Platykurtic

Kurtosis measures how peaked a return distribution is. A normal distribution has a kurtosis of 3, and that is the reference point for everything else.

A platykurtic distribution has kurtosis below 3. Subtract the 3 and you get a negative number, which the workbook calls negative excess kurtosis.

What does that look like in a fund? The returns come in at consistent frequencies around the mean, with no significant deviations. Nothing bunches up in one spot and nothing flies off to the sides.

Its opposite is leptokurtic, with kurtosis above 3. There the values either sit very close to the mean or land a long way from it. That is a high peak with fat tails.

For an investor the direction is clear. The workbook says a distribution with kurtosis above 3 is riskier, and that fat tails are a sign of inconsistent performance.

So a platykurtic record is the quieter one. Flat, even, and short of drama on both sides.

Section 9.6 defines the three cases against the same benchmark.

How it is computed. The workbook computes kurtosis in Microsoft Excel with =KURT(range), where range is the range of returns earned by a fund over any number of periods. Excess kurtosis is then the excess of the kurtosis value over 3.

The workbook's worked pair (Example 9.8.2). Six years of returns:

So Fund A is platykurtic and Fund B is leptokurtic. The workbook records this as Fund A exhibiting negative kurtosis and Fund B positive kurtosis — meaning negative and positive excess kurtosis. On comparison of risk based on kurtosis, Fund B is riskier than Fund A.

Why the shape matters and not just the spread. Kurtosis measures the level of deviations of data values from their mean. Distributions with fatter tails and higher peaks have high kurtosis, and investors must be diligent about funds whose return distributions have fat tails, because that indicates inconsistent performance. A platykurtic fund is the absence of that signal.

And the workbook's warning about reading it alone. On analysing Fund A and Fund B, standard deviation, skewness and kurtosis all agree that Fund B is riskier. But sophisticated investors should not analyse all the risk measures in isolation. An investor with a high risk appetite might still invest in Fund B after looking only at mean and standard deviation — and would thereby ignore the probability of outliers and the volatility of expected returns.

Narmada Market Neutral Fund, a Category III AIF, reports eight quarters of net returns. Its stated strategy is market-neutral, so a quiet distribution is the promise, not an accident.

Mean = 2.20%. The returns run from 1.8% to 2.6% and are spread fairly evenly across that band. No quarter bunches at the mean and none escapes the band. Run =KURT() on the range and the result is comfortably below 3, so the excess kurtosis is negative and the distribution is platykurtic.

Annualised, roughly 8.8%, delivered in eight almost identical instalments.

Now the same mean, delivered leptokurtically. Vindhya Opportunities Fund also averages 2.20% a quarter:

Six quarters sit almost exactly on the mean; two are far away. That is the leptokurtic signature the workbook describes — values either around the mean or substantially deviating from it — and =KURT() on this range returns a figure well above 3.

What the difference costs. On a Rs 20 crore commitment the two funds end the two years in much the same place. They do not feel the same on the way. Narmada's worst quarter takes Rs 20 crore to Rs 20.36 crore. Vindhya's worst quarter takes it to Rs 18.60 crore — a Rs 1.8 crore hole, at a moment nobody forecast.

An investor who has to report quarterly, or who might need to exit, cares a great deal about which of the two produced the 8.8%. That is the whole reason kurtosis is computed in addition to standard deviation.

One caveat on the arithmetic. The workbook itself notes that AIFs do not necessarily follow a normal distribution, and it computes these measures on five or six observations. Eight quarters shows the shape clearly enough to teach it; it is not a statistically settled result.

Chapter 9 (Fee Structure and Fund Performance), section 9.6, defines Platykurtic distributions in the sentence immediately after Leptokurtic, and Example 9.8.2 computes both for Fund A and Fund B.

The question is almost always the definition or the threshold: a distribution with kurtosis below 3, or excess kurtosis less than zero, is platykurtic. Expect it paired with leptokurtic in the same question, and expect the normal distribution's kurtosis of 3 as the anchor. The workbook's own figures — Fund A at 1.162 and Fund B at 5.034 — are ready-made for a question asking which fund is riskier on kurtosis. The answer is Fund B, and the reason is fat tails indicating inconsistent performance.

• Platykurtic is below 3; leptokurtic is above 3. The names are the easiest thing in this section to reverse.
• Kurtosis of 3 is normal, not zero. Excess kurtosis is zero for a normal distribution. Mixing up kurtosis and excess kurtosis shifts every answer by 3.
• The workbook calls Fund A's kurtosis negative. Its kurtosis is 1.162, which is positive; the excess kurtosis is −1.838. Read the workbook's phrasing as meaning negative excess kurtosis.
• Platykurtic means no significant deviations, not low returns. It is a statement about shape, not about level.
• Kurtosis is not standard deviation. A fund can have a modest standard deviation and still be leptokurtic, because a few extreme values with many clustered ones can leave the overall spread looking tame.
• Kurtosis says nothing about direction. That is skewness. A platykurtic distribution can still be skewed.
• AIFs do not necessarily follow a normal distribution. The workbook says so before introducing skewness and kurtosis, so the kurtosis-of-3 benchmark is a reference point rather than a description of an AIF.