Alpha

A manager reports significant positive alpha relative to a single-factor model using a broad market index. Consultant Aurelio Brandvold re-runs the analysis using a model that also includes a size factor and a value factor, and the alpha largely disappears. What does that result MOST likely mean?

1. A.The manager destroyed value, because a model showing no alpha indicates negative skill.Incorrect. Alpha near zero means the return is explained by factor exposures, not that value was destroyed. The manager may have delivered perfectly good returns.
2. B.The manager return was largely compensation for persistent size and value factor exposures rather than unique skill, and comparable exposure may be available far more cheaply.Correct. The single-factor model had misclassified priced factor tilts as alpha; the richer model prices them directly.
3. C.Adding factors to a regression always eliminates alpha, so the second result carries no information.Incorrect. Adding factors does not mechanically eliminate alpha. Managers whose returns are not explained by those factors retain their alpha in the richer model.
4. D.The manager violated the plan mandate by taking exposures outside the benchmark.Incorrect. Nothing in the facts indicates a mandate breach. Attribution identifies the SOURCE of return; it does not establish a compliance violation.

Why: A single-factor model attributes to alpha everything the market factor cannot explain. If a manager persistently tilts toward smaller companies and toward cheaper valuations, and those tilts have historically earned a return premium, a single-factor model will misread that systematic factor exposure as manager skill. Adding size and value factors gives the model a way to price those exposures directly. When alpha collapses on their addition, the natural interpretation is that the manager return came from persistent, replicable factor tilts rather than from unique insight. This matters commercially: factor exposure can often be obtained through a low-cost systematic vehicle, so an investor should not pay an active fee for something a rules-based fund delivers more cheaply. It does not prove the manager did anything wrong; it simply relocates the source of the return.

The Farrow Value Fund returned 13.4 percent over a year in which its benchmark market index returned 10 percent and the risk free rate was 2 percent. The fund's beta is 1.15. What is the fund's alpha?

1. A.+1.4 percentThis applies beta to the full 10 percent market return rather than to the 8 percent risk premium, overstating the expected return.
2. B.+3.4 percentThis subtracts the raw market return of 10 percent. It gives the fund no credit for taking 1.15 times the market's risk.
3. C.+11.4 percentThis subtracts only the risk free rate. Alpha measures excess return over the beta adjusted expectation, not over cash.
4. D.+2.2 percentCorrect. Expected return of 11.2 percent subtracted from the 13.4 percent actual return.

Why: Start with what the fund should have earned for the market risk it took: 2 + 1.15 x (10 - 2) = 2 + 9.2 = 11.2 percent. The fund actually delivered 13.4 percent, so alpha is 13.4 - 11.2 = +2.2 percent. Positive alpha means the manager produced more than the fund's beta exposure alone would explain.

A fund has a beta of 1.2. Over a year in which the market index returned 10 percent, the fund returned 15 percent. Ignoring the risk-free rate, the fund's alpha is approximately:

1. A.+15 percent - total return equals alpha when the risk-free rate is ignoredAlpha is the residual after removing market-driven return, never the whole return.
2. B.-3 percentSign error - the fund exceeded, not trailed, its expected return.
3. C.+5 percent - the fund's return minus the market's returnThis skips the beta adjustment; a 1.2-beta fund is EXPECTED to beat a rising market.
4. D.+3 percent - the fund beat its beta-adjusted expected return of 12 percentCorrect - expected return is 1.2 x 10 = 12 percent, and 15 - 12 = +3 alpha.

Why: Alpha measures performance beyond what the fund's market exposure explains. Expected return = beta times market return = 1.2 x 10 = 12 percent. Actual return of 15 percent exceeds that by 3 points, so alpha is +3 percent. The clue is that beta must be applied BEFORE comparing - alpha is never simply fund return minus market return unless beta is exactly 1. Review: risk-adjusted performance measures.