Index tracking For Mean variance investors Overview Index tracking
Introduction Methodology 1 Application ASX50 data set Real time/out of sample analysis Methodology 2 Limitations and extensions Introduction Last lecture we saw that the mean-variance portfolio optimisation often
resulted in zero weights for many stocks.
This may be unreasonable for some investors who may still want some exposure to
most (or all stocks) in the index. To overcome this, we could add additional constraints into our optimiser
eg BHP weight > 0.02. This week we consider another passive ESG strategy that can overcome this
potential limitation : Index tracking Introduction: ESG indices Thousands of ESG indices are now available. The MSCI for example has over 1500 ESG indices. There are many funds (which may or may not be exchange traded) that have
mandates to track any of the ESG indices that are available. This is a cost-effective way for investors to obtain a portfolio that meets various
ESG objectives. A fund could also for example combine an ETF that tracks an ESG index, with other
more traditional exposures (government bonds, gold, property etc). Introduction: ESG indices Introduction: ESG indices The STOXX Europe 600 ESG-X index is based on the STOXX Europe600 index, one of
Europe's key benchmarks. Standardized ESG exclusion screens applied Excludes companies that are non-compliant with Global Compact Principles: involved in controversial weapons (anti-personnel mines, biological and chemical weapons, cluster weapons,
depleted uranium, nuclear weapons and white phosphorus weapons);
tobacco producers and
either derive revenues from thermal coal extraction or exploration, or, have power generation
capacity that uses thermal coal OMX Stockholm 30 ESG Responsible Index (OMXS30ESG)
ESG responsible version of the OMX Stockholm 30 Index, which is the leading share index
on Nasdaq Stockholm.
ESG index applies a systematic criteria-based ESG screening where securities that fail
the criteria are excluded. Introduction: ESG index futures Futures written against the STOXX Europe 600 ESG-X index and the
OMSX30ESG index are now exchange traded Futures can be used for hedging and speculative purposes This should also add liquidity to the underlying index Speculators can obtain significant leverage ESG portfolios can better manage risk Methodology
We will consider the same data set as last week. Top 50 ASX listed stocks based on market capitalisation. Our objective will be to track the ASX50 index subject to ESG constraints. The file “Data.xlsx” is the same as last week. Contains the daily prices and continuously compounded returns on all stocks plus
the ASX200 and ASX50.
Our data set will commence July 4, 2019 and end June 10, 2021. Only two of the 50 stocks do not have data over the entire sample period: Magellan
Global Fund (MGOC) and TPG Telecom (TPG).
We will use a beta estimate to infer their stock returns based on the ASX200
(highlighted yellow in the spreadsheet).
, ,s t s m tr Beta r Methodology We base our methodology on
Andersson, Mats, Patrick Bolton, and Frédéric Samama. "Hedging climate
risk." Financial Analysts Journal 72.3 (2016): 13-32. They employ a factor approach to estimate the variance-covariance matrix Factor based approaches (including principle components) may be useful when the
number of assets is large >200. We will estimate the variance-covariance matrix directly (like last week) Methodology 1 The goal is to minimize the tracking error between the benchmark portfolio
and the ESG or “green” portfolio.
Tracking error is the divergence between the price behavior of a position or
portfolio and the price behavior of a benchmark. Can be viewed as an indicator of how actively a fund is managed and its risk level. Defined as the standard deviation of the difference in the returns between the
benchmark and the green portfolio. Methodology 1 If only seek to minimise in large negative values for
We can include >1 ESG constraint − , this will result Min TE sd( ) ' subject to Portfolio CO2 150T/$1M(USD)in revenue where sd is thestandard deviation is the return on thegreen portfolio is the return on the benchmark portfolio
is a 1vector of green g b g b g b g b g R R x x x x R R x N
weights, where N is the no of assets
is a 1vector of benchmark weights is the variance covariance matrix bx N N N Methodology 1 We seek to evaluate the performance of the green portfolio from July 1, 2020
to June 10, 2021 in real time. We will adopt a rolling window approach Starting June 30, 2020 estimate the daily covariance matrix using the last 252
trading days of returns (July 4, 2019 to June 30, 2020) Minimise the TE and set the portfolio weights for the coming day (July 1, 2020). At the end of the day, re-estimate the covariance matrix using the last 252 trading
days (July 5, 2019 to July 1, 2020).
Minimise the TE and re-balance the portfolio, setting the weight for the next day (July 2,
2020). This process of daily re-balancing occurs until the last day in the data set (June 10,
2021). Methodology 1 The benchmark portfolio weights will be equal to their market cap weights on
June 11, 2020. These weights will be constant over the entire period.
Ideally, we would set these weights equal to the actual weights for each day.
Like last week, we will set to zero the weights on the 10 stocks that do not
report C02.
Acts like a negative screen (removing firms that don’t take climate change
seriously). This will add tracking error, even before we start the optimization Methodology 1: Spreadsheet Market weights input into cells Green weights initially set to arbitrary
values say 1/50 Diff weights = Green weight-Market
weight Formula for the sum of the green
weights C02/$1M from last week Red highlights have weights at zero in
optimiser Co2 contribution: formula C02*weight Filename: Index tracking.xlsm Methodology 1: Spreadsheet CO2 contribution mkt = mkt weight * C02 CO2 mkt portfolio (sum that excludes red
highlights). This sets the upper limit that we
seek to beat. Tracking error: formula (previous slide) Cov matrix: Formula based on excess
returns matrix(same as last week) Excess returns matrix input: 252 days of
returns (D564:BA815), plus average returns
vector (D817:BA817)
Methodology 1: Spreadsheet For the code to work, we
need to have the following
details in the Name manager Methodology 1: Spreadsheet Note that the stocks with no
CO2 reporting have their
weights set to zero. We can now solve for the
green weights given the
covariance matrix. We now seek to do this with a
rolling window each day. To do
this we will use a VBA program Methodology 1: VBA code Methodology 1: VBA code Results matrix now contains in
each row:
tracking error portfolio returns weight vector
for each day Methodology 1: Results Average tracking error 6.07%. Green portfolio has outperformed the index i) Higher total return (24.4% v 20.3%) – difference is significant at 5% ii) Higher daily Sharpe ratio (0.1095 v 0.0907) iii) Highly correlated with index (0.9928) Methodology 1: In class We now seek to remove an additional 5 stocks from the portfolio. Re-perform the analysis after removing BHP, CSL, NAB, RIO, SYD What effect does this have on the asset allocation and tracking
error? Now reduce the total CO2 from 150 to 135 and re-perform the
analysis. Are the results consistent with your expectations?
Methodology 2 Min CO2/$1M(USD) in revenue subject to TE 7.5% where TE sd ' g b g b g b R R x x x x We will see that the TE is now binding and we can achieve a lower CO2 footprint Methodology 2: VBA code We change the cell we seek to minimise - CO2 of the green portfolio Filename: Index tracking 2.xlsm Methodology 2: VBA code Formulas/Name Manager 1) Added the name: Carbon (cell D505) 2) Change “Results” to have another column - DC242 changed to DD242 Include the minimised carbon in the range “Results”
- column DD in spreadsheet Methodology 2: Results 40.0 60.0 80.0 100.0 120.0 140.0 160.0 CO2/$1M USD revenue Tracking error is now on the boundary of 7.5% (compared with average of 6.1% before).
CO2 is much lower than before (always at upper bound of 150). Returns and their variability similar to before.
This approach however only allows you to consider 1 ESG factor, the previous approach enables >1 ESG factor Methodology 2: In class We now seek to examine the impact of changing the maximum
tracking error
Re-perform the analysis by Increasing/(decreasing) tracking error to 10% (5%) What effect do these changes have on the asset allocation, returns
and CO2 footprint? Limitations & extensions Same limitations as last lecture Consider impact of re-balancing at a lower frequency (eg weekly). Likely to increase tracking error. Use an industry average (median) for the stocks without CO2 reporting.
Likely to reduce tracking error but may materially mis-represent the CO2 footprint
of the portfolio. Update benchmark portfolio weights each day (as opposed to the fixed
weights as at June 11, 2021).
More computationally intensive but likely to reduce tracking error Rather than track a regular index, this approach can also be used to track any
of the growing number of ESG indices available. This would enable you to
track an ESG index but tailor your portfolio to impose some additional ESG
constraints.
Summary The last two lectures have illustrated two passive ESG strategies Efficient frontier estimation with and without ESG
Index tracking with ESG Results have tentatively shown that the incorporation of ESG into
standard portfolio allocation decisions may not necessarily come at a
cost to the investor and may improve outcomes 51作业君版权所有
