You have the following rates of return for a risky portfolio for several recent years. Assume that the stock pays no dividends. Year Beginning of Year Price # of Shares Bought or Sold 2011 $50.00 100 Bought 2012 $55.00 50 Bought 2013 $51.00 75 Sold 2014 $54.00 75 Sold What is the geometric average return for the period?

The geometric average return for the period 2.60%.

Explanation:

Note: The data in this question are merged together. They are therefore sorted before answering the question. See the attached pdf file for the complete question with the sorted data.

Also note: See the attached excel file for the calculation of the return for each year.

In the attached excel file, return is calculated using the following formula:

Return = (Current year price - Previous year price) / Previous year price

The formula for calculating the geometric average return is given as follows:

Geometric average return = [(1 + R1)(1 + R2)(1 + R3)...(1 + Rn)]^(1/n) – 1 ……….. (1)

Where;

Ri = Return over the years I, where i = 1, 2, 3, …. n

n = number of years = 3

R1 = 2012 return = 0.10

R2 = 2013 return = -0.0727272727272727

R3 = 0.0588235294117647

Substituting the values into equation (1), we have:

Geometric average return = ((1 + 0.10)(1 - 0.0727272727272727)(1 + 0.0588235294117647))^(1/3) – 1

Geometric average return = (1.10 * 0.927272727272727 * 1.0588235294117647)^(1/3) – 1

Geometric average return = 1.07999999999999^0.333333333333333 - 1

Geometric average return = 1.02598556800602 - 1

Geometric average return = 0.02598556800602 = 0.0260, or 2.60%

Therefore, the geometric average return for the period 2.60%.

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