Some stylized facts of Russian private pension funds

Didenko AlexanderInternational Financial Laboratory

Alexander.didenko@gmail.com

Questions

• What funds are efficient?• What metrics to use?• Is there any persistence?• Do they inform customers about risks?• Do they have behavioral biases?

Dataset and methods

• 30 quarters * 30 private pension funds• IIIQ’ 05 – IVQ’ 12• Data Envelopment Analysis • Malmquist productivity index• T- and KS-tests• Granger causality

DEA - conceptual model

Input 1

Input 2

Input N

Production Plans

Output 1

Output 1

Output 1

Data envelopment analysis

• We have j DMUs• Which use v inputs x• To produce u outputs y• DEA-efficiency is

defined as a ratio of a weighted sum of outputs to a weighted sum of inputs

Example from Coopers et al.

Malmquist index

• Decomposition of dynamic DEA to three components:– technical efficiency change on the best practice

technologies – change in scale efficiency– technical change measured as a shift in the

benchmark technology – which sum to total change

DEA – general model for funds

Financial Capital

Risk

Human Capital

Pension Funds

Return

Market Share

DEA – our specificaion

CVaR

E+R Ratio

Pension Funds

Active return

NAV Share

Diversification

CVaR

• Wuertz, Chalabi, Chen, Ellis (2009);

• RUPAI, RUPCI, RGBI• Alpha=0.05• Weekly data• Average quarterly CVaR

Diversification

• There are plenty of D. measures• We use that of Goetzmann, Kumar, 2008

H1. Funds convey useful info in names

• “professionally-looking” terms to indicate attitude to risk– “Balanced”– “Aggressive”,– etc.

• do funds really inform potential contributors about riskiness?• we classified funds by 5 categories of riskiness based on

names• affinity between CVaRs distribution of 5 classes• affinity of random subsamples inside classes• two-sample Kolmogorov-Smirnov and Student’s t tests

Affinity of CVaR distributions

• Classes 1, 2, 3 are way more homogeneous than any other class or total sample

• Classes 1 and 3 are very close• Class 4 is similar to class 2 and class 3• Only class 5 is REALLY different:– Distinctive both by T and KS measures– Homogeneous (after many resamplings)

H1. Busted/plausible?

BUSTED!

H2. Are funds prone to herding?

• We have information about aggregated portfolio structure

• We can test for– Correlation – Granger causation

• in changes of portfolio shares• Between funds and between quartiles of

capitalization/efficiency

Granger causality: equities

Sum of causation in eq.chng by fund

Sum of causation by cap quartile

We tested the same for:

• Malmquist efficiency quartiles• All 4 submeasures– No result

• Matrix of granger causation for randomly generated matrices with same proportions, means, sd’s– Results are similar to real granger-causation

matrices

H2. Herding/!Herding?

PLAUSIBLE

What specification to use?

• DRS, VRS, IRS, CRS, FDH? • Input/output/two-way?• We want to have some predictable measure• to have good logit-regression, we need sample

with some funds efficient and some – not• too much “efficiency” => bad

Dea

Malmquist productivity

• Same questions about specification• For our results be comparable • we have to use the same set of specifications

for DEA and Malmquist productivity

Window dressing?

Wow!

Dropping expense+reward ratio

H2. Funds do not window-dress?

PLAUSIBLE