In: Finance
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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 |
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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. | |||