Case 047Performance evaluation and manager selectionHard

A star manager has beaten the benchmark by 4% a year for seven years with 6.7% tracking error. After adjusting for size and momentum, alpha is 1.3% with 6.5% residual risk. Is it skill, and do you keep, cut or replace the fund?

The situation

Prakhar Opportunities Fund, an Indian flexi cap fund, has beaten its large cap benchmark by 4.0% a year after fees for 7 years, with tracking error of 6.7%. Its manager is well known and the fund charges an active fee well above index funds. A multi-manager platform you advise holds it as its largest equity position.

A regression of the fund's excess returns on factor returns shows a size loading of 0.4 and a momentum loading of 0.25. Over the period the size factor earned 4.0% a year and momentum 4.4%. What remains, the intercept, is 1.3% a year with residual risk of 6.5%.

Your task

How much of the record is skill, how confident can you be, and do you keep, cut or replace the fund?

Quick check

What is the t-statistic of the 1.3% alpha over seven years?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Most of the record is factor exposure: size explains 1.6 points and momentum 1.1, leaving 1.3% of alpha with a t-statistic of about 0.5, far short of evidence of skill. Even the raw 4% had a t of only 1.6. Cut the allocation and buy the size and momentum exposure more cheaply through factor funds; keep a smaller holding only if the manager can explain a repeatable source of return beyond the two tilts.

Step 1How much of the 4% is the manager, and how much is the tilt?

A cricket captain with a great home record may be a great captain, or may simply have played most games on pitches that suit his bowlers. Before crediting the manager, take out the returns any investor could have earned by holding the same tilts. A size loading of 0.4 on a factor that earned 4% a year explains 1.6 points; a momentum loading of 0.25 on 4.4% explains 1.1. Together that is 2.7 of the 4 points, 68% of the excess return. The alphaThe part of a return not explained by the market and the factor exposures included in the model; what is left for skill or luck. left over is 1.3%.

Of Prakhar's 4.0% a year excess return, 1.6 points come from its size tilt and 1.1 from its momentum tilt, leaving 1.3% of alpha, so about 68% of the record could have been bought as factor exposure.

Step 2How confident can you be that the 1.3% is skill?

A t-statistic asks how many standard errors the average sits from zero, and for a return series it is the information ratio times the square root of the years. The raw record gives 4 / 6.7 = 0.60, times the square root of 7, a t of 1.58; the alpha gives 1.3 / 6.5 = 0.20 and a t of 0.53. Neither clears the usual bar of 2. To get there an information ratio of 0.2 needs about 100 years of record: a working life, not an evaluation period. Seven years cannot tell skill at this level from luck.

The relationship

t = IR\sqrt{T} \qquad \frac{4.0}{6.7}\sqrt{7} \approx 1.58 \qquad \frac{1.3}{6.5}\sqrt{7} \approx 0.53 \qquad T_{t=2} = \left(\frac{2}{0.2}\right)^{2} = 100

IR	information ratio: excess return or alpha over its tracking or residual risk
T	years of record
2	the conventional threshold for significance

What it says in wordsThe raw record has a t of 1.58, the alpha after factors 0.53, and an information ratio of 0.2 needs about a hundred years to reach 2.

After seven years the raw record has a t-statistic of 1.58 and the factor-adjusted alpha only 0.53; at an information ratio of 0.20 it would take about 100 years for the record to clear the usual bar of 2.

Measure	Raw record	After size and momentum
Return over benchmark	4.0%	1.3%
Risk	6.7%	6.5%
Information ratio	0.60	0.20
t-statistic over 7 years	1.58	0.53
Years to reach t = 2	11	100

Adjusting for size and momentum cuts the information ratio from 0.60 to 0.20 and the t-statistic from 1.58 to 0.53, so the factor-adjusted record carries almost no statistical evidence of skill.

Step 3Keep, cut or replace?

Separate the two things the platform is buying. The 2.7 points of factor return are worth having, but they are available through size and momentum index funds at a fraction of the active fee, so paying a star's fee for them is the expensive way to own them. The 1.3% may be skill, but the record cannot show it. So cut the allocation from the largest position to a normal one, move the difference into cheaper factor exposure that keeps the tilts the platform wants, and keep the remainder only if the manager can explain a source of return the regression does not capture, such as stock selection within small caps, with evidence it repeats. Say the limits of the test: factor loadings drift, factor returns themselves are estimated, and a manager who times factors well would look factor-driven in this regression. That is a question to ask the manager, not a reason to skip the adjustment.

Where candidates lose it

The usual loss is admiring the 4% and the seven-year run without asking what an investor could have earned from the same tilts. Size and momentum both did well over the period, and a fund leaning into them would have beaten its large cap benchmark without any stock-picking skill.

The second is treating a t-statistic of 1.6 as nearly significant. It already fails the bar before the factor adjustment, and after it the evidence is weaker still. Seven years is a short record for an information ratio of this size.

What the interviewer asks next

The size factor has a bad three years. What would you expect the fund's excess return to do?
Which questions would you ask the manager to test whether the alpha is real?
How would your view change with fifteen years of record and the same numbers?

Company names and figures are illustrative.