Learning outcomes

After this module you should be able to:

1. Write any common technical indicator (moving average, breakout, RSI, relative volume, relative strength) as an explicit function of the price history, and state the trading rule built on it as a falsifiable hypothesis about conditional expected returns.
2. Prove that a moving-average crossover on log prices is a positively weighted sum of past returns, and derive the expected return of a linear trend rule in terms of drift and autocovariances.
3. Translate Weinstein, Minervini, O'Neil and Darvas into codable rule sets, list the parts that cannot be coded without point-in-time data, and compute the breakeven win rate of a swing system after Indian costs.
4. Derive the Lo–MacKinlay decomposition of momentum profits and explain, with a beta argument, why momentum crashes after bear markets.
5. Build an event-driven backtester with costs that provably has no look-ahead, and prove when a vectorised backtest gives the same answer.
6. Derive the asymptotic standard error of the Sharpe ratio, the probabilistic Sharpe ratio and the minimum track-record length, and compute them for a strategy.
7. Derive the expected maximum Sharpe ratio of N skill-less strategies from extreme-value theory, and compute the deflated Sharpe ratio.
8. Prove that Bonferroni and Holm control the family-wise error rate and that Benjamini–Hochberg controls the false discovery rate, and explain White's Reality Check and the probability of backtest overfitting.