Question

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the coefficient of variation for each fund. Round your answers to the nearest tenth. x: 15 0 37 22 35 24 25 -15 -15 -18 y: 8 -4 27 18 23 18 18 -4 -5 -8 ​ ​ for x-values: 145.9,% and for y-values: 193.3% for x-values: 120.7%, and for y-values: 233.6% for x-values: 193.3%, and for y-values: 145.9% for x-values: 120.7%, and for y-values: 145.9% for x-values: 193.3%, and for y-values: 233.6%

Answer 1

For x, mean is

Create the following table.

data	data-mean	(data - mean)2
15	4	16
0	-11	121
37	26	676
22	11	121
35	24	576
24	13	169
25	14	196
-15	-26	676
-15	-26	676
-18	-29	841

So CV for x is

Similarly for y

Create the following table.

data	data-mean	(data - mean)2
8	-1.1	1.21
-4	-13.1	171.61
27	17.9	320.41
18	8.9	79.21
23	13.9	193.21
18	8.9	79.21
18	8.9	79.21
-4	-13.1	171.61
-5	-14.1	198.81
-8	-17.1	292.41

So CV for y is

So answer is  x-values: 193.3%, and for y-values: 145.9%