Quantitative Trading, 2nd Edition

CHAPTER 6Money and Risk Management

All trading strategies suffer occasional losses, technically known as drawdowns. The drawdowns may last a few minutes or a few years. To profit from a quantitative trading business, it is essential to manage your risks in a way that limits your drawdowns to a tolerable level and yet be positioned to use optimal leverage of your equity to achieve maximum possible growth of your wealth. Furthermore, if you have more than one strategy, you will also need to find a way to optimally allocate capital among them so as to maximize overall risk-adjusted return.

The optimal allocation of capital and the optimal leverage to use so as to strike the right balance between risk management and maximum growth is the focus of this chapter, and the central tool we use is called the Kelly formula.

OPTIMAL CAPITAL ALLOCATION AND LEVERAGE

Suppose you plan to trade several strategies, each with their own expected returns and standard deviations. How should you allocate capital among them in an optimal way? Furthermore, what should be the overall leverage (ratio of the size of your portfolio to your account equity)? Dr. Edward Thorp, whom I mentioned in the preface, has written an excellent expository article on this subject in one of his papers (Thorp, 1997), and I shall follow his discussion closely in this chapter. (Dr. Thorp's discussion is centered on a portfolio of securities, and mine is constructed around a portfolio of strategies. However, the mathematics ...