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%.