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1. Estimate The Average Rate Of Return Of Each Stock Individually.
2) If Your Client Invested In a Stock Portfolio Comprising 50% Of Gm Common Stocks And 50% Of Ford Common Stocks, What Would Have Been The Rate Of Return On The Asset Portfolio Each Year?
3) What Would Have Been The Average Return On The Portfolio During The Period From 2003 To 2007.
4) Estimate The (Individual) Risk Of Each Stock.
5) Calculate The Risk For The Asset Portfolio (Both Common Stocks Taken Together).
6) What Is The Coefficient Correlation Between The Returns Of The Two Common Stocks?
7) Critically Discuss The Modern Portfolio Theory, Which Was Pioneered By Harry Markowitz, In Relation To Your Findings And Advise Your Client Accordingly In Layman’s Terms On The Profitability Of Your Client’s Asset Portfolio.
Modern Portfolio Theory (MPT) has been developed by Harry Markowitz which enables for the formation of most efficient portfolio that minimizes the risk of the investors and maximizes the returns in context of the portfolio as a whole (Mangram, 2013). The theory was first proposed in “The Journal of Finance” in the year 1952 by the stated author. The aim of the following report is to evaluate the various aspects of the theory by applying the principles on the given stocks and related returns and risks.
The theory is based on the two key principles as stated follows. The first principle is that the chief goal of any investment is to maximise the risk for any levels of risk (Pfiffelmann, Roger and Bourachnikova, 2016). This is followed by the second principle that the creation of a diversified portfolio can lead to the reduction of the overall risk, and the assets chosen must be unrelated to each other to balance out the overall portfolio risk (Jewczyn, 2013). The analysis of the theory is conducted in relation to the stocks GM and the Ford as elaborated follows.
In order to construct a portfolio, the two areas that are chiefly considered are the returns and the risks. The individual average returns of both the stocks have been computed in the table below for the concerned period of five years, as shown below.
|
Year |
GM Common Stock Return |
Ford Common Stock Return |
|
|
2003 |
-10.00% |
-3.00% |
|
|
2004 |
18.50% |
21.29% |
|
|
2005 |
36.87% |
44.25% |
|
|
2006 |
14.33% |
3.67% |
|
|
2007 |
33.00% |
28.30% |
|
|
Average rate of return of a stock = |
Sum of returns/Number of years |
||
|
Average rate of return of GM stock = |
(-10+18.50+36.87+14.33+33)/5 |
||
|
Average rate of return of GM stock = |
18.54% |
||
|
Average rate of return of Ford stock = |
(-3+21.29+44.25+3.67+28.30)/5 |
||
|
Average rate of return of Ford stock = |
18.90% |
||
As evident from the calculations conducted above, it is to be noted that the individual average returns of the stocks GM and Ford has been computed out to be 18.54% and 18.90% respectively. This means, an efficient portfolio as per the MPT must be one that leads to the overall returns more than the above stated returns.
The second principle of the MPT states that an efficient portfolio is the one that leads to the minimization of the risk of the overall portfolio. As depicted in the below tables, the individual variances/ risk or the standard deviation of the stocks GM and Ford are 18.56 % and 19.03% respectively.
|
Year |
GM Common Stock Return |
GM Stock Return - Average Return (18.54%) |
Square of difference in column C |
|
2003 |
-10.00% |
-28.54% |
0.08 |
|
2004 |
18.50% |
-0.04% |
0.00 |
|
2005 |
36.87% |
18.33% |
0.03 |
|
2006 |
14.33% |
-4.21% |
0.00 |
|
2007 |
33.00% |
14.46% |
0.02 |
|
SUM |
0.1377 |
||
|
Total risk of a stock is depicted by the Standard Deviation |
|||
|
Standard deviation of stock GM= |
SQRT (SUM/n-1) |
||
|
Standard deviation of stock GM= |
SQRT(0.1377/4) |
||
|
Standard deviation of stock GM= |
0.1856 |
||
|
Total individual risk of stock GM = |
18.56% |
||
|
Year |
Ford Common Stock Return |
Ford Stock Return - Average Return (18.90%) |
Square of difference in column H |
|
2003 |
-3.00% |
-21.90% |
0.05 |
|
2004 |
21.29% |
2.39% |
0.00 |
|
2005 |
44.25% |
25.35% |
0.06 |
|
2006 |
3.67% |
-15.23% |
0.02 |
|
2007 |
28.30% |
9.40% |
0.01 |
|
SUM |
0.1448 |
||
|
Standard deviation of stock Ford= |
SQRT (SUM/n-1) |
||
|
Standard deviation of stock Ford= |
SQRT(0.1448/4) |
||
|
Standard deviation of stock Ford= |
0.1903 |
||
|
Total individual risk of stock Ford = |
19.03% |
||
Thus, an efficient portfolio or the ideal portfolio combination comprising of the two stocks would be the one that leads to the minimization of the above stated total risks of each of the stock.
For the first phase of the analysis of the MPT, the initial weights of the securities has been taken as 50% each. When equal weights are allotted to the securities, the portfolio return and the portfolio risk has been worked out as follows.
|
Year |
GM |
Ford |
Weighted Return |
||||
|
2003 |
(-10% * 0.50) |
(-3% * 0.50) |
-6.5% |
||||
|
2004 |
(18.50% * 0.50) |
(21.29% * 0.50) |
19.9% |
||||
|
2005 |
(36.87% * 0.50) |
(44.25% * 0.50) |
40.6% |
||||
|
2006 |
(14.33% * 0.50) |
(3.67% * 0.50) |
9.0% |
||||
|
2007 |
(33% * 0.50) |
(28.30% * 0.50) |
30.7% |
||||
|
Average Return on Portfolio = |
Sum of weighted returns / Number of years |
||||||
|
Portfolio Return = |
(-6.5%+19.9%+40.6%+9%+30.7%)/5 |
||||||
|
Portfolio Return = |
18.72% |
||||||
|
Portfolio risk = |
SQRT( (0.50*0.1856)^2 + (0.50* 01903)^2 + (2*0.5*0.5*0.9131*0.1856*0.1903) |
||||||
|
Portfolio risk = |
SQRT( (0.50*0.1856)^2 + (0.50* 01903)^2 + (2*0.5*0.5*0.9131*0.1856*0.1903) |
||||||
|
Portfolio risk = |
((0.5*0.1856)^2 + (0.5* 1903)^2 + (2*0.5*0.5*0.9131*0.1856*0.1903))^0.5 |
||||||
|
Portfolio risk = |
18.36% |
||||||
Applying the principle of the MPT, the efficient frontier table was formed to analyse the best possible combination of the return and risk trade off, for the portfolio as a whole.
|
GM |
Ford |
|||
|
Returns |
18.54% |
18.90% |
||
|
SD |
18.56% |
19.03% |
||
|
GM |
FORD |
Rp |
SD |
|
|
Weights |
0.00 |
1.00 |
18.90% |
19.03% |
|
0.10 |
0.90 |
18.87% |
18.84% |
|
|
0.20 |
0.80 |
18.83% |
18.67% |
|
|
0.30 |
0.70 |
18.79% |
18.54% |
|
|
0.40 |
0.60 |
18.76% |
18.45% |
|
|
0.50 |
0.50 |
18.72% |
18.38% |
|
|
0.60 |
0.40 |
18.68% |
18.35% |
|
|
0.70 |
0.30 |
18.65% |
18.35% |
|
|
0.80 |
0.20 |
18.61% |
18.39% |
|
|
0.90 |
0.10 |
18.58% |
18.46% |
|
|
1.00 |
0.00 |
18.54% |
18.56% |
Thus, as evident from the tabular and the graphical representation above, the most attractive investment opportunity is the one where the weightage of the GM and the Ford shares are that of 60% and 40% respectively. The portfolio return in that case has been worked out to be 18.68% and the portfolio risk has been worked out to be 18.35%. Thus, this is the most favourable combination in the portfolio comprising of the two stated stocks.
Conclusion
As per the discussions conducted in the previous parts, it has been concluded that the modern portfolio theory as developed by Harry Markowitz enables and guides an investor to choose a most efficient portfolio combination. The various aspects of the theory were analysed in the report above, and the recommendation is extended to client to invest 60 % in GM stocks and 40% in Ford stocks. Accordingly, the investor is suggested to increase the investment in the GM stock to the tune of 10%.
References
Mangram, M. E. (2013), ‘A simplified perspective of the Markowitz portfolio theory,’ Global journal of business research, Vol. 7, No. 1, pp. 59-70. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2147880
Pfiffelmann, M., Roger, T. and Bourachnikova, O. (2016), ‘When behavioral portfolio theory meets Markowitz theory. Economic Modelling,’ Vol. 53, pp. 419-435. DOI: 10.1016/j.econmod.2015.10.041
Jewczyn, N. (2013), ‘Modern portfolio theory, apt, and the capm: The years 1952 to 1986,’ The International Journal of Social Science Research, Vol. 2, No. 1, pp. 74-87. http://mustangjournals.com/MJBE/v6_MJBE_2014_forwebsite.pdf
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