utility functions that differ only with regard to the coefficient of risk aversion. Relative to the investor with a higher coefficient of risk aversion, the optimal portfolio for the investor with a lower coefficient of risk aversion will most likely have:
1. a lower level of risk and return.
2. a higher level of risk and return.
3. the same level of risk and return.

Solution

B is correct. A less risk-averse investor’s highest utility curve, given the lower coefficient of risk aversion, is likely to touch the capital allocation line at a point that would represent a portfolio with higher risk and more expected return.

A is incorrect because for a high coefficient of risk aversion, the investor will seek a lot of return for a bit of extra risk and will have an optimal portfolio that is tangential to the capital allocation line at a lower level of risk and return relative to the investor with a lower coefficient of risk aversion.

C is incorrect because only investors with identical coefficients of risk aversion would select the same optimal portfolio.

Why so? I thought more risk averse the investor is, higher the return he expects.

You thought wrong.

The most risk averse investor will stick all of their money in a risk-free investment: under their mattress.  What return will they expect in that case?

Simplify the complicated side; don't complify the simplicated side.

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