Question

1. Suppose that there are two risky assets to invest in. One offers a higher return than the other, but it also has a higher standard deviation. Will one of these assets always lie on the efficient frontier? Explain. HINTS: RETURN, STANDARD DEVIATION, EFFICIENT FRONTIER, SECTION (EFFICIENT PORTFOLIO) EXPECTED RETURN AND STANDARD DEVIATION RELATIONSHIP EFFICIENT FRONTIER) 2. Discuss why is the relationship between expected return and standard deviation for portfolios of risky and risk-free assets linear HINTS: EXPECTED RETURN AND STANDARD DEVIATION RELATIONSHIP EFFICIENT FRONTIER) 3. Explain how the homogeneous expectations assumption leads to the conclusion in the Capital Asset pricing Model (CAPM) that the optimal risky portfolio is the market portfolio. HINTS: HOMOGENEOUS EXPECTATION, CAPM 4. Suppose that investors generally become less risk averse. Explain what effect would this have on stock prices and on expected returns. HINTS: RISK APPETITE, RISK INDIFFERENCE, RISK ADVERSE, RISK TAKER

Answer 1

The efficient frontier is the set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return.

Optimal portfolios that comprise the efficient frontier tend to have a higher degree of diversification than the sub-optimal ones, which are typically less diversified.

The investor would select securities that lie on the right end of the efficient frontier. The right end of the efficient frontier includes securities that are expected to have a high degree of risk coupled with high potential returns, which is suitable for highly risk-tolerant investors. Conversely, securities that lie on the left end of the efficient frontier would be suitable for risk-averse investors.

Efficient Portfolios: That is when investors seek to maximize the expected return from their investment given some level of risk they are willing to accept. Risk Aversion: Individuals according to those theories are assumed to be risk averse: is one who, when faced with two investments with the same expected return but two di¤erent risks, will prefer the one with the lower risk. Risky assets: Those are the ones which the return that will be realized in the future is uncertain. Corporate bonds are riskier than public bonds, because of the possibility of default, in‡ation and so on. Assets in which the return that will be realized in the future is known with certainty today are referred to as risk-free assets or riskless assets.

Since riskiness a¤ects return, we must be able to measure the degree of risk associated with an investment in order to understand the relationship between risk and return. The most common measures are the Variance and the Standard Deviation. In …nancial context, we use the variance to measure the variability of returns from the average return; the greater the deviation from the average, the more variable the rate of return and the higher the level of risk

Capital asset pricing model (CAPM) is a model which establishes a relationship between the required return and the systematic risk of an investment. It estimates the required return as the sum of risk free rate and product of the security’s beta coefficient and equity risk premium.

Capital asset pricing model effectively notches the equity risk premium up or down based on the beta coefficient of the relevant stock which is reflected in the higher or lower required return.

Suppose a risk-averse investor is comparing the COV for three investment items. He wants to determine which offers the best risk/reward ratio. The three different potential investment items are stock XYZ, broad market index DEF and bond ABC.

Assume stock XYZ has a volatility, or standard deviation, of 15% and an expected return of 19%. The COV is 0.79 (15% ÷ 19%). Suppose the broad market index DEF has a standard deviation of 8% and an expected return of 19%. The coefficient of variation is 0.42 (8% ÷ 19%). The third investment, bond, ABC, has a volatility of 5% and an expected return of 8%. The coefficient of variation of bond ABC is 0.63 (5% ÷ 8%).

The risk-averse investor would choose to invest in the broad market index DEF because it offers the best risk/reward ratio and the lowest volatility percentage per unit of return. The investor would not look to invest in stock XYZ because it is more volatile than the index; however, both have the same expected return. Bond ABC carries the least risk, but the expected return is not favorable.