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This lecture delves into the definition of trading strategies in mathematical finance, emphasizing the transformation of raw returns into new assets. It explores the role of strategies in biasing price returns and provides examples of buy and hold strategies. The lecture discusses the scientific model behind trading strategies, the process of backtesting, and the challenges of testing strategies in non-stationary markets. It also covers the concepts of mean-reversion versus trend following in US equities and the importance of assessing and replicating fund performance. The lecture concludes with a critical analysis of fitting wrong models to financial data and the implications of overfitting strategies on the S&P 500.