Based on current dividend yields and expected capital gains, the expected rates of return on portfolios and are 11% and 14%, respectively. The beta of are 11% and 14%, respectively. The beta of is1.5. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 Index is 12%. The standard deviation of portfolio italicsis 10% annually, while that of is 31 %, and that of the index is 20%.a. If you currently hold a market index portfolio, would you choose to add either of these portfolios to your holdings? Explain.b. If instead you could invest in bills and one of these portfolios, which would you choose?

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06-04-2020
Business

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Based on current dividend yields and expected capital gains, the expected rates of return on portfolios and are 11% and 14%, respectively. The beta of are 11% and 14%, respectively. The beta of is1.5. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 Index is 12%. The standard deviation of portfolio italicsis 10% annually, while that of is 31 %, and that of the index is 20%.a. If you currently hold a market index portfolio, would you choose to add either of these portfolios to your holdings? Explain.b. If instead you could invest in bills and one of these portfolios, which would you choose?

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chamberlainuket chamberlainuket · Answer 1 · 2020-04-08T07:14:01+02:00

Answer:

CAPM (capital asset pricing model) shows a relationship that exists between expected return and risk. This model states that the expected rate of return is equivalent to risk premium plus risk free-rate.

The expected return of any financial asset can be calculated with the help of CAPM equation.

Here,

is risk-free return

is systematic risk of the asset

is expected rate of return on the market.

Step 2 of 9

There are two portfolios. Those are portfolio A and portfolio B. The expected rate of return and beta of portfolio A are 11% 0.8 respectively. The expected rate of return and beta of portfolio B are 14% 1.5 respectively. The given expected rates of returns are based on the dividend yield and capital gains.

The standard deviations of portfolios A and B are 10% and 31% respectively. The market standard deviation is 20%.

The risk-free rate is 6%. The expected rate of return on the market is 12%.

Step 3 of 9

a.

To evaluate which portfolio is desirable, the expected return of both portfolios has to be found out and this is done by using the equation of capital asset pricing model (CAPM).

Calculate the expected return of the portfolio A by substituting given values in CAPM equation as follows:

Therefore, the expected return of portfolio A is

Step 4 of 9

Calculate the expected of the portfolio B by substituting known values in CAPM equation:

Therefore, the expected return of portfolio B is .

It is evident from the above computation that the expected return of portfolio A is 10.8% while that of portfolio B is 15%. Return of portfolio A is less than that of the market index that is S&P 500 of 12%.

It is known that the market index return is based on the practical market portfolios i.e. based on the actual returns of the stocks in the portfolio. Hence, it is much more realistic in nature. Thus, the portfolio which is giving returns higher than the market index is not feasible in nature and cannot be relied upon.

Therefore, Portfolio A is desirable and not portfolio B.

Step 5 of 9

b.

If the investor can made investment only in T-bills and one of the portfolios, the one with greater slope of the CAL (capital allocation line)/ reward-to-volatility ratio will be selected.

CAL (capital allocation line) shows the different possible combinations of risk and return of portfolio by changing the proportion of different assets that constitute the portfolio.

Following is the formula of the reward-to-volatility ratio:

Here,

Step 6 of 9

Calculate the reward-to-volatility ratio of market index portfolio by substituting 0.06 for risk-free rate, 0.12 for expected rate of return, and 0.20 for the standard deviation of portfolio in the formula of reward-to-volatility ratio as follows:

Therefore, reward-to-volatility ratio market index portfolio is 0.30 (or) 30%

Step 7 of 9

Calculate the reward-to-volatility ratio of portfolio A by substituting 0.06 for risk-free rate, 0.11 for expected rate of return, and 0.10 for the standard deviation of portfolio in the formula of reward-to-volatility ratio as follows:

Therefore, reward-to-volatility ratio portfolio A is 0.50 (or) 50%.

Step 8 of 9

Calculate the reward-to-volatility ratio of portfolio B by substituting 0.06 for risk-free rate, 0.14 for expected rate of return, and 0.10 for the standard deviation of portfolio in the formula of reward-to-volatility ratio as follows:

Therefore, reward-to-volatility ratio portfolio B is 0.2581 (or) 25.81%.

Step 9 of 9

The reward-to-volatility ratio of portfolio A is 0.5 and that of portfolio B is 0.2581. Thus, it can be concluded that the reward-to-volatility ratio of portfolio A is greater than that of portfolio B.

Therefore, the portfolio A should be chosen by the investor as the best substitute for market portfolio.