Answer: Arithmetic mean return.

## Explanation Let's calculate each type of return to determine which one equals -5.34%. **1. Arithmetic Mean Return:** \[ \text{Arithmetic Mean} = \frac{6\% + (-37\%) + 27\%}{3} = \frac{-4\%}{3} = -1.33\% \] **2. Geometric Mean Return:** \[ \text{Geometric Mean} = \left[(1 + 0.06) \times (1 - 0.37) \times (1 + 0.27)\right]^{1/3} - 1 \] \[ = \left[1.06 \times 0.63 \times 1.27\right]^{1/3} - 1 \] \[ = \left[0.848\right]^{1/3} - 1 \] \[ \approx 0.945 - 1 = -5.5\% \] **3. Money-Weighted Return (IRR):** This requires cash flow information which is not provided. The money-weighted return depends on the timing and size of cash flows into and out of the portfolio. **4. Time-Weighted Return:** The time-weighted return is calculated as the geometric mean of the period returns: \[ \text{TWR} = \left[(1 + 0.06) \times (1 - 0.37) \times (1 + 0.27)\right] - 1 \] \[ = 1.06 \times 0.63 \times 1.27 - 1 \] \[ = 0.848 - 1 = -15.2\% \] **Comparison:** - Arithmetic mean: -1.33% - Geometric mean: -5.5% (approximately -5.34% with rounding) - Time-weighted return: -15.2% The manager's reported return of -5.34% is closest to the geometric mean return of approximately -5.5% (the slight difference is due to rounding). **Why not the others?** - **Arithmetic mean** (-1.33%) is too high - **Money-weighted return** cannot be calculated without cash flow data - **Time-weighted return** (-15.2%) is too low Therefore, the manager has reported the **geometric mean return**.

Author: LeetQuiz Editorial Team