Introduction
In considering the possibility of investing in Kramer Industries, located in Montana, Allied Group management should focus on identifying the potential risks associated with adding this firm to the portfolio. For this purpose, estimating the average return for the stock as well as the standard deviation can prove helpful. The aim of this paper is to present calculations and discussion of the company’s average returns along with the standard deviation as well as to justify an appropriate decision on the part of the Allied Group.
The Average Return for the Stock (1990–2010)
It is possible to calculate the arithmetic average return for the stock using the following formula: (year 1 return +… + year n return) / n, where in the case of Kramer Industries, five years of data are available from a twenty-year period. Thus, calculations include adding the available percentages for annual earnings and then dividing the sum by the number of years addressed. During the period 1990–2010, Kramer Industries reported an 8% loss as well as 23%, 26%, 31%, and 18% earnings.
In focusing on calculating the average return, the provided formula yields the following result: (‑8+23+26+31+18) / 5 = 18%. Using these figures, the average return over the period of twenty years for the stock can be calculated for Kramer Industries by way of finding the mean from the provided data for five of the years. Thus, the annual average return can be reported to be 18%.
The Standard Deviation for the Stock (1990–2010)
In order to calculate the standard deviation for the stock during the twenty-year period (1990–2010) under consideration, it is necessary to apply the formula for the population standard deviation: σ = ([Σ(x – u)2] / N)1/2, where u is the average of the stock and N is the number of years. The first step is to calculate the variance related to the mean. The variance in this case is 186.8. To determine the population standard deviation, it is necessary to find the square root of the identified variance. In this case, the standard deviation equals 13.667 or 13.7%.
When calculating the sample standard deviation, having access to data for only five years, it is helpful to use the following formula: σ = ([Σ(x – u)2] / N-1)1/2. With this formula, it is possible to use the provided sample to calculate the variance for the entire population or, in this case, the period of twenty years (Brigham & Houston, 2016). Thus, the sample standard deviation equals 15.28%, but it can be argued that this figure will be less accurate than in the case where information for the whole set of data is provided.
The Average Return on the Portfolio
From applying a simple formula for calculating the average return on the portfolio for the Allied Group, results show that after adding Kramer Industries stock to this portfolio, the return will decrease from the current return of 19.5%. The average return on the portfolio will become 18.75%, which is lower than the current mean of 19.5%. Still, while analyzing the impact on the portfolio in terms of change in the average return and its effect on overall expected returns, it is important to pay attention to the standard deviation as a measure of risk to be taken into account when drawing conclusions and making decisions regarding additional investments.
Recommendations for Allied on Investing in the Stock
After analyzing all the data related to the returns for Kramer Industries, it is possible to state that Allied should invest in this company’s stock in spite of the potential that the average return on the portfolio might decrease. The reason is that the returns on investment are expected to increase in future years, contributing to the company’s prosperity. It is possible to predict positive changes in returns while measuring the volatility of the portfolio in the case of adding Kramer Industries. In this context, much attention must be paid to assessing the standard deviation and how it will potentially influence the expected returns.
Thus, it is important to calculate how Kramer Industries’ annual returns vary in terms of a focus on average returns, and determining the standard deviation provides this information. Considering the average return for the stock along with the standard deviation, it is possible to state that Kramer Industries will generate annual returns between about 3% and nearly 33% during the following years. Referring to these figures along with the standard deviation, it appears that the final portfolio will not be volatile, and risks for Allied will be minimal (Brigham & Houston, 2016). Therefore, it will be appropriate to add Kramer Industries to Allied’s portfolio, having the potential to receive higher annual returns with a focus on a decreased level of volatility.
Conclusion
Measuring average returns for a company’s stock and calculating the standard deviation are important procedures in deciding on investments. It is also essential to analyze returns in the context of volatility in order to make reasonable decisions in expanding a portfolio. According to the conducted calculations, it appears reasonable for the Allied Group to choose to invest in Kramer Industries to improve its portfolio.
Reference
Brigham, E. F., & Houston, J. F. (2016). Fundamentals of financial management (14th ed.). Boston, MA: Cengage Learning.