Question

1. The common stock of J&J Tool has yielded 4.2%, 9.7%, -15.4%, 12.5% over the past four years, respectively. What is the geometric average return?
a. 2.04%
b. 2.08%
c. 2.13%
d. 5.16%
e. 2.20%

2. One year ago, you bought a stock for $35.37 a share. You received a dividend of $1.00 per share last month and sold the stock today for $36.12 a share. What is the total return of this investment?
a. 4.95%
b. 4.98%
c. 5.02%
d. 5.04%
e. 5.11%

3. The stock of Chocolate Galore is expected to produce the following returns given the various states of the economy. What is the expected return on this stock?

State of economy           Probability of state           Rate of return   

Recession                                0.10                             -0.09

Normal                                    0.65                             0.07

Boom                                      0.25                              0.12

a. 6.61 percent
b. 6.65 percent
c. 6.68 percent
d. 6.69 percent
e. 6.72 percent

Use the table below for Problems 4 and 5.

State of economy         Probability of state                        Rate of return

                                                                        Stock A           Stock B           

Boom                                      0.4                      0.05                 -0.03                

Normal                                    0.6                      0.12                 0.14                 

4. Given the above information, what is the standard deviation of stock A?    
a. 0.0317
b. 0.0328
c. 0.0339
d. 0.0343
e. 0.0351

5. Given the above information, what is the covariance of stock A and stock B?      
a. 0.00275
b. 0.00276
c. 0.00279
d. 0.00281
e. 0.00286

Answer 1

Q1) c) 2.13%

Explanation:

Geometric return= [(1+0.042) (1+0.097) (1-0.154) (1+0.125)]^1/4 - 1

= [(1.042) (1.097) (0.846) (1.125)]^0.25 - 1

= (1.0879)^0.25 - 1

= 1.0213 - 1

= 0.0213 or 2.13%

Q2) A) 4.95%

Explanation:

Total return= ending price - beginning price + dividend/ beginning price

= 36.12 - 35.37 + 1 / 35.37

= 1.75 / 35.37

= 4.95%

Q3) B) 6.65%

Explanation:

Expected return = probability × return

= 0.1 × -0.09 + 0.65 × 0.07 + 0.25 × 0.12

= -0.009 + 0.0455 + 0.03

= 0.0665 or 6.65%

Q4) D) 0.0343

Explanation:

Expected return = probability × return

= 0.4 × 5% + 0.6 × 12%

= 2% + 7.2%

= 9.2%

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

= √ 0.4 (0.05 - 0.092)^2 + 0.6 (0.12 - 0.092)^2

= √ 0.4 (-0.042)^2 + 0.6 (0.028)^2

= √ 0.4 (0.001764) + 0.6 (0.000784)

= √ 0.0007056 + 0.0004704

= √ 0.001176

= 0.0343