Question

Over the past four years, the common stock of Jess Electronics Co. produced annual returns of 7.2, 5.8, 11.2, and 13.6 percent, respectively. Treasury bills produced returns of 3.4, 3.3, 4.1, and 4.0 percent, respectively over the same period. What is the standard deviation of the risk premium on Jess Electronics Co. stock for this time period? (Hint: First, calculate the risk premium for the stock in each of the years. Then, use these 4 annual risk premiums to calculate the standard deviation in the normal way that standard deviation is calculated.).
A. 2.23 percent
B. 4.46 percent
C. 3.22 percent
D. 2.86 percent
E. 4.61 percent

Answer 1

Answer:

Standard Deviation = 0.032 or 3.2%

Therefore, Option  C) 3.22 percent is the correct answer

Explanation:

Given the data in the question;

lets make a table;

year     market       Treasury bills      Risk              deviation             square of

           returns            returns         premium        from mean           deviation

                A                    B                   (A - B)         Avg - (A - B)      (Avg-(A-B))²

1             7.2%                3.4%                3.8%            -0.0195               0.0004

2            5.8%                3.3%                2.5%            -0.0325              0.0011

3            11.2%                4.1%                 7.1%              0.0135               0.0002

4            13.6%               4.0%                9.6%             0.0385              0.0015

sum(∑)                                                    23%                                        0.0032

Average Avg = ∑(A-B) /n = 23/4 = 5.75%    

so Variance = ∑(Avg-(A-B))² / n-1 = 0.0032 / (4-1) = 0.0032 / 3 = 0.0010      

Standard Deviation = √variance = √0.0010 = 0.0316 ≈ 0.032 or 3.2%

Therefore, Option  C) 3.22 percent is the correct answer