Troublesome coefficient of variation question.

[th_05]

Given the following data for three possibile investments, A, B and C, calculate the coefficient of variation and with the aid of a diagram explain which is the least risky investment.

Expected Profit: A - 100 B - 120 C - 140
Standard Devi.: A - 10 B - 30 C - 20

I presume to calculate the COV you divide the standard deviation by the mean, to give you:

A: 100/10 = 0.1 B: 30/120 = 0.25 C: 20/140 = 0.14

I am struggling with how/what sort of diagram to use and how to explain which is the least risky investment. Any ideas would be great.

 

[statdad]

Are you to assume that the underlying distributions are normal for each investment? If so, you have the mean and standard deviation for each investment; draw the bell curves.

For evaluating which is riskiest: the use of the coefficient of variation is pretty informal: begin by stating, in your own words, what the c.v. tells you (I don't mean in terms of what percentage of the mean the standard deviation is, I mean the interpretation). You may find yourself answering the question when you do that.

 

[th_05]

Are you to assume that the underlying distributions are normal for each investment? If so, you have the mean and standard deviation for each investment; draw the bell curves.

For evaluating which is riskiest: the use of the coefficient of variation is pretty informal: begin by stating, in your own words, what the c.v. tells you (I don't mean in terms of what percentage of the mean the standard deviation is, I mean the interpretation). You may find yourself answering the question when you do that.

Thanks very much. It is normal distribution yes, I have not used c.v. before so what exactly does this tell me? And shall I draw out a curve for each investment?

 

[statdad]

The c.v. gives the size of the standard deviation relative to the mean. For a problem in which c.v. - 12.5%, the standard deviation is 12.5% as large as the mean. (we usually report the c.v. as a percentage). It is a measure of "relative variability" - meaning it is one way to compare the variability of different groups. Loosely speaking, the larger the c.v., the more variable (spread out) the data values are around the mean.

Try this: consider two normal distributions, one with mean 100 and sigma = 20, the other with mean 100 and sigma = 35. Draw each of them, as accurately as possible, and note which curve is "fatter". Now compare the c.v.s for each: the fatter curve has the larger c.v.

That little example is easily visualized because the two means are equal, but the same concept will apply in your problem: the larger the c.v., the more variable the values around the mean.

For your second question, yes, draw the appropriate bell curve for each group - again, as accurately as possible.