Question

You are thinking about investing money in the stock market and have narrowed your choices to one of two stocks: TD Bank or Cenovas Energy. For TD Bank you have the following statistics:

•  Mean monthly closing price: $75.00      • Sample standard deviation: $6.00

The monthly closing stock prices of Cenovas Energy for the last eight months is shown below:

Closing Stock Price:  ($) 14.00  14.50  11.00  13.00  13.75  11.00   8.75  10.00

1. Calculate the mean stock price of Cenovas Energy.  [2 marks]
     
2. Calculate the standard deviation for the sample prices of Cenovas Energy.  [2 marks]
   
3. What is the median stock price for Cenovas Energy?  [2 marks]

4. What is the range in Cenovas Energy’s stock price?   [2 mark]

5. Calculate the coefficient of variation for each stock.  [2 marks]
   TD Bank:                                                                 Cenovas Energy:                               
6. Which stock is riskier?  Use one of the 5 measures above.  Explain why it is most appropriate.  [2 marks]
   

Answer 1

Given The monthly closing stock prices of Cenovas Energy for the last eight months is shown below:

14.00  14.50  11.00  13.00  13.75  11.00   8.75  10.00

Question (a)

Mean stock price of Cenovas Energy = Sum of all the monthly closing stock prices / Number of months

= 96 / 8

= 12

So Mean stock price of Cenovas Energy = $12

Question (b)

Standard deviation for the sample prices of Cenovas Energy = (Xi - Mean)2 / (n -1)

= [ (14 - 12)2 + (14.5 - 12)2 + (11 - 12)2​​​​​​​ + (13 - 12)2​​​​​​​ + (13.75 - 12)2​​​​​​​ + (11 - 12)2​​​​​​​ + (8.75 - 12)2​​​​​​​ + (10 - 12)2​​​​​​​ ] / (8-1)

= 30.875 / 7

= 4.410714

= 2.10017

So Standard deviation for the sample prices of Cenovas Energy = $2.10017

Question (c)

Median stock price for Cenovas Energy

Arraging the eight months closing stock price of Cenovas Energy in ascending order we have

8.75 10.00 11.00 11.00 13.00 13.75 14.00 14.50

Median here will be average of 4th and 5th ​​​​​​​values in ascending order

Median stock perice for Cenovas Energy = (11.00 + 13.00) / 2

= 24/2

= 12

So Median stock perice for Cenovas Energy = $12

Question (d)

Range in Cenovas Energy’s stock price = Highest Price - lowest price

= 14.50 - 8.75

= 5.75

So Range in Cenovas Energy’s stock price = $5.75

Question (e)

Coefficient of variation = (Standard deviation / Mean)

Coefficient of variation for TD bank = (6.00 / 75.00)

= 0.08 or 8%

Coefficient of variation for Cenovas Energy = (2.10017 / 12)

= 0.175014 or 17.5014%

Question (f)

The higher the coefficient of variation, the more riskier the stock is

Here the coefficient of variation of Cenovas Energy is more than the Coefficient of variation for TD bank

So Cenovas Energy is the riskier stock

Coefficient of variation is the appropriate measure for comparing risks here because the Means of both the stocks have a huge difference between them. Using coefficient of variation will normalize the standard deviation with respect to the mean

So coefficent of variation is the appropriate measure here