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This thesis consists of an introductory part and five self-contained papers related to the profitability of momentum strategies and optimal leverage rules.

Paper [I] tests the success rate of trades and the returns of the Opening Range Breakout (ORB) day trading strategy. A trader that trades the ORB strategy seeks to identify large intraday price movements and trades only when the price moves beyond some predetermined threshold. We present an ORB strategy based on normally distributed returns to identify such days, and find that our ORB trading strategy result in significantly higher returns than zero as well as an increased success rate in relation to a fair game when applied to a long time series of crude oil futures contracts. The characteristics of such an approach over conventional statistical tests is that it involves the joint distribution of low, high, open and close over a given time horizon.

Paper [II] assesses the returns of the Opening Range Breakout (ORB) day trading strategy across volatility states of the underlying asset. We calculate the average daily returns of the ORB strategy for each volatility state when applied on long time series of crude oil and S&P 500 index futures contracts. We find an average difference in returns between the highest and lowest volatility state of around 200 basis points per day for crude oil, and of around 150 basis points per day for the S&P 500. Our result suggests that ORB strategy traders can be profitable, even in the long-run, but that the success in day trading to a large extent depend on the volatility of the underlying asset.

Paper [III] performs empirical analysis on short-term and long-term Commodity Trading Advisor (CTA) strategies regarding their exposures to unanticipated risk shocks. Previous research documents that CTA strategies in general offer diversification opportunities during equity market crisis situations when evaluated as a group, but do not separate between short-term and long-term CTA strategies. When separating between short-term and long-term CTA strategies, this paper finds that only short-term CTA strategies provide a significant, and consistent, exposure to unanticipated risk shocks while long-term CTA strategies do not. For the purpose of diversifying a portfolio during equity market crisis situations, our result suggests that an investor should allocate to short-term CTA strategies rather than to long-term CTA strategies.

Paper [IV] posits that it is possible to obtain an optimal leverage factor for financial instruments equipped with embedded leverage. By applying the Kelly criterion for optimal leverage, we show that there exists a uniquely optimal level of leverage for maximizing the long-run profit of embedded leverage instruments. The implication of an existing unique optimum is that a smaller leverage factor than optimal leads to a lower long-term profit than is feasible, but also that a larger leverage factor leads to a lower long-term profit than is feasible. Our empirical analysis shows how an optimal level of embedded leverage can increase the profitability of Exchange Traded Products.

Paper [V] systematically analyses the effect of leverage on long-run profit when trading the Opening Range Breakout (ORB) day trading strategy. This paper clarifies the relation to two optimal leverage rules proposed for maximizing trading profit; the Kelly criterion and the Optimal fraction criterion. Our empirical analysis shows how leverage can increase day trading profit in-sample and out-of-sample when applied to a long time series of DAX 30 index futures contracts.

Traders may use leverage to scale up the returns and use stop orders to limit their losses. Typically used for controlling risk, stop loss orders may actually increase long-run trading profit. This paper derives a criterion for maximizing long-run trading profit with respect to leverage and stop loss order placement, as both may affect profitability. In a trading application, we study how stopping losses and leverage affects trading profit. We find empirical support that stop loss order placement together with leverage can have a substantial effect on long-run profit.

This paper measures the returns of a popular day trading strategy – the Opening Range Breakout (ORB) strategy – across volatility states. We calculate the average daily returns of the ORB strategy for each volatility state of the underlying asset when applied on long time series of crude oil and S&P 500 futures contracts. We find an average difference in returns between the highest and the lowest volatility state of around 200 basis points per day for crude oil, and of around 150 basis points per day for the S&P 500. This finding suggests that the success in day trading can depend to a large extent on the volatility of the underlying asset.

The optimal return magnification of an exchange traded product relative to the returns of its underlying security can increase its profitability.

This paper measures the returns of a popular day trading strategy, the Opening Range Breakout strategy (ORB), across volatility states. We calculate the average daily returns of the ORB strategy for each volatility state of the underlying asset when applied on long time series of crude oil and S&P 500 futures contracts. We find an average difference in returns between the highest and the lowest volatility state of around 200 basis points per day for crude oil, and of around 150 basis points per day for the S&P 500. This finding suggests that the success in day trading can depend to a large extent on the volatility of the underlying asset.

Paper [I] tests the success rate of trades and the returns of the Opening Range Breakout (ORB) strategy. A trader that trades on the ORB strategy seeks to identify large intraday price movements and trades only when the price moves beyond some predetermined threshold. We present an ORB strategy based on normally distributed returns to identify such days and find that our ORB trading strategy result in significantly higher returns than zero as well as an increased success rate in relation to a fair game. The characteristics of such an approach over conventional statistical tests is that it involves the joint distribution of low, high, open and close over a given time horizon.

Paper [II] measures the returns of a popular day trading strategy, the Opening Range Breakout strategy (ORB), across volatility states. We calculate the average daily returns of the ORB strategy for each volatility state of the underlying asset when applied on long time series of crude oil and S&P 500 futures contracts. We find an average difference in returns between the highest and the lowest volatility state of around 200 basis points per day for crude oil, and of around 150 basis points per day for the S&P 500. This finding suggests that the success in day trading can depend to a large extent on the volatility of the underlying asset.

Paper [III] performs empirical analysis on short-term and long-term Commodity Trading Advisor (CTA) strategies regarding their exposures to unanticipated risk shocks. Previous research documents that CTA strategies offer diversification opportunities during equity market crisis situations when evaluated as a group, but do not separate between short-term and long-term CTA strategies. When separating between short-term and long-term CTA strategies, this paper finds that only short-term CTA strategies provide a significant, and consistent, exposure to unanticipated risk shocks while long-term CTA strategies do not. For the purpose of diversifying a portfolio during equity market crisis situations, this result suggests that an investor should allocate to short-term CTA strategies rather than to long-term CTA strategies.

In this paper, we argue that the value addition from investing in short-term futures trading strategies is their reconcilability with unanticipated risk shocks. We perform empirical analysis on short-term and long-term CTA, i.e., trend-following, strategies and find that the exclusive characteristic of short-term CTAs is their significant and consistent long position in unanticipated risk shocks. Unlike long-term CTA strategies, their exposure to these risk shocks is prevalent in different states of the risk cycle. Our findings imply that short-term futures trading strategies can offer considerable diversification opportunities for investors during equity market crisis situations.

By using money management, an investor may determine the optimal leverage factor to apply on each trade, for maximizing the profitability of investing. Research suggests that the stopping of losses may increase the profitability of a trading strategy when returns follow momentum. This paper contributes to the literature by proposing the first money management criterion that incorporates optimal stopping of losses. In an empirical trading study, we are able to substantially improve the profitability when using this criterion, relative to the existing criteria. We conclude that money management should incorporate stopping of losses when returns follow momentum.

Is it possible to beat the market by mechanical trading rules based on historical and publicly known information? Such rules have long been used by investors and in this paper, we test the success rate of trades and profitability of the Open Range Breakout (ORB) strategy. An investor that trades on the ORB strategy seeks to identify large intraday price movements and trades only when the price moves beyond some predetermined threshold. We present an ORB strategy based on normally distributed returns to identify such days and find that our ORB trading strategy result in significantly higher returns than zero as well as an increased success rate in relation to a fair game. The characteristics of such an approach over conventional statistical tests is that it involves the joint distribution of low, high, open and close over a given time horizon.