Calculate Geometric Mean Rate of Return for a Stock
What is the geometric mean rate of return for a particular stock?
Suppose the rate of return for a particular stock during the past four years was +15%, +10%, −10% and +20%. Compute the geometric mean rate of return.
Answer:
Based on given options, the geometric mean rate of return for the given stock is 7.3%. The correct option is c.
To compute the geometric mean rate of return, we need to multiply all the individual rates of return and then take the nth root, where n is the number of years. In this case, the calculation would be:
(1 + 0.15) * (1 + 0.10) * (1 - 0.10) * (1 + 0.20) = 1.105
Then, we take the fourth root of 1.105:
(1.105) ^ (1/4) ≈ 1.0726
Finally, we subtract 1 and multiply by 100 to convert it to a percentage:
(1.0726 - 1) * 100 ≈ 7.3%
Therefore, the geometric mean rate of return for the given stock is approximately 7.3%.