Question

Two stocks, stock A and B, are available in the stock market. The price of the stock A today is $50. The price of stock A next year will be $40 if the economy is in a recession, $55 if the economy is normal, and $60 if the economy is expanding. The probabilities of recession, normal times, and expansion are 0.1, 0.8, and 0.1, respectively. Stock A pays no dividends and has a correlation of 0.8 with the market portfolio. Stock B has an expected return of 9 percent, a standard deviation of 12 percent, a correlation with the market portfolio of 0.2 and a correlation with stock A of 0.6. The market portfolio has a standard deviation of 10 percent. Assume CAPM holds.

Required:

1. If you are a typical risk-averse investor with a well-diversified portfolio which stock would you prefer? Why?

2. What are the expected return and standard deviation of a portfolio consisting of 70 percent of stock A and 30 percent of stock B?

3. What are your considerations if you would like to include additional stocks in your investment portfolio? Explain briefly.

4. You believe that stock market is efficient, and investors are not able to generate abnormal return from the market. Explain your possible strategies based on your belief.

Answer 1

1. A . Expected return of stock A

=[40 X .1]+[55 X .8]+[60 x .1]

=[ .4+4.4+.6]

= 5.6%

Expected return of stock= 9%

I will be selecting stock B, because the correlation of stock B with the market is very low so it will offer a diversify strategy. Stock B also has a higher rate of return.

1. B. Expected return of the portfolio-

=[(5.6 ×.7)+(9 x. 3)]

=6.62%

Standard deviation of the portfolio

= [.7*10+.3*12]

= 10.6

1.C.consideration I would be looking to add additional stocks in my portfolio would be low correlation because low correlation stocks are highly diversified because they will not move in line with the market portfolio.

I will also be choosing such stocks who will offer a higher rate of return the market portfolio having low risk.

I will also be looking for such stocks who will offer a lower standard deviation because the deviation from the mean would be lowest in certain areas and they will offer a higher rate of stability.

1.D. If stock market is efficient and investors are not able to generate abnormal return from the market then in such cases, one should always be looking for passive kind of investment which will be investment into similar stocks, which will be replicating the proportion of the index and it will help the investor in atleast maintaining the similar rate of return to that of market and never underperforming the market because those portfolios are in line with the risk and reward with the stock market indexes.