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“Past performance is no guarantee of future results”, but helps a bit

ogonzalez

asset management

Playing with Prophet on Financial Time Series (Again)

rcobo

asset management

Shift or Stick? Should we really ‘sell in May’?

jsanchezalmaraz

asset management

What to expect when you are the SPX

mrivera

asset management

K-Means in investment solutions: fact or fiction

T. Fuertes

asset management

How to… use bootstrapping in Portfolio Management

psanchezcri

asset management

Playing with Prophet on Financial Time Series

rcobo

asset management

Dual Momentum Analysis

J. González

asset management

Random forest: many is better than one

xristica

asset management

Using Multidimensional Scaling on financial time series

rcobo

asset management

Comparing ETF Sector Exposure Using Chord Diagrams

rcobo

asset management

Euro Stoxx Strategy with Machine Learning

fjrodriguez2

asset management

Hierarchical clustering, using it to invest

T. Fuertes

asset management

Lasso applied in Portfolio Management

psanchezcri

asset management

Markov Switching Regimes say… bear or bullish?

mplanaslasa

asset management

Exploring Extreme Asset Returns

rcobo

asset management

Playing around with future contracts

J. González

asset management

BETA: Upside Downside

j3

asset management

Approach to Dividend Adjustment Factor Calculation

J. González

asset management

Are Low-Volatility Stocks Expensive?

jsanchezalmaraz

asset management

Predict returns using historical patterns

fjrodriguez2

asset management

Dream team: Combining classifiers

xristica

asset management

Stock classification with ISOMAP

j3

asset management

Could the Stochastic Oscillator be a good way to earn money?

T. Fuertes

asset management

Correlation and Cointegration

j3

asset management

Momentum premium factor (II): Dual momentum

J. González

asset management

‘Sell in May and go away’…

jsanchezalmaraz

asset management

S&P 500 y Relative Strength Index II

Tech

asset management

Performance and correlated assets

T. Fuertes

asset management

Reproducing the S&P500 by clustering

fuzzyperson

asset management

Size Effect Anomaly

T. Fuertes

asset management

Predicting Gold using Currencies

libesa

asset management

Inverse ETFs versus short selling: a misleading equivalence

J. González

asset management

S&P 500 y Relative Strength Index

Tech

asset management

Seasonality systems

J. González

asset management

Una aproximación Risk Parity

mplanaslasa

asset management

Using Decomposition to Improve Time Series Prediction

libesa

asset management

Las cadenas de Markov

j3

asset management

Momentum premium factor sobre S&P 500

J. González

asset management

Fractales y series financieras II

Tech

asset management

El gestor vago o inteligente…

jsanchezalmaraz

asset management

¿Por qué usar rendimientos logarítmicos?

jsanchezalmaraz

asset management

Fuzzy Logic

fuzzyperson

asset management

El filtro de Kalman

mplanaslasa

asset management

Fractales y series financieras

Tech

asset management

Volatility of volatility. A new premium factor?

J. González

asset management

Dynamic Markowitz Efficient Frontier

plopezcasado

28/07/2015

1
Dynamic Markowitz Efficient Frontier

Markowitz Model is a famous method in the Portfolio Investment Theory. This model provides efficient portfolios, (i.e. portfolios with the highest profitability and lowest risk possible) through mathematical programming.

The set of portfolios composes the efficient frontier. The strategy is based on quadratic optimisation, therefore minimizing the estimated risk and negative return. We often calculate the efficient frontier by using a fixed temporal window based on historical data. The real market doesn’t use big windows of data to calculate the mean-variance portfolio, but the portfolio is updated more frecquently; every day, for example.

It’s interesting to analyse the evolution of the frontier based on the timeline. Here, we have included the results of a dynamic frontier in a static representation with two alternatives: expansive method and six months rolling method.

Expansive Method

We consider a three-year window of value returns of the companies that compose the index IBEX-35 between 02/01/2012 and 02/01/2015. The first frontier was calculated using 120 observations. The next one has 121, and then we continue adding daily returns. The final frontier will have every historic dataset observation.

option1

Each color represents the year of the last observation added. That provides 261 lines of each color, except 2012 and 2015, as we only have parts of these years in the dataset. The first thing we notice is the extreme risk values at 2014  (all green lines). Furthermore, incorporating new observations into the dataset results in decreasing return.

Six Month Rolling Method

In finance, it’s very common to analyse a series’ evolution by choosing a window which is moved along the time. This method is knowed as Rolling, and it consists of performing a progressive scanning of the serie. As we can imagine, the window’s width will have an influence on the results. Below, we chose a six-month window (126 days, to be exact).

Option2When we consider a fixed period, without accumulating old observations, risk and renturn of the portfolios move in different way. In 2012 the risk increases in comparison to other years.  Specifically, it’s over 0.3%, whereas in 2013 and  2014 it falls bellow 0.1%. Return is higher in most of 2013, despite parts where risk shot up.

So, dynamic efficient frontier can be the answer to see at a glance the effect of adding new observations with a fixed initial date, or in a rolling period. However, as conclusions can be very different according to the method and parameters we choose, care must be taken with this approach.

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Your post is very interesting!

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