Question

The efficient set of portfolios

The following graph represents the relationship between the efficient set of possible portfolios and various investors.

EXPECTED RATE OF RETURN (Percent) Investor Green Investor Blue Efficient Frontier 4 6 8 10 RISK (Portfolio's standard deviation)

Assuming that the black line represents the efficient frontier, which of the following best describes portfolios that lie to the left of this line?

___Indifferent

___Unattainable

___Efficient

___Inefficient

On the preceding graph, the green and blue lines represent the indifference curves of two investors, investor Green and investor Blue. Which of these investors is more risk averse?

___Not enough information is given.

___Investor Green is more risk averse.

___They are equally risk averse.

___Investor Blue is more risk averse.

What does the tangency point between the indifference curve for investor Green and the efficient frontier represent?

___The optimal portfolio for investor Blue

___The suboptimal but acceptable portfolio for investor Green

___The optimal portfolio for investor Green

___An acceptable but not an optimal portfolio for investor Green

Answer 1

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Answer(1): Inefficient

Answer(2): Investor Blue is more risk averse

Answer(3): The optimal portfolio for investor Green

1) Ans: Inefficient Efficient portfolio frontier is a graph representing the most efficient portfolios that can be created out of a given basket of assets. These portfolios offer the highest expected return for a given level of risk and are created by taking different proportions of the given assets. Any portfolio that lies to the right of the efficient portfolio frontier is inefficient as it provides a lower expected return for a given level of risk as compared to a corresponding portfolio that lies on the efficient frontier. This can be observed by considering any point to the right of efficient portfolio. For any such arbitrary portfolio, there lies a point on the frontier that offers the same level of expected return for lower risk, or higher expected return for the same level of risk. 2) Ans: Investor blue requires a lower risk premium Every investor is different in that they all have different risk appetites. Some are risk-averse and therefore, prefer to invest in assets that are less risky such as government bonds. Others prefer to take riskier bets. An indifference curve of a particular investor shows the combination of risk and return that the investor is indifferent about. In the given example, the green curve represents the different combinations of risk and return that investor green is indifferent about. This suggests that for a risk of approx. 2, investor green would require an expected return of 5 (approx.). If the risk goes up to 6, he would require a return of 8, and he would be indifferent about either of those portfolios. In other words, both these portfolios have the same utility for investor green. Now, risk premium is the extra return that an investor requires to compensate for the additional risk that he/she takes on. Here, Investor Blue requires a lower risk premium because for the same level of risk, the expected return required by investor blue is much lower that that for investor green. This can be observed by drawing a vertical line that intersects both the blue and green curves. The vertical line denotes a particular level of risk. For any such vertical line, the expected return required by investor green (green curve) is more than that required by investor blue (blue curve). Therefore, blue requires a lower risk premium.

3) Ans: The optimal portfolio for investor green The tangency point between an investor's indifference curve and the efficient portfolio is always the optimal portfolio for that particular investor. This is because that point satisfies both the risk appetite of that investor and is also an efficient portfolio This holds true for only the tangency point and not for any other intersection point (such as in the case of the blue curve) because in such a case, there are many different portfolios on the efficient frontier that are much better suited for the particular investor. For example, in the case of investor blue, there are many portfolios on the efficient frontier that lie above the blue indifference curve. All these portfolios provide a higher expected return for a given level of risk than what is expected by investor blue. This suggests that in this case, there is no one optimal portfolio that is best suited for investor blue.

1) Ans: Inefficient Efficient portfolio frontier is a graph representing the most efficient portfolios that can be created out of a given basket of assets. These portfolios offer the highest expected return for a given level of risk and are created by taking different proportions of the given assets. Any portfolio that lies to the right of the efficient portfolio frontier is inefficient as it provides a lower expected return for a given level of risk as compared to a corresponding portfolio that lies on the efficient frontier. This can be observed by considering any point to the right of efficient portfolio. For any such arbitrary portfolio, there lies a point on the frontier that offers the same level of expected return for lower risk, or higher expected return for the same level of risk. 2) Ans: Investor blue requires a lower risk premium Every investor is different in that they all have different risk appetites. Some are risk-averse and therefore, prefer to invest in assets that are less risky such as government bonds. Others prefer to take riskier bets. An indifference curve of a particular investor shows the combination of risk and return that the investor is indifferent about. In the given example, the green curve represents the different combinations of risk and return that investor green is indifferent about. This suggests that for a risk of approx. 2, investor green would require an expected return of 5 (approx.). If the risk goes up to 6, he would require a return of 8, and he would be indifferent about either of those portfolios. In other words, both these portfolios have the same utility for investor green. Now, risk premium is the extra return that an investor requires to compensate for the additional risk that he/she takes on. Here, Investor Blue requires a lower risk premium because for the same level of risk, the expected return required by investor blue is much lower that that for investor green. This can be observed by drawing a vertical line that intersects both the blue and green curves. The vertical line denotes a particular level of risk. For any such vertical line, the expected return required by investor green (green curve) is more than that required by investor blue (blue curve). Therefore, blue requires a lower risk premium.

3) Ans: The optimal portfolio for investor green The tangency point between an investor's indifference curve and the efficient portfolio is always the optimal portfolio for that particular investor. This is because that point satisfies both the risk appetite of that investor and is also an efficient portfolio This holds true for only the tangency point and not for any other intersection point (such as in the case of the blue curve) because in such a case, there are many different portfolios on the efficient frontier that are much better suited for the particular investor. For example, in the case of investor blue, there are many portfolios on the efficient frontier that lie above the blue indifference curve. All these portfolios provide a higher expected return for a given level of risk than what is expected by investor blue. This suggests that in this case, there is no one optimal portfolio that is best suited for investor blue.