Calculate time-weighted and money-weighted returns and the main risk-adjusted performance measures.
An investor starts with $100. In period 1 the fund gains 10%, to $110. She adds $100, making $210. In period 2 the fund loses 5%, ending at $199.50.
The fund made money but the investor lost, because more of her money was invested during the bad period. Studies of fund flows find investors' money-weighted returns usually lag the funds' time-weighted returns for exactly this reason: they buy after gains and sell after losses.
Example: a fund returned 12% with volatility of 18% and beta of 1.2. The market returned 10% with volatility of 15%. The risk-free rate was 3%.
| Measure | Formula | Fund | Market |
|---|---|---|---|
| Sharpe ratio | (Return minus risk-free) / volatility | 0.50 | 0.47 |
| Treynor ratio | (Return minus risk-free) / beta | 7.5 | 7.0 |
| Jensen's alpha | Return minus [risk-free + beta x (market minus risk-free)] | 12% minus 11.4% = +0.6% | 0 |
| M-squared | Risk-free + Sharpe x market volatility | 10.5% | 10.0% |
A valid benchmark is specified in advance, investable, and matches the fund's style and risk. A small-cap fund compared with a large-cap index proves nothing.
Performance attribution splits active return into allocation (overweighting the sectors or asset classes that did well) and selection (picking better securities within each).
With a tracking error of 5% a year, a manager with a true alpha of 2% needs roughly 25 years of data for the result to be statistically significant at the usual standard. Short track records say very little. Published fund databases also suffer from survivorship bias, because failed funds disappear from the averages.
A fund returned 10% with a downside deviation (below a 3% target) of 8%. Sortino = (10% minus 3%) / 8% = 0.875. A fund whose volatility comes mostly from large gains will look better on Sortino than on Sharpe.
Richard Grinold showed that a manager's information ratio is approximately:
where IC (information coefficient) is the correlation between forecasts and outcomes and breadth is the number of independent bets a year. A manager with an IC of 0.05, a small but real edge, making 100 independent bets a year has an IR of about 0.5. Skill can be modest if it is applied widely; a concentrated manager needs a much larger edge for the same result.
A portfolio and its benchmark hold two sectors.
| Sector | Portfolio weight | Portfolio return | Benchmark weight | Benchmark return |
|---|---|---|---|---|
| Technology | 40% | 15% | 30% | 12% |
| Other | 60% | 5% | 70% | 6% |
| Total | 9.0% | 7.8% |
The active return of 1.2 points splits into:
Total: 0.6 + 0.2 + 0.4 = 1.2. The manager's edge came mainly from the sector bet, not stock picking.
The Global Investment Performance Standards (GIPS) set rules for how firms calculate and present returns: composites that include all fee-paying accounts managed to a strategy (so firms cannot show only their best accounts), time-weighted returns, gross and net of fees, and full disclosure. Ask whether a manager claims GIPS compliance.
A manager who produces 1% of alpha before fees and charges 1% delivers none to the client. Always evaluate net-of-fee results against a low-cost alternative, not against zero.
Using three years of your own or your paper portfolio's monthly values and cash flows, compute TWR and MWR. Then compute Sharpe, beta, alpha and tracking error against a suitable index.
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