Kurtosis

Standard deviation says how spread out returns are on average. It does not say whether that spread comes from many moderate wobbles or from a calm fund interrupted by the occasional extreme year. Kurtosis looks at that second question.

The workbook describes it as "the degree to which a distribution is more or less 'peaked' than a normal distribution". A peaked distribution indicates outliers with large deviations from the mean. Distributions with fatter tails and higher peaks have high kurtosis, and investors "must be diligent about funds exhibiting return distributions with fatter tails, as it is an indicator of inconsistent performance".

The benchmark is the normal distribution, which the workbook gives a kurtosis of 3. The amount by which a fund's kurtosis exceeds 3 is its excess kurtosis.

The two labels:

Computing it. The workbook uses Excel: =KURT(range).

The workbook's Example 11.2 (same six years of returns as the skewness example):

The workbook's conclusion: Fund A shows negative excess kurtosis, Fund B positive excess kurtosis, so on kurtosis, Fund B is riskier. Standard deviation, skewness and kurtosis all point the same way.

Reading them together. An investor with a high risk appetite might still choose Fund B from mean and standard deviation alone; without skewness and kurtosis, the workbook says, that investor "would ignore the probability of outliers and volatility of expected returns".

Excess kurtosis = Kurtosis - 3        (workbook convention)

Kurtosis > 3  (excess > 0)  -> leptokurtic, fatter tails, riskier
Kurtosis < 3  (excess < 0)  -> platykurtic
Kurtosis = 3               -> normal distribution

Illustrative. Ms Fernandes compares three Category III AIFs on five years of monthly returns. The fund administrator reports kurtosis on the workbook's convention (normal = 3):

Deccan Event-Driven has had the best average return. But a kurtosis of 4.2 means its returns have been either very close to the average or very far from it — the pattern of a fund that makes steady money until a deal breaks. That is the case the workbook's sample question describes: a kurtosis of 4.2 is leptokurtic, implying the presence of outliers and higher risk.

Sahyadri, at 2.4, has had returns spread consistently around its mean with no significant extreme deviations.

Ms Fernandes does not reject Deccan outright. She sizes her allocation to it smaller, which is the kind of decision the workbook says a fuller set of risk measures should drive.

Chapter 6 (Fees Structure, Fund Performance and Benchmarking) covers kurtosis at 6.2.4.2 immediately after skewness, with the Fund A and Fund B example, and one of the chapter's sample questions asks for the correct inference from a kurtosis of 4.2. Expect questions on the normal-distribution value of 3, on leptokurtic versus platykurtic, on computing excess kurtosis, and on what fat tails mean for a Category III AIF investor.

• Normal distribution: kurtosis 3, excess kurtosis 0. Skewness of a normal distribution is 0 — do not mix the two.
• Leptokurtic = above 3 = riskier. Platykurtic = below 3. "Lepto" is the fat-tailed, outlier-prone one.
• Excess kurtosis = kurtosis − 3. A kurtosis of 4.2 is an excess of +1.2, not −0.8.
• A check on the workbook's arithmetic. The figures 1.162 and 5.034 in Example 11.2 are exactly what the sample excess-kurtosis formula gives for those returns — the formula that Excel's =KURT uses, which already subtracts 3. So on a strict reading the funds' excess kurtosis would be 1.162 and 5.034, making both leptokurtic, rather than −1.838 and 2.034. The comparison (Fund B riskier) does not change. For the exam, apply the workbook's rule: kurtosis above 3 is leptokurtic, and subtract 3 for excess.
• Kurtosis is about tails and peakedness, not symmetry. Symmetry is skewness.
• Do not analyse any single measure in isolation — the workbook's explicit conclusion.