Quantitative Finance

One of the findings of the recent literature is that the 2008 financial crisis caused reduction in international diversification benefits. To fully understand the possible potential from diversification, we build an empirical model which combines generalised autoregressive score copula functions with high frequency data, and allows us to capture and forecast the conditional time-varying joint distribution of stock returns. Using this novel methodology and fresh data covering five years after the crisis, we compute the conditional diversification benefits to answer the question, whether it is still interesting for an international investor to diversify. As diversification tools, we consider the Czech PX and the German DAX broad stock indices, and we find that the diversification benefits strongly vary over the 2008--2013 crisis years.

In this paper we propose and discuss different 0-1 linear models in order to solve the cardinality constrained portfolio problem by using factor models. Factor models are used to build portfolios to track indexes, together with other objectives, also need a smaller number of parameters to estimate than the classical Markowitz model. The addition of the cardinality constraints limits the number of securities in the portfolio. Restricting the number of securities in the portfolio allows us to obtain a concentrated portfolio, reduce the risk and limit transaction costs. To solve this problem, a pure 0-1 model is presented in this work, the 0-1 model is constructed by means of a piecewise linear approximation. We also present a new quadratic combinatorial problem, called a minimum edge-weighted clique problem, to obtain an equality weighted cardinality constrained portfolio. A piecewise linear approximation for this problem is presented in the context of a multi factor model. For a single factor model, we present a fast heuristic, based on some theoretical results to obtain an equality weighted cardinality constraint portfolio. The consideration of a piecewise linear approximation allow us to reduce significantly the computation time required for the equivalent quadratic problem. Computational results from the 0-1 models are compared to those using a state-of-the-art Quadratic MIP solver.

The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use historical data to estimate it. Even though sample covariance matrix is an unbiased estimator of the population covariance matrix, it includes a great amount of estimation error especially when the number of observed data is not much bigger than number of assets. As it is difficult to estimate the covariance matrix with high dimensionality all at once, clustering stocks is proposed to come up with covariance matrix in two steps: firstly, within a cluster and secondly, between clusters. It decreases the estimation error by reducing the number of features in the data matrix. The motivation of this dissertation is that the estimation error can still remain high even after clustering, if a large amount of stocks is clustered together in a single group. This research proposes to utilize a bounded clustering method in order to limit the maximum cluster size. The result of experiments shows that not only the gap between in-sample volatility and out-of-sample volatility decreases, but also the out-of-sample volatility gets reduced. It implies that we need a bounded clustering algorithm so that maximum clustering size can be precisely controlled to find the best portfolio performance.

In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors. We give a numerical algorithm to compute the optimal investment-consumption strategy for an infinite collective of identical investors with exponential Kihlstrom--Mirman preferences, investing in the Black--Scholes market in continuous time but consuming in discrete time. Our algorithm can also be applied to an individual investor. We derive an analytic formula for the optimal consumption in the special case of an individual who chooses not to invest in the financial markets. We prove that our problem formulation for a fund with an infinite number of members is a good approximation to a fund with a large, but finite number of members.

In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors. We compute analytically the optimal investment-consumption strategy for a fund of n identical investors with homogeneous Epstein--Zin preferences, investing in the Black--Scholes market in continuous time but consuming in discrete time. Our result holds for arbitrary mortality distributions. We also compute the optimal strategy for an infinite fund of investors, and prove the convergence of the optimal strategy as n→∞ . The proof of convergence shows that effective strategies for inhomogeneous funds can be obtained using the optimal strategies found in this paper for homogeneous funds, using the results of [2]. We find that a constant consumption strategy is suboptimal even for infinite collectives investing in markets where assets provide no return so long as investors are "satisfaction risk-averse." This suggests that annuities and defined benefit investments will always be suboptimal investments. We present numerical results examining the importance of the fund size, n , and the market parameters.

We quantify the benefit of collectivised investment funds, in which the assets of members who die are shared among the survivors. For our model, with realistic parameter choices, an annuity or individual fund requires approximately 20\% more initial capital to provide as good an outcome as a collectivised investment fund. We demonstrate the importance of the new concept of pension adequacy in defining investor preferences and determining optimal fund management. We show how to manage heterogeneous funds of investors with diverse needs. Our framework can be applied to existing pension products, such as Collective Defined Contribution schemes.

We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-negative, while in the former case they can be negative. Second, the effects of both linear and nonlinear (impact) costs are different in these two cases due to turnover reduction when the trades are crossed. Third, the turnover reduction depends on the universe of traded alpha streams, so if some alpha streams have zero allocations, turnover reduction needs to be recomputed, hence an iterative procedure. We discuss an algorithm for finding allocation weights with crossing and linear costs. We also discuss a simple approximation when nonlinear costs are added, making the allocation problem tractable while still capturing nonlinear portfolio capacity bound effects. We also define "regression with costs" as a limit of optimization with costs, useful in often-occurring cases with singular alpha covariance matrix.

We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications typically there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted) regression over SCM principal components. Regression often produces alpha weights with insufficient diversification and/or skewed distribution against, e.g., turnover. This can be rectified by imposing bounds on alpha weights within the regression procedure. Bounded regression can also be applied to stock and other asset portfolio construction. We discuss illustrative examples.

Smart beta, also known as strategic beta or factor investing, is the idea of selecting an investment portfolio in a simple rule-based manner that systematically captures market inefficiencies, thereby enhancing risk-adjusted returns above capitalization-weighted benchmarks. We explore the idea of applying a smart strategy in reverse, yielding a "bad beta" portfolio which can be shorted, thus allowing long and short positions on independent smart beta strategies to generate beta neutral returns. In this article we detail the construction of a monthly reweighted portfolio involving two independent smart beta strategies; the first component is a long-short beta-neutral strategy derived from running an adaptive boosting classifier on a suite of momentum indicators. The second component is a minimized volatility portfolio which exploits the observation that low-volatility stocks tend to yield higher risk-adjusted returns than high-volatility stocks. Working off a market benchmark Sharpe Ratio of 0.42, we find that the market neutral component achieves a ratio of 0.61, the low volatility approach achieves a ratio of 0.90, while the combined leveraged strategy achieves a ratio of 0.96. In six months of live trading, the combined strategy achieved a Sharpe Ratio of 1.35. These results reinforce the effectiveness of smart beta strategies, and demonstrate that combining multiple strategies simultaneously can yield better performance than that achieved by any single component in isolation.

Out of the companies, Dolby is the company with the best overall financial and operation health. According to the table that accounted its financial statements for the past three years, Dolby has stable profit margins that generates a revenue in the billions, the only company in ten figures.