We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level. We develop a bound on the drawdown probability; using this bound instead of the original risk constraint yields a convex optimization problem that guarantees the drawdown risk constraint holds. N...

Risk management of drawdowns and portfolio optimization with drawdown constraints is becoming increasingly important among practitioners. In this paper, we introduce new types of contracts which depend on the maximum drawdown or on the average drawdown. Trading drawdown contracts would address directly the concerns of portfolio managers who would like to manage them. The maximum or the average ...

Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown risk as Conditional Expected Drawdown (CED), which is the tail mean of maximum drawdown distributions. We show that CED is a degree one positive homogenous ri...

[1] Year-to-year variations in summer drawdown of Northern Hemisphere atmospheric carbon dioxide (CO2) are compared with corresponding year-to-year variations in sealevel pressure (SLP), surface air temperature, and the productivity of land vegetation as inferred from the satellite-derived normalized difference vegetation index (NDVI). Annual values of CO2 drawdown for the years 1980–2000 are e...

We propose a new one-parameter family of risk functions defined on portfolio return sample -paths, which is called conditional drawdown-at-risk (CDaR). These risk functions depend on the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α , the CDaR is defined as the mean of the worst % 100 ) 1 ( ∗ − α drawdowns. The CDaR ...

This paper develops a bi-objective portfolio selection problem that maximizes returns and minimizes a risk measure called conditional Drawdown (CDD). The drawdown measures include the maximal Drawdown and Average Drawdown as its limiting case. The CDD family of risk functional is similar to conditional value at Risk (CVaR). In this paper, the fuzzy method has been used to solve the bi-objec...

The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CDaR yield the capital asset pricing model (CAPM)...

Maximum drawdown is a risk measure that plays an important role in portfolio management. In this paper, we address the question of computing the expected value of the maximum drawdown using a partial differential equation (PDE) approach. First, we derive a two-dimensional convection-diffusion pricing equation for the maximum drawdown in the Black-Scholes framework. Due to the properties of the ...

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 − α) ∗ 100% drawdowns. The CDD m...

In this article, we study the concept of maximum drawdown and its relevance to the prevention of portfolio losses. Maximum drawdown is defined as the largest market drop during a given time interval. We show that maximum drawdown can serve as an additional tool for portfolio managers on top of already existing contracts, such as put or lookback options.