Answer 1)
Referring to the calculations performed in Part 1, we found the following results related to each stock:
The above results indicate that Amgen Inc, offered highest average monthly return of 1.68%, followed by Raytheon Inc. with 1.60% and then the market index S&P 100 with the return of 1.09%. Our results go with the risk-return relationship as the stock with highest return, i.e. Amgen Inc. attracts maximum volatility. Here we have measured the stock volatility with standard deviation and as a core notion of the concept of portfolio management, high returns are followed with high risk and the concept is validated here. For Instance, as already discussed, Amgen Inc. that offers highest return of 1.68% on monthly average basis, has a standard deviation(volatility factor) of 5.31%, followed by Raytheon Inc. that offers 1.60% monthly average return with volatility factor of 5.28%. Finally, market index S&P 100 that offers least return of 1.09% also has least volatility of 3.74%.
Thus, our results proves that the stock selection process is indeed based on risk-tolerance profile of the investors and the desirability of high risk always comes with high stock volatility in the form of standard deviation.
Answer 2)
A confidence interval is computed as:
(Sample Statistic- critical value(standard error))<=population parameter<=(Sample Statistic+ critical value(standard error))
As for 95% confidence interval, the interpretation of the resultant interval indicates that there is a 95% probability that the true population parameter is contained in this interval.
i) 95% CI for Stock 1:
Mean Monthly Returns(+) 1.96(Standard Error)
= 0.0167+ 1.96(0.05313/(60)1/2)
=0.0167+ 1.96(.00685)
=0.030126
And, Mean Monthly Returns(-) 1.96(Standard Error)
= = 0.0167- 1.96(0.05313/(60)1/2)
=0.0167- 1.96(.00685)
=-.0032
Hence, CI for Stock 1= .0032 to .03012
ii) 95% CI for Stock 2:
Mean Monthly Returns(+) 1.96(Standard Error)
=0.0159+ 1.96(0.527/(60)1/2)
=0.0159+ 1.96(.0068)
=.0292
And, Mean Monthly Returns(-) 1.96(Standard Error)
=0.0159- 1.96(0.527/(60)1/2)
=0.0159- 1.96(.0068)
=-.0025
Hence, CI for Stock 2= .0025 to 0.0292
iii) 95% CI for Market Index:
Mean Monthly Returns(+) 1.96(Standard Error)
=0.010+ 1.96(0.0373/(60)1/2)
=0.010+ 1.96(.2889)
=0.576
Mean Monthly Returns(-) 1.96(Standard Error)
=0.010- 1.96(0.0373/(60)1/2)
=0.010- 1.96(.2889)
=0.556
Hence, CI for Market Index= 0.556 to 0.576
Answer 3)
Calculating required rate of return for each stock:
Stock 1: RFR+ Beta(Market Premium)
=2.35+ .56(5)
=5.15%
Stock 2: RFR+ Beta(Market Premium)
=2.35+ .75(5)
=6.10%
Market Index= RFR+ Beta(Market Premium)
= 2.35+ 1(5)
= 7.35%
Annualized Monthly Returns: APY = (1 + R)^12-1
Stock 1: (1.016)12- 1= 20.98%
Stock 2: (1.015)12-1= 19.60%
Market Index: (1.010)12- 1= 12.70%
Conclusion:
Since all the stocks are expected to earn higher than the return based on systemic risk(CAPM), they all are undervalued and hence, they should be purchased by the investors.
Answer 4)
b) Referring to the above table, the expected return is significantly higher than the required rate of return as indicated by CAPM model. Important to note that while calculating required return we used Beta of the portfolio calculated in the same table.
Answer 5)
5.2:
Referring to the calculations performed between Stock 1 and Stock 2, we found that there is less than perfect correlation between the two stocks of 0.41 and a smaller co-variance multiple of 0.0011. Important to note that the covariance multiple indicates the extent to which two stocks move together over time. Hence, with co-variance as less as 0.0011 means that knowing the return for one stock will not provide any major information relating to other stock.
Our interpretation was turn valid when we found the correlation multiple to be less than perfectly correlated, i.e 0.41. Important to note that correlation is a standardized measure of the co-movement between the stocks. Hence, the stocks could provide diversification benefits to the portfolio as there is very less linear relationship between two stocks.
5.3:
Yes, as expected by witnessing the co-variance and correlation multiple, the stocks has provided the diversification benefit to our portfolio by reducing the risk(standard deviation). Important to note, while each stock individually has standard deviation of 0.053 and 0.52, respectively, the two-stock portfolio has reduced standard deviation multiple of 0.0427. Hence, stocks with less than perfect correlation provided us with the diversification benefit.
