You are a share analyst for an investment firm and are investigating the return on shares in the Eastern Mining Corporation over the last four years. The return on Eastern Mining Corporation shares over the last four years is presented.
Calculate the geometric mean rate of return (R) on Eastern Mining Corporation shares over the last four years. Give your answer as a percentage per annum to 2 decimal places.
R = % pa
Return on Eastern Mining Corporation shares
Year Return
2009 44%
2008 17%
2007 -11%
2006 19%
To calculate the geometric mean rate of return (R) on Eastern Mining Corporation shares over the last four years, follow these steps:
1. Convert the returns to decimal form:
- 2009: 44% = 0.44
- 2008: 17% = 0.17
- 2007: -11% = -0.11
- 2006: 19% = 0.19
2. Add 1 to each decimal return to get the growth factor:
- 2009: Growth factor = 1 + 0.44 = 1.44
- 2008: Growth factor = 1 + 0.17 = 1.17
- 2007: Growth factor = 1 - 0.11 = 0.89
- 2006: Growth factor = 1 + 0.19 = 1.19
3. Calculate the overall growth factor by multiplying the individual growth factors:
Overall growth factor = (1.44) * (1.17) * (0.89) * (1.19) = 1.4309
4. Calculate the geometric mean rate of return (R) by taking the fourth root of the overall growth factor and subtracting 1:
R = 4th root of (Overall growth factor) - 1 = 4th root of 1.4309 - 1 ≈ 0.1076
5. Finally, convert the result to a percentage per annum:
R = 0.1076 * 100 ≈ 10.76% per annum
Therefore, the geometric mean rate of return (R) on Eastern Mining Corporation shares over the last four years is approximately 10.76% per annum.