Interpreting Skew and Kurtosis in Sorted Portfolio Returns

Summary

The author describes sorting investments into ten portfolio buckets using six attributes, including returns, and measuring the attributes at time t before investing at t+1. The proposed comparison is between return distributions on the measurement day and statistics for the actual investment day. The author asks for guidance on interpreting skewness and kurtosis in those tables, but the tables and their numerical statistics are not included in the document, so no distributional conclusions can be drawn from the text alone.

The author adds that the lowest-return bucket on the measurement day reportedly has the highest CAPM alpha, with alpha declining across buckets toward the highest-return group. That observation is explicitly qualified by potentially very large transaction costs, which are not accounted for. The note raises a potentially useful timing and portfolio-sort comparison, but lacks the data needed to assess its statistical significance, robustness, or net investability.

Key ideas

• The portfolios are sorted into ten buckets using six characteristics, including returns.
• Measurements at time t are used to form an investment intended for t+1.
• The author seeks to interpret skewness and kurtosis in return distributions across the buckets.
• The stated CAPM alpha pattern may be materially reduced by transaction costs.
• Without the tables, the distribution shape and significance of the reported pattern cannot be assessed.

Tags

# Interpretation of Skew and Kurtoisis - strategy backtesting


# Interpretation of Skew and Kurtoisis - strategy backtesting












I am working on my dissertation and i would like to provide a nice interpretation of two tables which i will present below.

I have 10 portfolio buckets which i sort on 6 different attributes. One of these attributes is return. I take the measurement at time "t" and I proceed to simulate the investment at "t+1"

The first table represent mean and returns if the investment was to be simulated at time "t". in other words it shows my return distribution on the day i take the measurement. This is presented below:

As u can see bucket bucket 1 has the lowest returns on the day i take the measurement. These increase as i approach bucket 10.

Below i show you the statistics of the same 10 portfolios for the actual investment day. (t+1)

Stats has never been my forte. I am not asking for a full interpretation however a few pointers to get me started would be very useful.

for the curious, not accounting for insanely large transaction costs, bucket 1 generates a CAPM alpha of 29.8% a year. this perfectly decreases at we approach bucket 10.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.