On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important

The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to subsequent lows. Motivated by the fact that this issue is of paramount concern to conservative investors, we dispense with the classical variance as the risk metric and work with drawdown and mean return as the risk-reward pair. In this setting, the main results in this paper address the so-called "efficiency" of linear time-invariant (LTI) investment feedback strategies which correspond to Markowitz-style schemes in the finance literature. Our analysis begins with the following principle which is widely used in finance: Given two investment opportunities, if one of them has higher risk and lower return, it will be deemed to be inefficient or strictly dominated and generally rejected in the marketplace. In this framework, with risk-reward pair as described above, our main result is that classical Markowitz-style strategies are inefficient. To establish this, we use a new investment strategy which involves a time-varying linear feedback block K(k), called the drawdown modulator. Using this instead of the original LTI feedback block K in the Markowitz scheme, the desired domination is obtained. As a bonus, it is also seen that the modulator assures a worst-case level of drawdown protection with probability one.Comment: This paper has been published in Proceedings of 56th IEEE Conference on Decision and Control (CDC) 201

Nova student portfolio: enhancing performance through different investment styles

This paper tried to build a strategy that beats the S&P 500using its constituents, when incorporating moving average crossover on sectors as well as using value and growth factors to pick stocks, using weekly rebalancing. Moreover, this strategy was implemented in a portfolio composed by40% Equity and 60% Bonds and tested with transaction costs(even though its realistic as the NSP does not pay fees). Finally, the results show that a long-portfolio of 40 stocks on S&P 500 equities, with a weekly holding period, presents only satisfactory results for certain types of investors

Momentum, Value and Quality Investing in European Markets

This thesis examines the risk-adjusted performance of momentum, value and quality strategies as well as strategies that combine the selected strategies using different methods. The thesis aims to investigate if the previously documented anomalies present abnormal returns in the European market, and if the performance and abnormal returns can be improved by combining the individual factors together. Earlier research on momentum, value and quality is abundant, but research combining the three factors into one using integrating, mixing and average rank methods is limited, and has provided mixed results. Majority of literature supports the view that integrating method of multifactor portfolio construction is the most efficient one, while alternate views argue that the results of the integrating method are not robust due to low diversification or data-snooping, or that the mixing method is superior due to lower transaction costs. A third alternative of average ranks is considered which could potentially have more robust results due to better diversification as well as lower transaction costs, as has been evidenced by previous literature. This thesis adds to the existing research by researching the gross profitability premium together with momentum and value, while also expanding the existing literature of momentum, value and quality combinations by expanding the time and data coverage to the European level. First, the results are provided for each individual factor independently. In the second stage, the portfolios are sorted by size to investigate if any of the results are due to the size effect. In the third stage, the factors are combined pairwise by the three methods, and in the last stage, the three factors are combined using the three methods. The granular approach allows to examine if the three factors benefit from each other, and to what degree, and if the results are due to size effect. Previous literature has shown that factor portfolio abnormal returns are often greater among small firms but exist in other size groups as well. Results show that momentum, value and quality strategies can generate abnormal returns, and beat the market with risk-adjusted performance. The individual single-factor strategies can be enhanced by incorporating other factors into the strategy either by integrating, mixing, or averaging the factors. The risk-adjusted performance is improved with even the simple mixing method, whereas the results can be improved even further by incorporating more elaborate combination methods depending on the investment objective. The different methods come with their own benefits and caveats, which are further discussed in the thesis. The multifactor portfolios have characteristics similar to those of single-factor portfolios, but generally have better risk-adjusted performance than the single-factor counterparts.Tutkielman tarkoituksena on tutkia momentum, arvo- ja laatustrategioiden riskikorjattua suorituskykyä, sekä edellä mainittuja strategioita yhdistelevien monifaktoristrategioiden riskikorjattua suorituskykyä. Tutkielman tavoitteena on tutkia, mikäli nämä strategiat tuottavat epänormaaleja tuottoja Euroopan rahoitusmarkkinoilla, ja mikäli riskikorjattua suorituskykyä ja epänormaaleja tuottoja voidaan parantaa faktoreita yhdistämällä. Momentum, arvo- ja laatu ovat kattavasti tutkittuja aiheita, mutta tutkimustieto niiden yhdistämisestä eri tavoin on rajattua, ja tulokset ovat olleet vaihtelevia. Suurin osa aiemmasta kirjallisuudesta tukee näkökantaa siitä, että integroiva menetelmä on tehokkain tapa yhdistää kaksi tai useampaa faktoria monifaktoriportfolioksi, mutta vastaväitteiden mukaan tapa ei tuota kestäviä tuloksia matalan hajautustason tai datalouhinnan vuoksi. Toisen näkökannan mukaan portfolioita sekoittava lähestymistapa on tehokkain tapa hajautuksen sekä matalien kaupankäyntikulujen takia. Tutkielmassa tutkitaan myös kolmatta lähestymistapaa, faktorien keskiarvoistamista, joka voi johtaa kestävämpiin tuloksiin hyvän hajautuksen ja matalalampien kaupankäyntikulujen takia, kuten aiempi tutkimus on osoittanut. Tämä tutkielma lisää kirjallisuuden kattavuutta tutkimalla momentum- ja arvopreemioita yhdessä bruttotuottavuus- eli laatupreemion kanssa samalla lisäten kirjallisuuden maantieteellistä kattavuutta Euroopan tasolle sekä lisäten ajallista kattavuutta. Ensimmäisessä vaiheessa jokaista faktoria tutkitaan itsenäisesti. Toisessa vaiheessa faktoriportfoliot järjestetään koon mukaan ja arvioidaan johtuvatko tulokset otoksen yritysten pienestä koosta. Kolmannessa vaiheessa faktorit yhdistetään pareittain edellä mainituilla tavoilla. Seuraavassa vaiheessa kaikki kolme faktoria yhdistetään edellä mainituilla tavoilla, ja viimeisessä vaiheessa arvioidaan johtuvatko tulokset yritysten pienestä koosta. Vaiheittaisen lähestymistavan avulla voidaan tutkia, hyötyvätkö faktorit toisistaan, missä määrin, ja johtuvatko tulokset kokoilmiöstä. Aiempi tutkimus on osoittanut, että faktoriportfolioiden epänormaalit tuotot ovat suurempia pienempien yritysten keskuudessa, mutta epänormaaleja tuottoja on saavutettavissa myös muissa kokoluokissa. Tulokset osoittavat, että momentum-, arvo- ja laatustrategiat voivat tuottaa epänormaaleja tuottoja, ja suoriutua markkinaa paremmin riskikorjatun suorituskyvyn perusteella. Yksittäisiä faktoristrategioita voidaan parantaa sisällyttämällä strategiaan muita faktoreita joko integroimalla, sekoittamalla tai keskiarvoistamalla faktoreita. Riskikorjattua suorituskykyä voi parantaa myös yksinkertaisimmalla sekoitusmenetelmällä, ja tuloksia voidaan parantaa muilla menetelmillä sijoitustavoitteen mukaan. Eri menetelmillä on omat hyötynsä ja haittansa, jotka ovat tutkielman keskustelun aiheena. Monifaktoriportfoliot vastaavat ominaisuuksiltaan yksifaktoriportfolioita, mutta niillä on pääsääntöisesti parempi riskikorjattu suorituskyky

Time-series and cross-sectional price momentum: Applying the Dual Momentum strategy from a Norwegian perspective

Master's thesis in Business Administration: Executive MBATime-series and cross-sectional price momentum have been observed in the majority of asset classes around the globe. This thesis investigates and replicates the Dual Momentum strategy created by Antonacci (2014) from a Norwegian perspective. The Dual Momentum strategy combines both time-series and cross-sectional price momentum and applies the price momentum to indexes. Using indexes simplifies and reduces the transaction cost compared to momentum strategies that involve large stock portfolios. The Dual Momentum strategy uses the current price and the historical price less the risk-free rate to determine if an asset’s momentum is positive over the last twelve months. The asset with the highest momentum is held, unless the momentum is negative, then high-quality bonds are held until the momentum returns to positive. In this thesis OBX and ST5X serve as the Norwegian assets, and 39 different foreign indexes have been tested as the third asset of the Dual Momentum strategy. The results show impressive risk-adjusted returns, lower standard deviations, higher sharpe ratio and lower maximum drawdowns than holding OBX as a passive index investment in the same period. The vast majority of the Dual Momentum portfolios return significant positive alphas after the CAPM model, Fama-French and Carhart factors are applied in regression analysis. The thesis validates the Dual Momentum strategy from the Norwegian perspective in the tested sample period of 21 years. The strategy produces higher risk-adjusted returns in the sample period than the benchmark, and the findings are in line with the current price momentum literature

On Solving Robust Log-Optimal Portfolio: A Supporting Hyperplane Approximation Approach

A {log-optimal} portfolio is any portfolio that maximizes the expected logarithmic growth (ELG) of an investor's wealth. This maximization problem typically assumes that the information of the true distribution of returns is known to the trader in advance. However, in practice, the return distributions are indeed {ambiguous}; i.e., the true distribution is unknown to the trader or it is partially known at best. To this end, a {distributional robust log-optimal portfolio problem} formulation arises naturally. While the problem formulation takes into account the ambiguity on return distributions, the problem needs not to be tractable in general. To address this, in this paper, we propose a {supporting hyperplane approximation} approach that allows us to reformulate a class of distributional robust log-optimal portfolio problems into a linear program, which can be solved very efficiently. Our framework is flexible enough to allow {transaction costs}, {leverage and shorting}, {survival trades}, and {diversification considerations}. In addition, given an acceptable approximation error, an efficient algorithm for rapidly calculating the optimal number of hyperplanes is provided. Some empirical studies using historical stock price data are also provided to support our theory.Comment: submitted for possible publicatio

Systematic investing: momentum and volatility as indicator for market timing

In Financial Markets, academic questions revolve around the assumption that asset prices reflect all available information and exhibit a random walk. Direct implications of this hypotheses are that no market participant can consistently earn excess returns on a risk-adjusted basis, except by luck or by using non-public information. This thesis examines whether the assumption that historical data cannot be enough to consistently outperform the market holds. Based on the evidence that asset returns are negatively skewed with few fat-tails, the systematic multi-asset strategy presented in this thesis more than triples the risk-reward compared to the traditional 60/40 portfolio by incorporating trend-following and market risk assessments

Large dynamic covariance matrices: Enhancements based on intraday data

Multivariate GARCH models do not perform well in large dimensions due to the so-called curse of dimensionality. The recent DCC-NL model of Engle et al. (2019) is able to overcome this curse via nonlinear shrinkage estimation of the unconditional correlation matrix. In this paper, we show how performance can be increased further by using open/high/low/close (OHLC) price data instead of simply using daily returns. A key innovation, for the improved modeling of not only dynamic variances but also of dynamic correlations, is the concept of a regularized return, obtained from a volatility proxy in conjunction with a smoothed sign of the observed return

Strategic asset selection taxonomy : fund of hedge funds

Includes bibliographical references (leaves 68-70).This thesis develops a logical methodology to be used to assess the hedge fund managers' return time series in comparison with their peers. This enables Fund of Hedge Funds portfolio manager to identify those with required factors to be included in a portfolio. The models that had been used as the industry standard for some time are derived on the assumption of normal distribution. Hence they use only mean and standard deviation to explain all data phenomenal attributes of time series. This study project uses higher order moments and some performance measures to rank order feasible portfolios of different hedge fund strategies based on their calculated metrics. Then determine the significance of t-Statistics, thus to observe the likelihood of achieving a particular return level relative to the downside associated with that target return and also on the behavioral hypothesis that investors prefer more to less. The study proposes and examines an alternative performance measures to facilitate the investment decision making. An indication of how this may be applied across a broad range of problems in hedge funds analysis. Some performance measures capture the higher order moments of the return distributions. This method makes intuitive sense since one of the key mandates of the hedge funds is to seek to capture most upside while protecting against downside