Finance Introduction Valuation for Securities, Capital structures

Question

a) Janet is considering investing in a corporate bond with possible one-year returns distributed as follows:

Returns      6%   9%  11% 13% 16%

Probability 0.15 0.20 0.30 0.20 0.15 

Required:

Determine the expected return and standard deviation of the above security.

Answer 1

To determine the expected return and standard deviation of the above security, we will use the following formulas:

Expected return = Σ (return x probability)

Standard deviation = √Σ ((return - expected return)^2 x probability)

First, we will calculate the expected return:

Expected return = (6% x 0.15) + (9% x 0.20) + (11% x 0.30) + (13% x 0.20) + (16% x 0.15) = 10.35%

Next, we will calculate the standard deviation:

(return - expected return)^2 x probability:

(6% - 10.35%)^2 x 0.15 = 8.94 x 0.15 = 1.34

(9% - 10.35%)^2 x 0.20 = 1.29 x 0.20 = 0.26

(11% - 10.35%)^2 x 0.30 = 0.36 x 0.30 = 0.11

(13% - 10.35%)^2 x 0.20 = 2.56 x 0.20 = 0.51

(16% - 10.35%)^2 x 0.15 = 5.76 x 0.15 = 0.87

Standard deviation = √(1.34 + 0.26 + 0.11 + 0.51 + 0.87) = √3.09 = 1.76%

Therefore, the expected return of the corporate bond is 10.35% and the standard deviation is 1.76%.