Outliers
Also written Outlier · Extreme returns · Outlier returns
Extreme returns in a fund's track record, whether highly positive or highly negative — the thing skewness and kurtosis are computed to detect.
In plain language
Look at a fund's yearly returns and one number often refuses to sit with the others. Five years near 20%, and then one year at −0.50%.
That odd number is an outlier. The workbook defines them simply: outliers are extreme returns, whether highly positive or highly negative.
Now the surprising part. A prudent investor does not want outliers even on the upside.
Why? Because an outlier says something about the fund, not about that one year. The workbook is blunt: outliers signify increased market risk and a volatile fund strategy. A manager who can produce a 40% year can produce a −40% year, and you do not get to pick which.
The average return hides all of this. Two funds can average the same and have completely different shapes.
So the workbook brings in two more measures. Skewness asks whether the outliers sit above or below the average. Kurtosis asks how peaked the distribution is, which shows how far the extremes reach. Both exist to interpret the effect of outliers.
How it works
Section 9.6 introduces outliers through the workbook's two running funds, and then builds both higher-moment risk measures on top of them.
The definition and the warning. Outliers are extreme returns, whether highly positive or highly negative returns. Prudent investors would never prefer historical performance of a fund to exhibit outliers, as it signifies increased market risk and a volatile fund strategy. To interpret the effect of outliers, the risk measures of skewness and kurtosis are important.
Where the outlier shows up graphically. In the workbook's Exhibit 2, Fund B has a mean of 15.98% and a normal distribution constructed by taking increments of 3 σ either side of the mean. In Year 2 the fund generated a return of −0.50%. Because of that return, the curve moves beyond the y-axis to represent the negative return as an outlier.
Mind which data set a figure belongs to. The workbook runs these funds twice. Example 9.7 and Example 9.8 use five years, giving Fund A a mean of 13.87% with a standard deviation of 2.06%, and Fund B a mean of 15.98% with 8.44%. Examples 9.8.1 and 9.8.2 add a sixth year and recompute: Fund A 13.87% and 1.88%, Fund B 16.78% and 7.91%. Two means for Fund B, and neither is wrong — they are five-year and six-year figures.
The two funds, six years of returns:
| Yr 1 | Yr 2 | Yr 3 | Yr 4 | Yr 5 | Yr 6 | |
|---|---|---|---|---|---|---|
| Fund A | 12.50% | 11.25% | 13.65% | 17.30% | 14.65% | 13.85% |
| Fund B | 21.50% | −0.50% | 16.75% | 20.25% | 21.90% | 20.80% |
| Measure | Fund A | Fund B |
|---|---|---|
| Mean | 13.87% | 16.78% |
| Standard deviation | 1.88% | 7.91% |
| Skewness (Excel SKEW) | 0.705 | −2.222 |
| Kurtosis (Excel KURT) | 1.162 | 5.034 |
| Excess kurtosis (less 3) | −1.838 | +2.034 |
What skewness does with an outlier. Skewness refers to the extent to which a distribution is not symmetrical across the mean, and it is a result of outliers, either above or below it. A normal distribution is perfectly symmetrical and therefore has a skewness of zero. Positive skew means large outliers above the mean and a long right tail, and the mean sits above the mode. Negative skew means large outliers below the mean and a long left tail, with the mean below the mode. Skewness greater than zero is positive, less than zero is negative. Investors will not prefer a skewed distribution at all, but positive skewness is preferred over negative skewness.
What kurtosis does with an outlier. Kurtosis is the degree to which a distribution is more or less peaked than a normal distribution, which has a kurtosis of 3. A peaked distribution indicates the presence of outliers with large deviations from the mean. Above 3 is riskier; distributions with fatter tails and higher peaks have high kurtosis, and fat tails are an indicator of inconsistent performance.
The workbook's conclusion, and the caution attached to it. Standard deviation, skewness and kurtosis all conclude that Fund B is riskier than Fund A. But sophisticated investors should not analyse all the risk measures in isolation. An investor with a high risk appetite might still choose Fund B on the mean and standard deviation alone — and in doing so would ignore the probability of outliers and the volatility of expected returns.
A worked example
Two Category III AIFs, five years of net returns, both averaging close to 14%.
| Yr 1 | Yr 2 | Yr 3 | Yr 4 | Yr 5 | Mean | |
|---|---|---|---|---|---|---|
| Fund P | 13.0% | 14.5% | 12.8% | 15.2% | 14.0% | 13.90% |
| Fund Q | 18.0% | −22.0% | 19.5% | 21.0% | 33.0% | 13.90% |
Identical means. An investor comparing only the mean sees two identical funds.
Fund P has no outliers. Its returns sit in a band of 2.4 percentage points.
Fund Q has three. The −22.0% in Year 2 is a negative outlier. The +33.0% in Year 5 is a positive one. And the workbook's point is that the positive one is not good news — it is evidence of the same volatile strategy that produced the negative one.
What each measure would say.
| Measure | Fund P | Fund Q | Reading |
|---|---|---|---|
| Standard deviation | About 1% | About 21% | Q swings twenty times as hard |
| Skewness | Near zero | Negative, because the −22% deviates further from the mean than the +33% | Q's tail is on the wrong side |
| Kurtosis | Below 3 | Above 3 | Q is peaked, with fat tails |
The rupee consequence on a Rs 10 crore commitment. Fund P compounds steadily. Fund Q's Year 2 takes Rs 10 crore to Rs 7.8 crore, and Year 2 to Year 5 has to earn back that hole before it earns anything. An investor who needed to exit at the end of Year 2 — for a tax payment, a grant commitment or a drawdown elsewhere — realised a 22% loss on a fund whose five-year average was 13.90%.
And the workbook's own caution applies. On mean and standard deviation alone, an investor with a high risk appetite might still pick Fund Q. Doing so without looking at the skewness and kurtosis means ignoring the probability of outliers entirely. That is the mistake the two higher measures exist to prevent.
Why NISM asks about it
Chapter 9 (Fee Structure and Fund Performance), section 9.6, introduces outliers immediately before Skewness and Kurtosis, and the two measures are explained as tools for interpreting them. Examples 9.8.1 and 9.8.2 carry the Fund A and Fund B figures.
The definition question is a favourite because it has a counter-intuitive answer: outliers are extreme returns whether positive or negative, and a prudent investor would not want them in a track record at all. Expect a follow-up on why — because they signify increased market risk and a volatile fund strategy. Expect also the linkage question: which two risk measures are used to interpret the effect of outliers (skewness and kurtosis), and the reasoning that skewness is a result of outliers while a peaked distribution indicates the presence of outliers.
Common exam traps
- A positive outlier is not a good thing. The workbook says prudent investors would never prefer a track record that exhibits outliers, on either side.
- Outliers are about extremity, not sign. Both a 40% year and a −40% year are outliers.
- Standard deviation alone does not reveal them. Two funds with the same mean and similar standard deviations can have very different tails, which is why skewness and kurtosis exist.
- Skewness detects which side the outliers are on; kurtosis detects how far they reach. They answer different questions about the same outliers.
- Positive skew is preferred over negative skew, but no skew is preferred over both. The workbook states the preference and the ideal separately.
- The mean moves away from the mode as outliers are added. Mean above mode is positive skew; mean below mode is negative skew.
- Do not read the measures in isolation. The workbook's own conclusion says a high-risk-appetite investor could still choose the riskier fund, but only after seeing all four numbers.
Where this is taught
Free preparation for NISM Series XIX-CRelated terms
- Standard deviationA measure of how far returns typically stray from their own average — the standard statistic for total risk, counting company-specific and market-wide causes alike.
- VarianceA measure of how widely a scheme's periodic returns fluctuate around its own average return — the square of standard deviation, and a risk measure relevant to both debt and equity schemes.
- Downside riskThe probability of a loss on account of falling asset prices in changing market conditions — the half of volatility investors actually mind, measured by maximum drawdown and value at risk.
- Semi varianceA downside-risk measure that looks only at the dispersion of returns below the mean (or a target return), ignoring the upside swings that standard deviation counts equally alongside the downside ones.
- KurtosisA measure of how peaked a return distribution is and how fat its tails are. The workbook takes a normal distribution as kurtosis 3; above 3 (leptokurtic) signals outliers and higher risk.
- Maximum DrawdownThe largest peak-to-trough fall in a Category III AIF's AUM over a reporting period, quoted as a percentage of the peak — the worst loss an investor could have suffered in that window.
- SkewnessA measure of how far a fund's return distribution departs from symmetry around its mean. Zero is symmetrical; positive has a long right tail; negative has a long left tail and is riskier.
- LeptokurticA return distribution with kurtosis above 3 (excess kurtosis above zero): values bunch near the mean or sit far from it — a high peak with fat tails, which the workbook reads as riskier.
- PlatykurticA return distribution with kurtosis below 3, so excess kurtosis is negative: values cluster at consistent frequencies around the mean with no significant deviations.