Risks and Returns Questions – Term Paper

Question 1

Investment returns or return on investment refers to the proceeds gained from the sale of an investment. The amount earned can be either above or below the original invested amount. In this context, the “best gain” can be obtained through Alta Inds at 50%, despite the fact that these returns depend on the economy. On the other hand, the “worst case” returns could again be obtained through Alta Inds, which could be as little as 22% as shown in the provided table. This returns will also depend on the economy that is this returns will be as result of economic depression. My client except 100,000 dollars by the end of the year and hence a 10% return on the amount invested (1,000 dollars) could yield this amount.

Question 2

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The t-bill returns remain the same despite the dynamic economic state.  From the data presented the 8% return will be gained in all economic conditions. Therefore, it will be the t-bill is risk-free. However, regarding purchasing power, it remains at risk. It is because the inflation rate is deducted from the 8 percent return as the returns gained are inclusive of the inflation premium. Moreover, T-bills is exposed to the risk of reinvestment rate, and an investor is likely to count losses if the prices declined. Therefore, it is true to say that T-bills is not entirely risk-free in the US since various types of risks can impact some actual securities (Rubaltelli, Ferretti, & Rubichi, (2014).

 Question 3

The deviation in returns between Alta ind’s and Repo Men is due to their type of correlation with the economy. The returns received from the Alta Industries positively correlate with the economy as the firms maintain high sales and high profits. Hence the industries experience similar changes as the economy does. A positive correlation refers to the tandem movement of variables that is if one variable increases the other dependent variable decreases as well and vice versa. In contrast, Repo Men industries are considered resistant to economic changes, since they have a negative correlation with the economy. A negative correlation occurs when the relationship between two variables is not dependent on each other, and an increase in one results in a decrease in the other variable, and vice versa. This type of correlation is almost unrealistic as all shares have a particular relationship to the market (Senthilnathan, 2008).

Question 4

a) Expected returns

The following formula is used to compute the rate of expected returns

 The expected rate return calculation for the each portfolio is shown below.

Alta inds= 0.1(-22.0%) + 0.2(-2.0%) + 0.4(20.0%) + 0.2(35.0%) +     0.1(50.0%) = 17.4%.

T-bills =  0.1(6.0%) + 0.2(6.0%) + 0.4(6.0%) + 0.2(6.0%) +     0.1(6.0%) =8.0%.

Repo Men =0.1(28.0%) + 0.2(14.70%) + 0.4(0.0%) + 0.2(-10.0%) +     0.1(-20.0%) = 1.7%.

Am Foam = 0.1(10.0%) + 0.2(-10.0%) + 0.4(7.0%) + 0.2(45.0%) +     0.1(30.0%) = 13.8%.

M = 0.1(13.0%) + 0.2(1.0%) + 0.4(15.0%) + 0.2(19.0%) +     0.1(43.0%) =15.0%.

b) Standard deviation

It is computed with the formula 

Alta  = [(-22.0  17.4)2(0.1) + (-2.0  17.4)2(0.2) + (20.0  17.4)2(0.4)

             + (35.0 – 17.4)2(0.2) + (50.0 – 17.4)2(0.1)]0.5

           = 20.0%.

 Following the above complete computation, standard deviations for the other alternatives will be as shown below

M  = 15.3%.

 T-bills  = 0.0%

Am Foam  = 18.8%.

 Repo Men = 13.4%.

c) Coefficient of variation

The coefficient of variation for the provided portfolio will be calculated as shown below.

Repo Men  = 7.9.

T-bills  = 0.0

Market  = 1.0.

Alta Inds = 1.1

American Foam = 1.4.

Question 5

Diversification of Portfolio has an impact on the view of most investors. Coefficient correlation is important in measuring the risk of investors. This is even more important to the undiversified investors. Most investors pay more attention to the influence of the economy on his or her portfolio than the stand’s alone risk, which includes diversifiable risks that can be avoided by holding the economy in a portfolio that is well diversified. When the whole market portfolio is held the market risk remains, both Correlation coefficient and σ can be used to measure the stand-alone risk and the volatility of the stock concerning the market.  The independent risk of a portfolio is relatively less than that of an individual stock. This can be because the two are negatively correlated, and a rise in the Alta Inds does not equate to an increase in the Repo Men and vice versa. A combination of the two stocks eliminates or shares the risks involved in the each stock if the stock was held in isolation for instance in a simple one stock portfolio.

Question 6

Holding a simple one stock portfolio could not guarantee any compensation in case of any risk. Additionally, this type of stock portfolio is exposed to an even higher risk. However, the returns of the single portfolio could be high enough to compensate for the risk, but the need for diversified investors will be necessary. More investors could cause an increase in price and eventually a decrease in returns. Therefore, it is impossible to find market stocks with returns that can compensate for the diversifiable risk of the stock.

Question 7

Market risk relates to how security contributes to the overall risk of the market portfolio. Market risk is measured by the beta coefficient of stock that determines the volatility that is on the market. The stocks’ beta coefficient is calculated with us a graph, with stock on the Y_axis and returns on the X-axis. The slope of the characteristic or regression line shows the relative volatility of the market. The “characteristic” line is used to show the relationship between the individual stock and the general stock market. From the data provided in table two, we can be able to draw the graph shown below and establish a regression line, which defines the relationship between the provided variables.

Above the group with regression results, slope coefficient will lie at -20. Which indicates that the average stock does not move with the economy or rather the market, the betas of most stocks usually range from 0.05 to 1.5. ;A negative beta is unrealistic since the returns should positively correlate or show a limited correlation with the general stock market. The practical value of r2;;is ;0.29 and it is possible to have a portfolio of greater than 0.9. ;

Question 8

The security Market equation is ri;= rrf;+ (rm;- rrf)bi.

Since T-bill is considered risk free as earlier explained, it can be used as a reference for the risk free rate, which is 8%. Hence, rrf= 8%;;on the other hand rm;=15%. Therefore the rate of returns for the alternatives will be computed as follows.


Alta Inds:

Am Foam:

Repo Men:

Market : ;

A table that shows the Comparison of the expected rates of return with the required rates of return

Question 9

Repo Men has a negative beta coefficient, which indicates a negative market risk. If the Repo Men stoke normal that is not either positive or negative, its portfolio risk could be relatively cheap. Hence, it has a required rate of return that is below the risk-free rate. A financier can consider investing in a negative expected return stock, for instance, the Repo Men stock since the higher returns can still be yielded, even when the work income ceases. This type is stock has significant similarities with insurance policies. For instance, the risk insurance policies whereby companies that seek this cover only pay premiums when normal operations have been compromised (Penman, S. 2016).

Question 10

Holding to the fact that the beta of portfolio is weighted average of stocks; betas in the portfolio, the following computation can be performed

Required return bp = .

bp = 0.5(bAlta) + 0.5(bRepo) = ;0.5(1.29) + 0.5(-0.86) = 0.215,

rp;= rRF;+ (rM;- rRF)bp =8.0% + (15.0% – 8.0%)(0.215) ;;;;; = 8.0% + 7%(0.215) = 9.51% ;;9.5%.;

;bp;= 0.5(1.29) + 0.5(0.68) = 0.985.

;;;; rp;= 8.0% + 7%(0.985) = 14.9%.

Therefore, the required return for a portfolio that consists of 50 percent Alta industries and 50 percent American foam will be 14.9% and this is what I would recommend for my client.


Penman, S. (2016). Valuation: Accounting for Risk and the Expected Return.;Abacus,;52(1), 106-130. http://dx.doi.org/10.1111/abac.12067

Rubaltelli, E., Ferretti, R., ; Rubichi, S (2014). The Risk-Return Trade Off: Expected and Required Return.SSRN Electronic Journal. http://dx.doi.org/10.2139/ssrn.913807

Senthilnathan, S (2008). Risk, Return and Portfolio Theory A Contextual Note.;SSRN Electronic Journal. http://dx.doi.org/10.2139/ssrn.2627423