State of economy 
Prob 
Stock A 
Exp return 
Recession 
0.3 
0.05 
(0.0150) 
Normal 
0.35 
0.09 
0.0315 
Boom 
0.35 
0.13 
0.0455 

Expected return 
0.0620 
State of economy 
Prob 
Stock B 
Exp return 
Recession 
0.3 
1% 
(0.0030) 
Normal 
0.35 
2% 
0.0070 
Boom 
0.35 
16% 
0.0560 

Expected return 
0.0600 
Return on stock A 
Average expected 
XY 
(XY)2 
Probability 
Probability *(XY)2 
(0.0500) 
0.0620 
(0.11200) 
0.0125 
0.3 
0.0038 
0.1300 
0.0620 
0.06800 
0.0046 
0.35 
0.0016 
0.0900 
0.0620 
0.02800 
0.0008 
0.35 
0.0003 



Variance 
0.0057 
Return on stock B 
Average expected 
XY 
(XY)2 
Probability 
Probability *(XY)2 
0.1600 
0.0600 
0.10000 
0.0100 
0.35 
0.0035 
0.0200 
0.0600 
(0.04000) 
0.0016 
0.35 
0.0006 
(0.0100) 
0.0600 
(0.07000) 
0.0049 
0.3 
0.0015 



Variance 
0.0055 
Return on stock A 
Average expected 
XY 
(XY)2 
Probability 
Probability *(XY)2 
0.1300 
0.0620 
0.06800 
0.0046 
0.35 
0.0016 
0.0900 
0.0620 
0.02800 
0.0008 
0.35 
0.0003 
(0.0500) 
0.0620 
(0.11200) 
0.0125 
0.3 
0.0038 



Standard deviation 
0.0752 
Return on stock B 
Average expected 
XY 
(XY)2 
Probability 
Probability *(XY)2 
0.1600 
0.0600 
0.10000 
0.0100 
0.35 
0.0035 
0.0200 
0.0600 
(0.04000) 
0.0016 
0.35 
0.0006 
(0.0100) 
0.0600 
(0.07000) 
0.0049 
0.3 
0.0015 



Standard deviation 
0.0744 
Coefficient of Variation of Stock A 
Value 
Standard deviation 
0.0752 
Expected return 
0.0620 
Coefficient variation 
1.2130 
Coefficient of Variation of Stock B 
Value 
Standard deviation 
0.0744 
Expected return 
0.0600 
Coefficient variation 
1.2394 
Return on stock A 
Average expected 
Z= XY 
Return on stock B 
Average expected 
Z= XY 
Z*Z 
Probability 
Probability *(Z*Z) 
0.13 
0.062 
0.06800 
0.16 
0.06 
0.1 
0.0068 
0.35 
0.00238 
0.09 
0.062 
0.028 
0.02 
0.06 
0.04 
0.00112 
0.35 
0.000392 
0.05 
0.062 
0.112 
0.01 
0.06 
0.07 
0.00784 
0.3 
0.002352 






Covariance 
0.00434 
Correlation Coefficient of Stocks A and B 
Values 
Standard deviation Stock B 
0.0744 
Standard deviation Stock A 
0.0752 
Covariance A and B 
0.0043 
Correlation Coefficient of Stocks A and B 
0.7760 
Portfolio Return 
Stock A 
Stock B 
Returns 
0.0372 
0.0240 
Expected return 
0.0620 
0.06 
Portfolio invested 
0.60 
0.40 
Portfolio returns 
0.0612 

Portfolio Standard Deviation and Variance 
Values 
Stock B Weight 
40% 
Stock A Weight 
60% 
Standard deviation Stock B 
0.07436 
Standard deviation Stock A 
0.07521 
Portfolio Variance 
0.00500 
Correlation Coefficient of Stocks A and B 
0.77602 
Portfolio Standard deviation 
0.07074 
Weights of the Minimum Variance Portfolio 
Value 
Standard deviation Stock B 
0.07436397 
Standard deviation Stock A 
0.075206383 
Variance of Stock B 
0.00553 
Variance of Stock A 
0.005656 
Covariance between Stock A and Stock B 
0.00434 
Minimum Weight of Stock A 
47.49% 
Minimum Weight of Stock B 
52.51% 
Proof that these weights lead to the Minimum Variance Portfolio 
Value 
Stock B Weight 
53% 
Stock A Weight 
47% 
Standard deviation Stock B 
0.07436 
Standard deviation Stock A 
0.07521 
Correlation Coefficient of Stocks A and B 
0.77602 
Portfolio Standard deviation 
0.07046 
Portfolio Variance 
0.00496 
The reduction in overall investments risk could be identified from the declining standard deviation of the portfolio. The change mainly incurred by alternating the overall weights of the company.
Weights of the Optimal Risky Portfolio with a riskfree asset 
Values 
Stock A return 
0.06200 
Risk free rate 
0.04000 
Stock B return 
0.06000 
Standard deviation Stock B 
0.07436 
Standard deviation Stock A 
0.07521 
Variance of Stock B 
0.00553 
Variance of Stock A 
0.00566 
Covariance between Stock A and Stock B 
0.00434 
Optimal portfolio weight of Stock B 
33.60% 
Optimal portfolio weight of Stock A 
66.40% 
Proof that these weights lead to the Minimum Variance Portfolio 
Value 
Stock B Weight 
34% 
Stock A Weight 
66% 
Standard deviation Stock B 
0.07436 
Standard deviation Stock A 
0.07521 
Correlation Coefficient of Stocks A and B 
0.77602 
Portfolio Standard deviation 
0.07110 
Portfolio Variance 
0.00505 
Portfolio Return 
Stock A 
Stock B 
Expected return 
0.0620 
0.0600 
Returns 
0.0412 
0.0202 
Portfolio invested 
66% 
34% 
Portfolio returns 
0.0613 

With the help of optimal portfolio weights overall returns and risk of the portfolio increased.
With the help of minimum portfolio variance investors could effectively reduce the overall risk from investment and attain adequate return.
Market return 
Asset A 
Asset B 
Asset C 
Asset D 
Asset E 
Asset F 

Standard deviation 
3.7550% 
2.0736% 
3.6042% 
4.3643% 
4.4663% 
4.8939% 
3.3630% 
Variance 
0.00141 
0.00043 
0.001299 
0.00190475 
0.00199475 
0.002395 
0.001131 
Expected returns 
12.0000% 
7.0000% 
5.1000% 
12.0500% 
10.5500% 
14.5000% 
7.3000% 
Beta 

0.52 
0.89 
1.15 
1.17 
1.27 
0.89 
Covariance 

0.00073 
0.00126 
0.001625 
0.001645 
0.00179 
0.00126 
Rm 
12.% 






Rf 
0.05 






CAPM 

8.62% 
11.26% 
13.07% 
13.17% 
13.89% 
11.26% 
The table mainly helps in depicting the overall CAPM return of different assets, which could help investors make adequate investment decisions. The CAPM return is mainly higher than the expected return, as it accommodates beta. Thus, higher CAPM returns mainly indicate a higher risk involved in investment.
Market return 
Asset A 
Asset B 
Asset C 
Asset D 
Asset E 
Asset F 

coefficient of variation 
0.31 
0.30 
0.71 
0.36 
0.42 
0.34 
0.46 
Standard deviation 
3.7550% 
2.0736% 
3.6042% 
4.3643% 
4.4663% 
4.8939% 
3.3630% 
Expected returns 
12.0000% 
7.0000% 
5.1000% 
12.0500% 
10.5500% 
14.5000% 
7.3000% 
Rank 
1 
6 
3 
4 
2 
5 
The ranking conducted in the above table is mainly based on the minimum coefficient variance of the stocks. From the overall evaluation, Stock A is mainly identified as the stock having minimum coefficient from other stock, which could allow investors to attain low risk return.
The prospective theory mainly depicts the behavioural theory, which could help in identifying the problematic alternatives that engage risk. Moreover, perspective theory mainly helps in focusing real life experience, where it ignores optimal decisions conducted by individuals. In this context, some researchers argued that prospective theory mainly ignores psychological explanations and only focuses in descriptive models for providing relevant explanations. Some researchers mentioned that use of prospective theory mainly allows individuals to accommodate real life experience in their research, which could support the research with realistic data.
The economic concepts are mainly evaluated with the help of Utility theory, where significance of service and goods could be evaluated. The overall theory mainly aims in evaluating rational decisions, while making adequate section of services and goods. Furthermore, the theory mainly aims in making both responsibility and ranking, which care conducted on certain objectives. In this context, Bodie (2013) stated that the use of rational approach mainly allows companies to effectively evaluative behaviour of consumers and make adequate investment decisions.
The difference between prospective theory and utility theory are stated as bellow.
 Utility theory mainly helps in identifying the expected behaviour of an individual on certain topics. Furthermore, the theory many helps in identifying the choice of individuals on irrelevant topics or situations. Nonetheless, prospective theory mainly helps states that individuals mainly rely on risk adverse situation, whereas disliking the overall situations.
 The oral utility theory mainly depends start individual service preference are mainly dependent on their decisionmakings, where some are just sitting and some our risk averse. Nevertheless, the prospect theory indicates that all the investors are risk seeking for most losses and risk averse for most gains.
 The prospective theory mainly states that choices do not follow any kind of invariance assumption, different choices are provided to individuals regarding a certain situation. Furthermore, the expected theory realise they use to identify the invariance assumptions taken between two prospects.
 The prospect theory mainly states that individuals take risk aversion decisions to reduce the overall losses incurred from any operation. it also helps in identifying the risk aversion techniques that is taken during the decision making process by individuals to reduce overall risk. However, the expected theory mainly assumes the different choices that reflect the decision making of an individual. Furthermore, the study states that chance determines the overall outcomes, which is taken by individuals (Azar, & Lo, 2016).
 Furthermore, prospect theory includes common consequences of preferences, which changes according to the decisions made by individuals. This theory mainly contradicts the overall expected theory, which states that adding common consequences to prospectors could not change your alternative decisions made by the individual. Therefore, decisions made by individual’s interdependence from any kind of common consequences.
Figure 1: Stating returns provided from S&P 500 and 20year bond
(Source: As depicted in the case study)
The above figure mainly helps in understanding the whole return that is being provided from both S&P 500 index and US 20 year Bond. Stock returns during the ugly bear market of 1973 were relatively low in comparison to the US 20year bonds. From the holder figure it could also be identified that Bond return and stock return goes hand in hand (Bodie, 2013). There is relatively less difference between the overall bond's return and stock market return before 1990, after which the stock market expanded and provided higher returns from investment. However, the constant increment in the overall stock market did not decline returns provided from bond market. The returns from bond market also increased adequately in comparison to capital market returns. Furthermore, the expansion of returns between the bond and capital market was witnessed in 2000. Due to the immense returns provided from stock market. However, the overall returns contracted during the economic crisis of 2008, which meet both the returns from Bond and stock market scene in 2009. This only indicates that a constant income could be provided from bonds by reducing any kind of risk from investment. Furthermore, it is also evaluated that stocks in 1969 only surrender to the Government Bonds due to a recession any financial market, whereas it could provide a higher return from investment to the investors in your future. Carpenter, Lu & Whitelaw (2015) mentioned that Investments in bond market could only get a constant income, whereas stock market investments could allow investors to hop onto the bull market and earn exponential return.
Figure 2: Stating return provided by stock market in past 30 years
(Source: As depicted in the case study)
Therefore, the first debate mainly emphasizes on whether stock market could provide longterm returns from investments. However, from the overall figure it could be evaluated that stock market provides a constant and higher income from investment in comparison to bonds. Nevertheless, stock market returns allows investors together higher returns as depicted in the above figure where stock market returns was relatively higher than the bond from 1990 (Kang & Ratti, 2013). Returns from stock market eventually increased in comparison to the 20 year Bond enlisted in the figure. This only proves that in the end returns from stock market are relatively higher. This could allow investors to increase their overall growth and gather dividend from their Investments (Kang, Ratti & Yoon, 2015). This increment in the overall share value and a constant return in form of dividend could allow investors invest their overall some in the stock market. However, a decline in the stock market could be seen in 1973 where the capital market was in recession. After the recession returns from stock market generally increased and crossed the US 20 year Bond in 1980, after which the returns from stock market was relatively higher than the bond market. Moreover, in figure 2 the overall returns from stock market over the period of 30 years is relatively higher than in a short term. This only indicates that investments in stock market with a longterm perspective are a viable approach, which would allow investors to attain higher growth from Investments (Lee, Chen & Hartmann, 2015).
From the evaluation of Figure 2 returns generated by the stock market in the long term relatively increased, which satisfied concerns of first debate or argument. The higher returns that are provided by stock market can be evaluated from price action of S&P 500. This only confirms that return provided from stock market would eventually allow investors to increase the overall portfolio growth in the end. However, Magara (2016) stated that use of intense derivative markets and instruments meaning increases the overall volatility in stock market, which in turn increases the overall risk from investment. On the other hand, Mukherjee & Roy (2016) argued that due to the use of short selling stock market is able to deflate rising bubble in the system.
The second critics mainly indicates that due to the high risk involved in investments in stock market it is not adequate for the retirement portfolios. This only indicates that critics mainly view stock market, as a highly risky investment, which might reduce the overall return from investment due to high losses. The volatility in the stock market is mainly due to the changing returns that are provided from different companies. Furthermore, the accommodation of stock market investments in retirement portfolio eventually increases the overall risk, while reducing profitability from Investments. Retirement portfolios mainly focus in generating constant return for the investors, which will be used in supporting the expenses in retirement days (Powell, Qian, Shi & Zhu, 2015). However, the use of Bond investments could not support the aggregate return that is needed by the ultimate portfolio. Therefore, the critics thought in not adding the overall stock market companies in the retirement portfolios are correct. Thus, investments conducted by retirement portfolios needs to be a collection of both bond market and stock market. This combination of Investments conducted by retirement portfolios could eventually help in improving the overall returns and reducing risk from Investments. Investors to reduce the overall risk from investment and maintain a constant return have used the combination of stocks and bonds. Hence, applying the method using both stock market and bond market would eventually help the retirement portfolio to generate a higher income from investment (Travlos, Trigeorgis & Vafeas, 2015).
Therefore, it could be understood that investors that have long term perspective it effectively used in stock market return to generate a high income from investment. However, investors that are risk adverse needs to use combination of stocks and Bond for reducing the overall risk from investment. Hence, stock market returns are relatively higher in comparison to returns provided from bond market. Thus, investors could effectively use stock market returns to attain higher growth in the end. Furthermore, the combination of both stock and bond could eventually allow investors to reduce the risk and attain a constant income from their investments (Wachter, 2013).
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