In: Finance
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? |
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. |