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.
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, you need to follow these steps:
Step 1: Convert the percentage returns into decimal form.
Year Return (%) Return (decimal)
2009 44% 0.44
2008 17% 0.17
2007 -11% -0.11
2006 19% 0.19
Step 2: Add 1 to each decimal return value.
Year Return (decimal) Return + 1
2009 0.44 1.44
2008 0.17 1.17
2007 -0.11 0.89
2006 0.19 1.19
Step 3: Multiply all the "Return + 1" values together.
R = (1.44) * (1.17) * (0.89) * (1.19) = 1.2512098
Step 4: Calculate the geometric mean rate of return using the power of (1/number of years) and subtract 1.
R = (1.2512098)^(1/4) - 1 = 0.1209 = 12.09%
Therefore, the geometric mean rate of return (R) on Eastern Mining Corporation shares over the last four years is 12.09% per annum.