Rate of return, standard deviation, coefficient of variation Personal Finance Pr

Question

Rate of return, standard deviation, coefficient of variation Personal Finance Problem Mike is searching for a stock to include in his current stock portfolio. He is interested in Hi-Tech Inc., he has been impressed with the company's computer products and believes Hi-Tech is an innovative market player. However, Mike realizes that any time you consider a technology stock, risk is a major concern. The rule he follows is to include only securities with a coefficient of variation of returns below 1.04. Mike has obtained the following price information for the period 2012 through 2015: any dividends during these 4 years. fr the period 2012 through 2015Hi-Tech stock, being gr Hi-Tech stock, being growth-oriented, did not pay a. Calculate the rate ofreturn for each year, 2012 through 2015, for Hi-Tech stock. b. Assume that each year's return is equally probable and calculate the average return over this time period. c. Calculate the standard deviation of returns over the past 4 years. (Hint. Treat this data as a sample.) d. Based on b and c determine the coefficient of variation of returns for the security e. Given the calculation in d what should be Mike's decision regarding the inclusion of Hi-Tech stock in his portfolio?

Explanation / Answer

a. Calculation of rate of return Year Beginning End Change in Price Return % A B C = B-A C/A 2012 $       14.85 $                   22.49 $                                                           7.64 51.45% 2013 $       22.49 $                   64.89 $                                                         42.40 188.53% 2014 $       64.89 $                   71.27 $                                                           6.38 9.83% 2015 $       71.27 $                   91.68 $                                                         20.41 28.64% b. Calculation of Average Return Year Return % 2012 51.45% 2013 188.53% 2014 9.83% 2015 28.64% Sum 278.45% Average Return = 278.45% / 4 69.61% c. Calculation of standard Deviation Year Return % Average Return Deviation Deviation Square A B C =A-B C*C 2012         0.5145                     0.6961                                                        (0.1816)                                 0.0330 2013         1.8853                     0.6961                                                           1.1892                                 1.4141 2014         0.0983                     0.6961                                                        (0.5978)                                 0.3574 2015         0.2864                     0.6961                                                        (0.4097)                                 0.1679 Sum of deviation Square                                 1.9724 Sum of deviation Square/(4-1)                                 0.6575 Standard Deviation =                                 0.8108 (Sum of deviation Square/4)^(1.2) d Calculation of Coefficient of variation Coefficient of variation = Standard Deviation /Average Return =0.8108/0.6961 =              1.16

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