Confidence Weighted Mean Reversion Strategy for Online Portfolio Selection

Singapore Ministry of Education Academic Research Fund Tier

Long term portfolio construction

Financial analyst commonly advice individual investors with a long investment horizon to invest in portfolios comprised more of equities. This advice is usually coupled with the practice of shifting the investor's portfolio from risky asset holdings towards bonds and cash as the investor's target date gets closer. This view rests on the notion that equities tend to be less risky over the long horizon and that stock returns exhibit mean reversion overtime. The purpose of this dissertation is to find the optimal asset allocation over various investment horizons; and investigate how the optimal asset allocation changes over the long investment horizon. The study uses data from South Africa's financial market covering the period December 2001 to December 2014. The mean - variance framework generated the optimal asset allocation over 12 investment horizons. The study finds that, over 90 percent of the portfolio should be vested into fixed - income South African bonds, with little over 5 percent equities allocation, over longer investment periods. In addition, the study found evidence of time diversification on the JSE all shares index and the presence of mean reversion properties for the all s hares index. With these conclusions, implications and recommendations are suggeste

Optimal Dynamic Strategies on Gaussian Returns

Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals, (e.g., linear filters of past returns, such as simple moving averages, exponential weighted moving averages, forecasts from ARIMA models), we are able to derive closed-form expressions for the first four moments of the strategy's returns, in terms of correlations between the random signals and unknown future returns. By allowing for randomness in the asset-allocation and modelling the interaction of strategy weights with returns, we demonstrate that positive skewness and excess kurtosis are essential components of all positive Sharpe dynamic strategies, which is generally observed empirically; demonstrate that total least squares (TLS) or orthogonal least squares is more appropriate than OLS for maximizing the Sharpe ratio, while canonical correlation analysis (CCA) is similarly appropriate for the multi-asset case; derive standard errors on Sharpe ratios which are tighter than the commonly used standard errors from Lo; and derive standard errors on the skewness and kurtosis of strategies, apparently new results. We demonstrate these results are applicable asymptotically for a wide range of stationary time-series.Comment: Accepted by Journal of Investment Strategies. arXiv admin note: text overlap with arXiv:1905.0502