Question

the mean closing price of stock a over the past year is php12,000 with the standard deviation of php1,500. in the case of stock b, the mean is php10,000 with the standard deviation of php800. what are the coefficients of variation of stocks a and b? stock a = 15% & stock b = 12% stock a = 12.5% & stock b = 8% stock a = 6.5% & stock b = 6% stock a = 1.5% & stock b = 4%

Explanation:

Step1: Recall the formula for coefficient of variation (CV)

The formula for the coefficient of variation is \( CV = \frac{\text{Standard Deviation (SD)}}{\text{Mean (M)}} \times 100\% \)

Step2: Calculate CV for Stock A

For Stock A: Mean (\( M_A \)) = Php12,000, Standard Deviation (\( SD_A \)) = Php1,500
Using the formula:
\( CV_A=\frac{SD_A}{M_A}\times 100\%=\frac{1500}{12000}\times 100\% \)
Simplify \( \frac{1500}{12000}=\frac{1}{8} = 0.125 \)
Then \( 0.125\times 100\% = 12.5\% \)

Step3: Calculate CV for Stock B

For Stock B: Mean (\( M_B \)) = Php10,000, Standard Deviation (\( SD_B \)) = Php800
Using the formula:
\( CV_B=\frac{SD_B}{M_B}\times 100\%=\frac{800}{10000}\times 100\% \)
Simplify \( \frac{800}{10000}=0.08 \)
Then \( 0.08\times 100\% = 8\% \)

Answer:

Stock A = 12.5% & Stock B = 8%