Guys, Is this the right understanding: (a) Statified sampling/Cell matching 1. Starting with index components, match market caps with sector (FI) or market caps with value/growth (EQ) in a 2-axis grid 2. Pick certain representative securities 3. Buy these on the premice that you’ve replicated factor exposure at a lower cost than pure passive indexing (b) Optimization: 1. Match index components in a multi-dimensional grid, against a range of factors, in a way that takes into account the covariance between assets. 2. Pick certain representative securities 3. Buy these on the premice that you’ve achieved a more advanced mimicing of factor exposure at a lower cost than pure passive indexing Is Optimization, (b) the same as a ‘factor model’ for alligning risk exposures along the lines of PVD CF, Sector contrib to Duration, Issuer exposure, Secotr/Quality %…etc? Thanks APP
Stratified sampling: with fixed income, you’re characterizing the portfolio by risk factor - because you want to match the same risk factor exposures as the index. “Risk factors” mean changes to duration, convexity, yield curve twists, spread changes etc. Steps 2 & 3 sound right. The advantage is you’ve mimicked the index’s return and risk profile without having to buy all the bonds.
I’ve been through the books and made some notes below: And you know what? I still have no idea if stratified sampling uses an analogous approach for EQ and FI, and if Optimisation for EQ is like multi-factor model for FI… Can we figure this out? My notes below: For EQ investing: 1. Full replication - Use when there are up to 1000 stocks in Index - All portfolio positions are about the same weight as index - Use for large portfolios, using std basket trades 2. Stratified sampling (cell matching) - Multi-dimensional division of securities - E.g Market Cap /Sector /Value /Growth - Stock goes in cell that best describes it - Mgr selects sample of securities from each cell to reppresents the overall cell, with revised weights for these, representative, securities -The weight revision process (uses the same approach as GIPS carve-outs cash splitting) - UCIT LImits to % of PF in a given security (20%) 3. Optimisation - For smaller, managed accounts - Optimised Risk factor-matching based on a multi-factor model - E.g. market cap / sector / beta and maroeconomic factors e.g. interest rate - Covariance of these factors is taken into account. - Security proportions determined to minimise tracking risk. Optimisation positives - Compares well with stratified sampling approach for smaller portfolios Optimisation negatives. - Risk model likely to be imperfectly specified (and it relies on historic data). - The process maximally exploits risk factor differences of securities, but what if there’s a sampling error? ( Called’Overfitting’ the data) -Periodic trading req’d to maintain risk factor exposure. Hence predicted tracking risk typically understates actual tracking risk. 4. Hybrid approaches: -Fully replicate (for the largest stocks); Stratified for rest -Fully replicate (for the largest stocks); Optimised for rest. For FI Investing 1. Full replication: Same 2. Stratified Sampling: - Division of secutiies into risk factor categories. Simple secletion of securities to use as proxy for all those in the category 3. Multi-factor model (AKA Tracking errror minimisation) - Division of secutiies into risk factor categories. Advanced selection of securities to use as proxy for index, based on multiple factors, and the covariances between them. - Select most important factors to match from: * Duration & Convexity * Key rate Duration * PVD CF * Quality spread duration contribution * Sector &Quality % * Sector duration contribution * Issuer exposure * Cell weight (coupon.Sector/Maturity) [Exposure to MBS call risk/ -ve convexity]
Yes - optimization (from EQ) and multi-factor models (from FI) are the same.
interesting.
which is cheaper?
Stratified sampling, optimization requires computing power and human resources to run the models.
it says in the text book that optimization requires preidoic trading to keep the risk charactersitcs of the porfolio lined up with those of the index being tracked
(can someobdy explain what they mean by risk characteristics?) AND
and why then the predicted tracking risk typically understates actual tracking risk?
THANK YOU