You find a certain stock that had returns of 15 percent, 22 percent, 23 percent,

Question

You find a certain stock that had returns of 15 percent, 22 percent, 23 percent, and 10 percent for four of the last five years. The average return of the stock over this period was 9.5 percent.

What was the stock’s return for the missing year?

What is the standard deviation of the stock’s returns?

can you show all equations.

You find a certain stock that had returns of 15 percent, 22 percent, 23 percent, and 10 percent for four of the last five years. The average return of the stock over this period was 9.5 percent.

Explanation / Answer

Answer: Calculation of the stock’s return for the missing year:

Here, we know the average stock return, and four of the five returns used to compute the average return. We can work the average return equation backward to find the missing return. The average return is calculated as:

0.095 = (0.15 – 0.22 + 0.23 + 0.10 + R) / 5

0.475 = 0.26 + R

R= 0.215 or 21.5%

The missing return has to be 21.50 percent.

Answer: Calculation of the standard deviation of the stock’s returns:

Now we can use the equation for the variance to find:

2 = 1/5[(0.15 – 0.095) 2 + (–0.22 – 0.095) 2 + (0.23 – 0.095) 2 + (0.10 – 0.095) 2 + (0.2150 – 0.095) 2 ]

2 = 1/5[0.003025+0.099225+0.018225+0.000025+0.0144]

Variance =0.02698

And the standard deviation is: = 0.02698 = 0.1643, or 16.43%

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