NASAA Series 65, Uniform Investment Adviser Law ExaminationClient Investment Recommendations and StrategiesMedium
An investment adviser is evaluating a client's portfolio performance. The portfolio had an initial value of $100,000. After one year, the value increased to $110,000. At the end of the second year, the value was $105,000. No contributions or withdrawals were made. What is the time-weighted return for this two-year period?
- A2.5% annualized
- B4.88% annualized
- C7.5% annualized
- D5.0% annualized
Show answer & explanationAnswer & explanation
Correct answer: A. 2.5% annualized
The time-weighted return calculates the geometric mean of the annual returns. Year 1 return: ($110,000 - $100,000) / $100,000 = 10%. Year 2 return: ($105,000 - $110,000) / $110,000 = -4.545%. Geometric mean = [(1 + 0.10) * (1 - 0.04545)]^(1/2) - 1 = [1.10 * 0.95455]^(1/2) - 1 = [1.050]^(1/2) - 1 = 1.02469 - 1 = 0.02469 or approximately 2.47% annualized, which rounds to 2.5% for the given options.
Why the other options are wrong
- B. This is an incorrect calculation, possibly using a simple average or misapplying the geometric mean.
- C. This is an incorrect calculation, not reflecting the actual period returns accurately.
- D. This is an incorrect calculation; it might represent a simple average of the start and end values.
Time-Weighted Return (TWR)
A measure of portfolio performance that eliminates the distorting effects of cash inflows and outflows, reflecting the compound growth rate of the portfolio.
- Used to compare investment managers.
- Calculated by geometrically linking sub-period returns.
- Unaffected by client deposits or withdrawals.
Memory trick: Measure true growth, ignore the client's cash flow streams.