Portfolio optimization in a regime-switching market with derivatives

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The optimal asset allocation for South African real return investors

This research aims to establish the optimal asset allocations for targeting specific real returns over short, medium and long-term investment horizons. The joint returns are modelled with data-centric methods that are empirical and non-parametric in nature, and are able to capture the dependencies of returns over time. The asset classes that are considered are South African (SA) equities, SA bonds, SA cash, SA property, global equities, global bonds, global cash, and global property. The returns of each asset class are modelled, each class with its own empirical distribution based on monthly returns from 1972 to 2017. The monthly returns are grouped in a block of rolling periods of varying block lengths in order to attempt to capture dependencies across time. These blocks of data are resampled in order to simulate the distributions of returns of portfolios with their own unique empirical distribution. The optimal portfolios are derived using a genetic algorithm, showcasing how these extremely versatile optimisation tools can be used in combination with resampling methods to find the optimal portfolio for virtually any criterion. A comparison is also made to the traditional mean-variance optimal portfolios, yielding an estimate of the bias in mean-variance optimisation’s (MVO) optimal weights. It is investigated how these optimal portfolios are influenced by the choice of risk criterion and investment horizon. The effect of the most important and consequential nuisance parameter in this research’s model, the block length, is discussed. The relationships established between the characteristics of optimal portfolios and investment horizon and risk criterion and the comparisons with classic MVO should be of interest to investors and investment professionals alike. Economic and market regimes are “identified” on the basis of economic and market data, consequently the resampling probabilities will be unequal. The optimal weights conditional on regimes are derived. Both static and changing regimes are considered. Lastly, an out-of-sample backtest of the performance of the optimal portfolios conditional on the regime across time at six month intervals is conducted from 1983 to 2017. It shows that out of the three block lengths tested for a single investment horizon of 36 months, a block length of 24 months yielded the best overall risk-adjusted performance, on average. Conditioning for regimes is shown to generally outperform the unconditional approach. The improvements are marginal and further research is recommended to investigate the performance for longer investment horizons and other values of the two tuning parameters, block length and tactical pressure. The higher level aim of this work is to present a broad sense of how data-driven nonparametric methods can be used in conjunction with metaheuristic procedures. The objective of combining these techniques is to find optimal portfolios under very general conditions and with very few assumptions regarding the underlying distributions

Representative agent earnings momentum models: the impact of sequences of earnings surprises on stock market returns under the influence of the Law of Small Numbers and the Gambler's Fallacy

This thesis examines the response of a representative agent investor to sequences (streaks) of quarterly earnings surprises over a period of twelve quarters using the United States S&P500 constituent companies sample frame in the years 1991 to 2006. This examination follows the predictive performance of the representative agent model of Rabin (2002b) [Inference by believers in the law of small numbers. The Quarterly Journal of Economics. 117(3).p.775 816] and Barberis, Shleifer, and Vishny (1998) [A model of investor sentiment. Journal of Financial Economics. 49. p.307 343] for an investor who might be under the influence of the law of small numbers, or another closely related cognitive bias known as the gambler s fallacy. Chapters 4 and 5 present two related empirical studies on this broad theme. In chapter 4, for successive sequences of annualised quarterly earnings changes over a twelve-quarter horizon of quarterly earnings increases or falls, I ask whether the models can capture the likelihood of reversion. Secondly, I ask, what is the representative investor s response to observed sequences of quarterly earnings changes for my S&P500 constituent sample companies? I find a far greater frequency of extreme persistent quarterly earnings rises (of nine quarters and more) than falls and hence a more muted reaction to their occurrence from the market. Extreme cases of persistent quarterly earnings falls are far less common than extreme rises and are more salient in their impact on stock prices. I find evidence suggesting that information discreteness; that is the frequency with which small information about stock value filters into the market is one of the factors that foment earnings momentum in stocks. However, information discreteness does not subsume the impact of sequences of annualised quarterly earnings changes, or earnings streakiness as a strong candidate that drives earnings momentum in stock returns in my S&P500 constituent stock sample. Therefore, earnings streakiness and informational discreteness appear to have separate and additive effects in driving momentum in stock price. In chapter 5, the case for the informativeness of the streaks of earnings surprises is further strengthened. This is done by examining the explanatory power of streaks of earnings surprises in a shorter horizon of three days around the period when the effect of the nature of earnings news is most intense in the stock market. Even in shorter windows, investors in S&P500 companies seem to be influenced by the lengthening of negative and positive streaks of earnings surprises over the twelve quarters of quarterly earnings announcement I study here. This further supports my thesis that investors underreact to sequences of changes in their expectations about stock returns. This impact is further strengthened by high information uncertainties in streaks of positive earnings surprise. However, earnings streakiness is one discrete and separable element in the resolution of uncertainty around equity value for S&P 500 constituent companies. Most of the proxies for earnings surprise show this behaviour especially when market capitalisation, age and cash flow act as proxies of information uncertainty. The influence of the gambler s fallacy on the representative investor in the presence of information uncertainty becomes more pronounced when I examine increasing lengths of streaks of earnings surprises. The presence of post earnings announcement drift in my large capitalised S&P500 constituents sample firms confirms earnings momentum to be a pervasive phenomenon which cuts across different tiers of the stock markets including highly liquid stocks, followed by many analysts, which most large funds would hold

Application of Regime Switching and Random Matrix Theory for Portfolio Optimization

Market economies have been characterized by boom and bust cycles. Since the seminal work of Hamilton (1989), these large scale fluctuations have been referred to as regime switches. Ang and Bekaert (2002) were the first to consider the role of regime switches for stock market returns and portfolio optimisation. The key stylized facts regarding regime switching for stock index returns is that boom periods with positive mean stock returns are associated with low volatility, while bear markets with negative mean returns have high volatility. The correlation of asset returns also show asymmetry with greater correlation being found during stock market downturns. In view of the large portfolio losses from correlated negative movements in asset returns during the recent 2007 financial crisis, it has become imperative to incorporate regime sensitivity in portfolio management. This thesis forms an extensive application of regime sensitive statistics for stock returns in the management of equity portfolios for different markets. Starting with the application to a small 3 asset portfolio for UK stocks (in Chapter 4), the methodology is extended to large scale portfolio for the FTSE-100. In chapters 5 and 6, respectively, using stock index data from the subcontinent (India, Pakistan and Bangladesh) and for the Asia Pacific, optimal regime sensitive portfolios have been analysed with the MSCI AC Index (for Emerging and Asia Pacific Markets) being taken as the benchmark index. Portfolio performance has been studied using a dynamic end of month rebalancing of the portfolio on the basis of regime indicators given by market index and relevant regime dependent portfolio statistics. The cumulative end of period returns and risk adjusted Sharpe Ratio from this exercise is compared to the simple Markowitz mean-variance portfolio and market value portfolio. The regime switching optimal portfolio strategy has been found to dominate non-regime sensitive portfolio strategies in Asia Pacific and 3 asset portfolio for UK stocks cases but not in Subcontinent case (for the first half of out-sample period). In the case of the relationship of the sub-continental indexes vis-à-vis the MSCI benchmark index, the latter has negligible explanatory power for the former especially for the first half of out-sample period. Hence, the regime indicators based on MSCI emerging market index have detrimental effects on portfolio selection based on the sub-continental indexes. As regime sensitive variance–covariance matrices have implications for the selection of optimal portfolio weights, the final Chapter 7 uses the FTSE-100 and its constituent company data to compare and contrast the implications for optimal portfolio management of filtering the covariance matrix using Random Matrix Theory (RMT). While it is found that filtering the variance-covariance matrix using Marchenko-Pasteur bounds of RMT improves optimal portfolio choice in both non-regime and regime dependent cases, remarkably in the latter case for Regime 2 determined variance-covariance matrix, the RMT filter was least needed. This result is given in Chapter 7, Table 7.5-1. This confirms the significance of using Hamilton (1989) regime sensitive statistics for stock returns in identifying the ‘true’ non-noisy variance-covariance relationships. The RMT methodology is also useful for identifying the centrality, based on eigenvector analysis, of the constituent stocks in their role in driving crisis and non-crisis market conditions. A fully automated suite of programs in MATLAB have been developed for regime switching portfolio optimization with RMT filtering of the variance-covariance matrix

Portfolio optimization in a regime-switching market with derivatives

We consider the optimal asset allocation problem in a continuous-time regime-switching market. The problem is to maximize the expected utility of the terminal wealth of a portfolio that contains an option, an underlying stock and a risk-free bond. The difficulty that arises in our setting is finding a way to represent the return of the option by the returns of the stock and the risk-free bond in an incomplete regime-switching market. To overcome this difficulty, we introduce a functional operator to generate a sequence of value functions, and then show that the optimal value function is the limit of this sequence. The explicit form of each function in the sequence can be obtained by solving an auxiliary portfolio optimization problem in a single-regime market. And then the original optimal value function can be approximated by taking the limit. Additionally, we can also show that the optimal value function is a solution to a dynamic programming equation, which leads to the explicit forms for the optimal value function and the optimal portfolio process. Furthermore, we demonstrate that, as long as the current state of the Markov chain is given, it is still optimal for an investor in a multiple-regime market to simply allocate his/her wealth in the same way as in a single-regime market.9 page(s