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Part A:
a) Depicting the expected return of stock A:
 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
b) Depicting the expected return of stock B:
 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
c) Depicting the variance of stock A:
 Return on stock A Average expected X-Y (X-Y)2 Probability Probability *(X-Y)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
d) Depicting the variance of Stock B:
 Return on stock B Average expected X-Y (X-Y)2 Probability Probability *(X-Y)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
e) Depicting the standard Deviation of Stock A:
 Return on stock A Average expected X-Y (X-Y)2 Probability Probability *(X-Y)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
f) Depicting the standard Deviation of Stock B:
 Return on stock B Average expected X-Y (X-Y)2 Probability Probability *(X-Y)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
g) Depicting the coefficient of variation of stock A:
 Coefficient of Variation of Stock A Value Standard deviation 0.0752 Expected return 0.0620 Coefficient variation 1.2130
h) Depicting the coefficient of variation of stock B:
 Coefficient of Variation of Stock B Value Standard deviation 0.0744 Expected return 0.0600 Coefficient variation 1.2394
i) Depicting the Covariance of Stocks A and B:
 Return on stock A Average expected Z= X-Y Return on stock B Average expected Z= X-Y 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
j) Depicting the Correlation Coefficient of Stocks A and B:
 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
k) Depicting the Portfolio Return:
 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
l) Depicting the Portfolio Standard Deviation and Variance:
 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
m) Depicting the Weights of the Minimum Variance Portfolio:
 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%
n) Depicting the Proof that these weights lead to the Minimum Variance Portfolio:
 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.

o) Depicting the Weights of the Optimal Risky Portfolio with a risk-free asset:
 Weights of the Optimal Risky Portfolio with a risk-free 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%
p) Depicting the Proof that these weights lead to the Optimal Risky Portfolio:
 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.

q) Depicting on what would be conducted with the portfolio:

With the help of minimum portfolio variance investors could effectively reduce the overall risk from investment and attain adequate return.

Part B:
a) Calculating CAPM of stocks:
 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.

b) Summarising the risky stock in the basis of Coefficient of Variation:
 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.

Part C:
Depicting about Prospect Theory and providing the difference from Utility Theory, which is based on normative theories:

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 decision-makings, 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.
Part D:
Evaluating whether stocks on long run where advantage over your particular investment have horizon is evaluated and whether an investment as risky as stocks can belong to retirement portfolio:
The evaluation mainly helps in identifying the significance of stocks, which could help in improving the overall income of investors. however many searches indicate that stock returns are generally low  in the long run as it contributes a higher risk for investment which  increases chance of loss. Furthermore, there are different types of stocks in this capital market, which allows investors to generate the required return from investment in the end. On the other hand, Azar & Lo (2016) argued that investments in bonds could eventually allow investors to reduce the overall risk from investment and obtain a constant income. However, due to the constant income generated from bonds it does not allow the investors to obtain abnormal gains, which might help in improving its future returns. Stock returns in long term could eventually allow investors attain higher return in comparison from bonds. However, during the economic crisis investors mainly focus their overall investment in bonds, which has no risk and a constant return in comparison to the volatile capital market (Betton, Eckbo, Thompson & Thorburn, 2014).

Figure 1: Stating returns provided from S&P 500 and 20-year 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 20-year 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 long-term 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 long-term 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).

Reference:

Azar, P. D., & Lo, A. W. (2016). The wisdom of twitter crowds: Predicting stock market reactions to fomc meetings via twitter feeds. The Journal of Portfolio Management, 42(5), 123-134.

Betton, S., Eckbo, B. E., Thompson, R., & Thorburn, K. S. (2014). Merger negotiations with stock market feedback. The Journal of Finance, 69(4), 1705-1745.

Bodie, Z. (2013). Investments. McGraw-Hill.

Carpenter, J. N., Lu, F., & Whitelaw, R. F. (2015). The real value of China's stock market (No. w20957). National Bureau of Economic Research.

Kang, W., & Ratti, R. A. (2013). Oil shocks, policy uncertainty and stock market return. Journal of International Financial Markets, Institutions and Money, 26, 305-318.

Kang, W., Ratti, R. A., & Yoon, K. H. (2015). The impact of oil price shocks on the stock market return and volatility relationship. Journal of International Financial Markets, Institutions and Money, 34, 41-54.

Lee, R. P., Chen, Q., & Hartmann, N. N. (2015). Enhancing stock market return with new product preannouncements: the role of information quality and innovativeness. Journal of Product Innovation Management.

Magara, Y. (2016). The Effect Of Interest Rate Adjustment Announcements On Stock Market Returns At The Nairobi Securities Exchange (Doctoral dissertation, University Of Nairobi).

Mukherjee, P., & Roy, M. (2016). What Drives the Stock Market Return in India? An Exploration with Dynamic Factor Model. Journal of Emerging Market Finance, 15(1), 119-145.

Powell, J., Qian, M., Shi, J., & Zhu, Q. (2015). (In Press) Should stock market return forecasts be conditioned on politics?. Australian Journal of Management, 1-29.

Travlos, N. G., Trigeorgis, L., & Vafeas, N. (2015). Shareholder wealth effects of dividend policy changes in an emerging stock market: The case of Cyprus.

Wachter, J. A. (2013). Can Time?Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?. The Journal of Finance, 68(3), 987-1035.

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