Question

In: Finance

You have the following rates of return for a risky portfolio for several recent years. Assume...

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
2008 $115           280bought
2009 $120           230bought
2010 $116           255sold
2011 $119           255sold

What is the geometric average return for the period?

Solutions

Expert Solution

Solution:
Geometric average return for the period 1.15 %
Working Notes:
Year 2008 return r1
= (Beginning price of 2009 -Beginning price of 2008)/Beginning price of 2008
= (120 -115)/115
= 5/115
= 0.04347826
=4.347826087%
Year 2009 return   r2
= (Beginning price of 2010 -Beginning price of 2009)/Beginning price of 2009
= (116 -120)/120
= -4/120
= -0.0333333333
= -3.3333333333%
Year 2010 return    r3
= (Beginning price of 2011 -Beginning price of 2010)/Beginning price of 2010
= (119 -116)/116
= 3/116
= 0.02586206897
= 2.58620690%
Geometric average return for the period
= ((1+r1)(1+r2)(1+r3))^(1/3) - 1
= ((1+ 0.04347826)(1-0.0333333333)(1+ 0.02586206897))^(1/3) - 1
=0.011462316
=1.1462%
=1.15%
Please feel free to ask if anything about above solution in comment section of the question.

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