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 sample mean for x and for y. Round your answer to the nearest tenth. x: 11 0 36 22 34 24 25 -11 -11 -22 y: 9 -3 28 14 23 16 14 -3 -4 -9

Answer 1

Answer:

(a). Σx= 108, Σx^2 = 4984, Σy^2 = 2,157.

(b). 10.8, 0.1.

(C) and (d) => check explanation.

Step-by-step explanation:

To Calculate for Σx we will have to add all the values for x that is the summation of x-values.

Σx = 11 + 0 + 36 + 22 + 34 + 24 + 25 + -11 + -11 + -22 = 108.

Σx^2 = 11 × 11 + 0 × 0 + 36 × 36 + 22 × 22 + 34 × 34 + 24 ×24 + 25 × 25 + -11 × -11 + -11 × -11 + -22 × -22 = 4984.

Σy^2 = 9× 9 + -3 × -3 + 28 ×28 + 14 × 14 + 23 × 23 + 16 × 16 + 14× 14 + -3 ×-3 + -4 × -4 + -9 × -9= 2,157.

(b). Sample mean for x = 108/10 = 10.8.

Variance for x:

11 - 10.8 = 0.3

0 - 10.8 = -10.8

36 - 10.8 =25.2.

22 - 10.8=11.2.

34 - 10.8 = 23.2

24 -10.8 = 13.2.

25 - 10.8= 14.2

-11 - 10.8 = -21.8.

-11 - 10.8 = - 21.8

-22 -10.8 = -32.8.

Total=0.1

Standard deviation for x = √ s^2 = 0.3162

This can be done for y too

(c). 75% Chebyshev interval around the mean for x values = 10.8 + 2 (0.3162); 10.8 - 2(0.3162).

=> (11.4324, 10.1676).

(d). The coefficient of variation= (0.3162)/10.8 × 100 = 2.92%.