Practice Question
Your stock has the following returns throughout three years, respectively: 29%, 20%, and 5%. What is the geometric average annual return?
Step 1: Define the Variables
- Year 1 return: \( r_1 = 29\% = 0.29 \)
- Year 2 return: \( r_2 = 20\% = 0.20 \)
- Year 3 return: \( r_3 = 5\% = 0.05 \)
Step 2: Apply Geometric Average Formula
\[ R_g = \left( (1 + r_1)(1 + r_2)(1 + r_3) \right)^{\frac{1}{3}} - 1 \]
Step 3: Compute Intermediate Values
\[ 1.29 \times 1.20 \times 1.05 = 1.6242 \] \[ R_g = 1.6242^{1/3} - 1 \approx 1.1757 - 1 = 0.1757 \]
Step 4: Convert to Percentage
\[ 0.1757 \times 100 = 17.57\% \]
Conclusion: The geometric average annual return is approximately 17.57%.