Question

Rate of return, standard deviation, coefficient of variation. Personal Finance Problem Mae is searching for a stock to inclise in his current tock portfolo. He is interabod in H-Tech ire: the mejor concem. The rule he folows is to include only socurities with a coel: of variation of renums beliow 1.21. Mke has obtained the following price information for the period 2015 through 2018 . H.Tech stock, being growth-oriented, did nok pay any dividends during these 4 years

a. Celculate the rate of rotum for each year, 2015 through 2018 , for H-Tech stock
b. Assume that each year's retum is oqualy probablo and calculate the average retum over this time period
c. Calculate the standard deviation of returns ovor the past 4 years. (Hint. Treat this dois as a sample)
d. Based on b and c determine the coefticient of variation of rehums for the security.
e. Given the calculation in d what should be Mike's decision regarding the inclasion of H-Tech stock in his portolio?

Answer 1

To calculate the rate of return, average return, standard deviation of returns, and coefficient of variation for H-Tech stock, follow the provided formulas and calculations. Based on the coefficient of variation, Mike should decide whether to include H-Tech stock in his portfolio.

Step-by-step explanation:

To calculate the rate of return for each year, you need to use the following formula: rate of return = (ending price - starting price) / starting price. For example, to calculate the rate of return for 2015, you subtract the starting price of 2015 from the ending price of 2015 and divide the result by the starting price of 2015. Repeat this calculation for each year.

To calculate the average return over the time period, sum up all the annual returns and divide the result by the number of years (4 years in this case).

To calculate the standard deviation of returns, you need to use the following formula: standard deviation = sqrt( ( (return1 - average)^2 + (return2 - average)^2 + ... + (returnn - average)^2 ) / (n-1) ). Substitute the appropriate values and calculate the standard deviation.

The coefficient of variation is calculated by dividing the standard deviation by the average return and multiplying by 100. This will give you a measure of the relative risk per unit of return.

Based on the coefficient of variation, if it is below 1.21, Mike should include H-Tech stock in his portfolio. If it is above 1.21, it may have too much risk for his desired level of return.

Answer 2

To determine whether H-Tech stock should be included in Mike's portfolio, it is necessary to calculate the stock's rate of return, standard deviation, and coefficient of variation and compare the latter to his 1.21 threshold. This financial analysis will help Mike assess the past performance, volatility, and relative risk of the stock, in line with broader market trends.

Step-by-step explanation:

When assessing a potential stock for inclusion in a portfolio, it is crucial to analyze its rate of return, standard deviation, and coefficient of variation. These metrics provide insight into the investment's past performance, volatility, and relative risk. The rate of return is calculated based on the change in stock price each year. To obtain the average return across a time period, you would average these annual return rates. The standard deviation measures the amount of variation or dispersion from the average return, indicating how much the return fluctuates. The coefficient of variation is a standard deviation normalized by the average return, offering a measure of risk per unit of return. If Mike's investment rule is to include only securities with a coefficient of variation below 1.21, he can determine the suitability of H-Tech stock by calculating and comparing this metric against his threshold.

Historically, stocks have a higher average return than bonds or savings accounts due to their greater volatility and associated risks. The potential for both high returns and significant losses is inherent in stock investments, which appeals to those willing to assume higher risk for the possibility of higher rewards. Looking at long-term trends, such as those evident in the S&P 500 index returns, underscores the high-risk, high-reward nature of stock investments. Mike must consider these broader market principles when making his decision about H-Tech stock.