Question

Five investment alternatives have the following returns and standard deviations of returns.    
  

Alternatives		Returns: Expected Value				Standard Deviation
A		$	1,110			$	1,270
B			3,970				820
C			3,970				1,330
D			5,790				2,650
E			12,500				7,350

    
Calculate the coefficient of variation and rank the five alternatives from lowest risk to the highest risk by using the coefficient of variation. (Round your answers to 3 decimal places.)
  

Answer 1

Solution:

The coefficient of variation is a measure of risk per unit of return or reward.

The formula for calculating the coefficient of variation is

= Standard Deviation / Return

Thus the

1. Coefficient of variation for Investment Alternative A :

As per the Information given in the question we have

Return = $ 1,110   and Standard Deviation = $ 1,270

Applying the above values in the formula we have :

= 1,270 / 1,110 = 1.144

Coefficient of variation of Investment Alternative A = 1.144

2. Coefficient of variation for Investment Alternative B :

As per the Information given in the question we have

Return = $ 3,970 and Standard Deviation = $ 820

Applying the above values in the formula we have :

= 820 / 3,970 = 0.207

Coefficient of variation of Investment Alternative B = 0.207

3. Coefficient of variation for Investment Alternative C :

As per the Information given in the question we have

Return = $ 3,970 and Standard Deviation = $ 1,330

Applying the above values in the formula we have :

= 1,330 / 3,970 = 0.335

Coefficient of variation of Investment Alternative C = 0.335

4. Coefficient of variation for Investment Alternative D :

As per the Information given in the question we have

Return = $ 5,790   and Standard Deviation = $ 2,650

Applying the above values in the formula we have :

= 2,650 / 5,790 = 0.458

Coefficient of variation of Investment Alternative D = 0.458

5. Coefficient of variation for Investment Alternative E :

As per the Information given in the question we have

Return = $ 12,500   and Standard Deviation = $ 7,350

Applying the above values in the formula we have :

= 7,350 / 12,500 = 0.588

Coefficient of variation of Investment Alternative E = 0.588

The five alternatives from lowest risk to the highest risk by using the coefficient of variation can be ranked as follows

( Lowest to Highest  )

Rank 1 : Alternative B = 0.207

Rank 2 : Alternative C = 0.335

Rank 3 : Alternative D = 0.458

Rank 4 : Alternative E = 0.588

Rank 5 : Alternative A = 1.144