Main Content

maxdrawdown

Compute maximum drawdown for one or more price series

所有的页面崩溃

Syntax

MaxDD = maxdrawdown(Data)
MaxDD = maxdrawdown(___,Format)
[MaxDD,MaxDDIndex] = maxdrawdown(___)

Description

example

MaxDD= maxdrawdown(Data)computes maximum drawdown for each series in anN-vectorMaxDDand identifies start and end indexes of maximum drawdown periods for each series in a2-by-NmatrixMaxDDIndex.

example

MaxDD= maxdrawdown(___,Format)adds an optional argument forFormat.

example

[MaxDD,MaxDDIndex] = maxdrawdown(___)adds an optional output forMaxDDIndex.

例子

collapse all

Open Live Script

Calculate the maximum drawdown (MaxDD) using example data with a fund, market, and cash series:

loadFundMarketCashMaxDD = maxdrawdown(TestData)
MaxDD =1×30.1658 - 0.3381 0

The maximum drop in the given time period was 16.58% for the fund series, and 33.81% for the market series. There was no decline in the cash series, as expected, because the cash account never loses value.

maxdrawdownalso returns the indices (MaxDDIndex) of the maximum drawdown intervals for each series in an optional output argument.

[MaxDD, MaxDDIndex] = maxdrawdown(TestData)
MaxDD =1×30.1658 - 0.3381 0
MaxDDIndex =2×32 2 NaN 18 18 NaN

The first two series experience their maximum drawdowns from the second to the 18th month in the data. The indices for the third series areNaNs because it never has a drawdown.

The 16.58% value loss from month 2 to month 18 for the fund series is verified using the reported indices.

Start = MaxDDIndex(1,:); End = MaxDDIndex(2,:); (TestData(Start(1),1) - TestData(End(1),1))/TestData(Start(1),1)
ans = 0.1658

ans = 0.1658

Although the maximum drawdown is measured in terms of returns,maxdrawdowncan measure the drawdown in terms of absolute drop in value, or in terms of log-returns. To contrast these alternatives more clearly, you can work with the fund series, assuming an initial investment of 50 dollars:

Fund50 = 50*TestData(:,1); plot(Fund50); title('\bfFive-Year Fund Performance, Initial Investment 50 usd'); xlabel('Months'); ylabel('Value of Investment');

Figure contains an axes object. The axes object with title F i v e - Y e a r blank F u n d blank P e r f o r m a n c e , blank I n i t i a l blank I n v e s t m e n t blank 5 0 blank u s d contains an object of type line.

First, compute the standard maximum drawdown, which coincides with the results above because returns are independent of the initial amounts invested.

MaxDD50Ret = maxdrawdown(Fund50)
MaxDD50Ret = 0.1658

Next, compute the maximum drop in value, using the'arithmetic'argument.

[MaxDD50Arith, Ind50Arith] = maxdrawdown(Fund50,'arithmetic')
MaxDD50Arith = 8.4285
Ind50Arith =2×12 18

The value of this investment was $50.84 in month 2, but by month 18 the value was down to $42.41, a drop of $8.43. This is the largest loss in dollar value from a previous high in the given time period. In this case, the maximum drawdown period, from the 2nd to 18th month, is the same independently of whether drawdown is measured as return or as dollar value loss.

[MaxDD50LogRet, Ind50LogRet] = maxdrawdown(Fund50,'geometric')
MaxDD50LogRet = 0.1813
Ind50LogRet =2×12 18

Note, the last measure is equivalent to finding the arithmetic maximum drawdown for the log of the series.

MaxDD50LogRet2 = maxdrawdown(log(Fund50),'arithmetic')
MaxDD50LogRet2 = 0.1813

Input Arguments

collapse all

Total return price series, specified as aT-by-Nmatrix withTsamples ofNtotal return price series.

Data Types:double

Format ofData, specified as character vector with the following possible values:

  • 'return'(default) — Maximum drawdown in terms of maximum percentage drop from a peak.

  • 'arithmetic'

    — Maximum drawdown of an arithmetic Brownian motion with drift (differences of data from peak to trough) using the equation

    d X ( t ) = μ d t + σ d W ( t ) .

  • 'geometric'

    — Maximum drawdown of a geometric Brownian motion with drift (differences of log of data from peak to trough) using the equation

    d S ( t ) = μ 0 S ( t ) d t + σ 0 S ( t ) d W ( t )

Data Types:char

Output Arguments

collapse all

Maximum drawdown, returned as a1-by-Nvector with maximum drawdown for each ofNtime series.

Note

  • Drawdown is the percentage drop in total returns from the start to the end of a period. If the total equity time series is increasing over an entire period, drawdown is 0. Otherwise, it is a positive number. Maximum drawdown is an ex-ante proxy for downside risk that computes the largest drawdown over all intervals of time that can be formed within a specified interval of time.

  • Maximum drawdown is sensitive to quantization error.

Start and end indexes for each maximum drawdown period for each total equity time series, returned as a2-by-Nvector of start and end indexes. The first row of the vector contains the start indexes and the second row contains the end indexes of each maximum drawdown period.

References

[1] Christian S. Pederson and Ted Rudholm-Alfvin. "Selecting a Risk-Adjusted Shareholder Performance Measure."Journal of Asset Management.Vol. 4, No. 3, 2003, pp. 152–172.

版本;n History

Introduced in R2006b

See Also

Topics