Fig 1.
(a) The feature time-series data is best thought of as OHLC (Open-High-Low-Close) bar data. The filled box in the candle chart denotes the situation where the close price is lower than the open price, conversely the unfilled box has the close price higher than the open price. (b) Feature time-series investment period for the t-th time increment showing that the end of the t-th increment does not always have to coincide with the start of the next, here the t+1-th, investment period. The opening price is denote as om,t and the close price for the period as cm,t for the m-th asset.
Table 1.
Summary of random datasets.
Table 2.
Summary of real datasets.
Table 3.
Wealth (S) from investing in synthetic data.
Fig 2.
Synthetic data case wealth gained.
The wealth achieved by each randomly generated stock for (a) SDC 1 (b) SDC 2 (c) SDC 3 and (d) SDC 4.
Fig 3.
Synthetic data case wealth gained.
The wealth achieved by the active and absolute portfolios on (a) SDC 1 (b) SDC 2 (c) SDC 3 and (d) SDC 4 that consists of a time period of 1000 and 10 stocks.
Table 4.
Average p values of wealth (S) for active portfolios.
Table 5.
Average p values of wealth gained (S) from the absolute portfolio.
Table 6.
Comparison of p values of wealth gained (S) from the active portfolio.
Table 7.
Comparison of p values of wealth gained (S) from the absolute portfolio.
Table 8.
Wealth achieved by investing in combinations of stocks from NYSE dataset.
Fig 4.
Wealth gained in NYSE data experiments.
Comparison of the wealth gained from different methods when investing in (a) iroqu and kinar (b) 36 stocks from the NYSE dataset.
Table 9.
Wealth achieved by investing in various combinations of stocks from NYSE merged dataset.
Fig 5.
Wealth gained in NYSE merged data experiments.
Comparison of the wealth gained from different methods when investing in (a) comme and kinar (b) 23 stocks from the NYSE Merged dataset.
Table 10.
Wealth achieved by investing in various combinations of stocks from JSE OHLC dataset (close-to-close).
Table 11.
Wealth achieved by investing in various combinations of stocks from JSE OHLC dataset (close-to-open).
Table 12.
Wealth achieved by investing in various combinations of stocks from JSE OHLC dataset (open-to-close).
Table 13.
Wealth achieved by investing in various combinations of stocks from JSE OHLC dataset (open-to-open).
Fig 6.
Wealth gained close-to-close JSE OHLC data.
Comparison of the wealth gained from different methods when investing in (a) ANGJ and AGLJ (b) 10 stocks (c) 20 stocks (d) 30 stocks from the JSE OHLC close-close dataset. This does not account for price-impacts and frictions, nor for the need to approximate an expected close price just prior to market close as one solves for the portfolio controls, there will always be a difference between the controls solved for just prior to market close and those required once the market has closed and the official closing prices printed.
Fig 7.
Wealth from Different JSE OHLC data sets.
Comparison of wealth achieved from the absolute portfolio, active portfolio and Györfi nearest neighbour porfolio on the(a)close-to-close (b) open-to-close (c) close-to-open and (d) open-to-open JSE OHLC datasets. Here we find that there is no particular combination of OHLC data for which there is a systematic preference, e.g. close-to-close, the case of considering the close price change from one day end to another is not systematically more profitable than other combinations of data times. These tests do consider the reality of trading prior to a time point, for example market close, one cannot a-priori know what the close price will be, this has to be approximated. This excludes price-impact effects.
Table 14.
Wealth from stock-pairs of JSE intraday data.
Fig 8.
Wealth from JSE intraday data experiments.
Comparison of the wealth gained from different methods when investing in (a) ANGJ and AGLJ (b) 10 stocks from the JSE Intraday dataset.
Table 15.
JSE intraday data with cluster defined experts.
Fig 9.
Comparison of the wealth gained from different methods when investing in 20 stocks from the JSE Intraday dataset, the plot includes the results of using clusters on the stocks. It is important to note that the clustered portfolios have 150 experts and the portfolios without clusters have 50 experts.
Fig 10.
JSE intraday data running times.
Running time of the portfolios in seconds of the different strategies. This demonstrates the speed advantage of using the analytic quadratic approximation as compared to numerically solving the log-optimal constrained optimization at each time-step for each expert combination. As expected the fully invested analytic solution is fastest, the zero-cost portfolio next, because of the additional leverage constraint, and the slowest the algorithm that required the numerical solution of the optimization.