# Drawdown (economics)

The drawdown is the measure of the decline from a historical peak in some variable (typically the cumulative profit or total open equity of a financial trading strategy).[1]

The maximum drawdown (MDD) up to time is the maximum of the drawdown over the history of the variable. More formally, the MDD is defined as:

There are two main definitions of a drawdown:

1. How low it goes (the magnitude)

Putting it plainly, a drawdown is the “pain” period experienced by an investor between a peak (new highs) and subsequent valley (a low point before moving higher).[citation needed]

Next, the Maximum Drawdown, or more commonly referred to as Max DD. This is pretty much self explanatory, as the Max DD is the worst (the maximum) peak to valley loss since the investment’s inception.[citation needed]

In finance, the use of the maximum drawdown as an indicator of risk is particularly popular in the world of commodity trading advisors through the widespread use of three performance measures: the Calmar ratio, the Sterling ratio and the Burke ratio. These measures can be considered as a modification of the Sharpe ratio in the sense that the numerator is always the excess of mean returns over the risk-free rate while the standard deviation of returns in the denominator is replaced by some function of the drawdown.

1. How long it lasts (the duration)

The drawdown duration is the length of any peak to peak period, or the time between new equity highs.

The max drawdown duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs).

Banking or other finance definitions

Credit offered

Where an amount of credit is offered, a drawdown against the line of credit results in a debt (which may have associated interest terms if the debt is not cleared according to an agreement.)

Funds offered

Where funds are made available, such as for a specific purpose, drawdowns occur if the funds – or a portion of the funds – are released when conditions are met.

Optimization of drawdown

A passing glance at the mathematical definition of drawdown suggests significant difficulty in using an optimization framework to minimize the quantity, subject to other constraints; this is due to the non-convex nature of the problem. However, there is a way to turn the drawdown minimization problem into a linear program.[3][4]

They call this the conditional drawdown-at-risk (CDaR); this is a nod to conditional value-at-risk (CVaR), which may also be optimized using linear programming. There are two limiting cases to be aware of:

• is the average drawdown
• is the maximum drawdown

References

1. ^“What Is A Drawdown? – Fidelity”. www.fidelity.com. Retrieved 2019-08-04.
2. ^Magdon-Ismail, Malik; Atiya, Amir F.; Pratap, Amrit; Abu-Mostafa, Yaser S. (2004). “On the Maximum Drawdown of a Brownian Motion” (PDF). Journal of Applied Probability. 41 (1): 147–161.
3. ^Chekhlov, Alexei; Uryasev, Stanislav; Zabarankin, Michael (2003). “Portfolio Optimization with Drawdown Constraints” (PDF).
4. ^Chekhlov, Alexei; Uryasev, Stanislav; Zabarankin, Michael (2005). “Drawdown Measure in Portfolio Optimization” (PDF). International Journal of Theoretical and Applied Finance. 8 (1): 13–58.

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