Skewness
Also written Skew
A 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.
In plain language
Two funds can share the same average return and the same standard deviation and still be very different to own. One might occasionally deliver a surprisingly good year; the other might occasionally deliver a disastrous one. Mean and standard deviation cannot tell them apart. Skewness can.
The workbook defines it as "the extent to which a distribution is not symmetrical across the mean". A normal distribution is perfectly symmetrical and has a skewness of zero. Skewness arises from outliers — extreme returns — above or below the mean.
Outliers above the mean are sometimes beneficial; the ones investors must be diligent about lie below it. So while investors would prefer returns not to be skewed at all, positive skewness is preferred over negative skewness.
How it works
Positive skew (skewed right). Large outliers above the mean give the distribution a relatively long right tail. The mean shifts away from the mode, so in a positively skewed distribution the mean is higher than the mode.
Negative skew (skewed left). Large outliers below the mean give a long left tail. The mean is lower than the mode.
Mode and mean. The mode is the most frequent value — the peak of the curve. In a normal distribution, mean and mode coincide at the peak.
Computing it. The workbook uses Excel: =SKEW(range).
The workbook's Example 11.1, six years of returns:
| Returns | Mean | Standard deviation | Skewness | |
|---|---|---|---|---|
| Fund A | 12.50, 11.25, 13.65, 17.30, 14.65, 13.85 | 13.87% | 1.88% | 0.705 |
| Fund B | 21.50, -0.50, 16.75, 20.25, 21.90, 20.80 | 16.78% | 7.91% | -2.222 |
Fund A is positively skewed; Fund B is negatively skewed, driven by its -0.50% year. On skewness, Fund B is riskier than Fund A — even though its mean return is higher.
Why it matters for Category III. The workbook stresses that Category III AIFs do not necessarily follow a normal distribution, so skewness and kurtosis are needed alongside mean and standard deviation — and the risk measures should not be analysed in isolation.
A worked example
Illustrative, drawing on the workbook's Fund A and Fund B. Mr Venkatesh has Rs 5 crore to place and a high risk appetite. He looks first at the mean and standard deviation:
| Mean | Standard deviation | |
|---|---|---|
| Fund A | 13.87% | 1.88% |
| Fund B | 16.78% | 7.91% |
With his risk appetite, Fund B's extra 2.91 percentage points of average return look worth the higher volatility.
His advisor then shows him skewness: 0.705 for Fund A and -2.222 for Fund B. Fund B's returns bunch around 20–22% most years, but its distribution has a long left tail — one year of -0.50% dragged its mean down to 16.78%, below where most of its returns sit. That is the negative-skew pattern: the mean below the mode.
The practical reading: Fund B's typical year looks excellent, and its bad years are much worse than its typical year. Fund A's surprises, where they occur, have been on the upside. The workbook's conclusion is that an investor who ignores skewness and kurtosis would "ignore the probability of outliers" in Fund B.
Why NISM asks about it
Chapter 6 (Fees Structure, Fund Performance and Benchmarking) covers skewness at 6.2.4.2, after the normal distribution and before kurtosis, with the Fund A and Fund B example. The first sample question at the end of Chapter 6 asks which risk measure shows "the extent to which a distribution is not symmetrical across the mean" — skewness. Expect definition questions and interpretation of positive versus negative values and of mean versus mode.
Common exam traps
- Skewness is about symmetry; kurtosis is about peakedness and tails. The sample question offers both as options.
- Normal distribution: skewness 0 (and kurtosis 3).
- Positive skew: mean above mode. Negative skew: mean below mode.
- Positive skewness is preferred to negative, although investors would prefer no skew at all.
- A higher mean does not make a fund less risky. Fund B had the higher mean and the worse skewness.
- Excel function: =SKEW(range). Kurtosis uses =KURT(range).
Check yourself
1.Which risk measure is used to ascertain the extent to which a distribution is not symmetrical across the mean?
- a)Standard Deviation
- b)Mean
- c)Skewness
- d)Kurtosis
Show the answer
Answer: (c) Skewness
This is the workbook's own sample question and the stem quotes the definition almost word for word: skewness refers to the extent to which a distribution is not symmetrical across the mean, and arises from outliers above or below the mean. Kurtosis measures peakedness, not symmetry. Standard deviation measures dispersion of returns from the mean, and the mean is itself the centre point, not a risk measure.
Where this is taught
Free preparation for NISM Series XIX-BRelated terms
- Category III AIFThe AIF category for funds running diverse or complex trading strategies with leverage — hedge funds and their kin — and the only category denied tax pass-through status.
- Sharpe ratioReturn earned above the risk-free rate divided by standard deviation — how much reward an investment produced for each unit of total risk its holder had to live with.
- 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.
- 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.
- 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.
- OutliersExtreme returns in a fund's track record, whether highly positive or highly negative — the thing skewness and kurtosis are computed to detect.
- PlatykurticA return distribution with kurtosis below 3, so excess kurtosis is negative: values cluster at consistent frequencies around the mean with no significant deviations.