A visual and analytical walk from pure white noise to a true random walk.

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The article examines how simple autoregressive stochastic processes behave with the Dickey-Fuller test.

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This post explores how to use the Dickey–Fuller test to check the random‑walk hypothesis for time series using a pure NumPy implementation, and using Monte Carlo simulations to compute critical‑value tables.

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In this follow-up, I analyze 10 years of data on a select group of stocks to show that while higher take-profit and stop-loss thresholds boost win ratios and Sharpe ratios, longer holding times can lower annualized returns.

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In this article, I explore how adopting longer-term, resilient trading strategies with higher take-profit and stop-loss thresholds can deliver more consistent, risk-adjusted performance.

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In the previous two articles, we explored the coverage of random portfolios in log volatility—return space, both with and without a risk-free asset. We now take the next step, and calculate the Efficient Frontier and Capital Market Line of Markowitz’s theory.

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In a previous article I simulated random portfolios using Monte Carlo methods for the 2023 daily closing prices of the 100 stocks constituting the Nasdaq-100. Here I add the risk-free asset to the portfolio and examine how it affects the coverage in log volatility—return space.

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I examine the coverage of random portfolios in log volatility—return space using Monte Carlo methods with different randomization techniques for the 2023 daily closing prices of the 100 stocks constituting the Nasdaq-100.

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I clean up the code I wrote for earlier posts, and run simple trading experiments.

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I investigate the volatility of aggressive take-profit strategies on tech stocks.

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I investigate the volatility of some securities, and its stability over time.

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