empyrical
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quantopian
Calmar Ratio w/ EMDD
It would be great if you can add this. http://alumnus.caltech.edu/~amir/mdd-risk.pdf
function EDD = emaxdrawdown(Mu, Sigma, T)
%EMAXDRAWDOWN Compute expected maximum drawdown for a Brownian motion.
%
% EDD = emaxdrawdown(Mu, Sigma, T);
%
% Inputs:
% Mu - The drift term of a Brownian motion with drift.
% Sigma - The diffusion term of a Brownian motion with drift.
% T - A time period of interest or a vector of times.
%
% Outputs:
% EDD - Expected maximum drawdown for each time period in T.
%
% Notes:
% If a geometric Brownian motion with stochastic differential equation
% dS(t) = Mu0 * S(t) * dt + Sigma0 * S(t) * dW(t) ,
% convert to the form here by Ito's Lemma with X(t) = log(S(t)) such that
% Mu = M0 - 0.5 * Sigma0^2
% Sigma = Sigma0 .
%
% Maximum drawdown is non-negative since it is the change from a peak to a
% trough.
%
% References:
% Malik Magdon-Ismail, Amir F. Atiya, Amrit Pratap, and Yaser S. Abu-Mostafa,
% "On the Maximum Drawdown of a Brownian Motion", Journal of Applied
% Probability, Volume 41, Number 1, March 2004, pp. 147-161.
%
% See also MAXDRAWDOWN
% Copyright 2005 The MathWorks, Inc.
% $Revision: 1.1.6.2 $ $Date: 2005/12/12 23:16:10 $
if nargin < 3 || isempty(Mu) || isempty(Sigma) || isempty(T)
error('Finance:emaxdrawdown:MissingInputArg', ...
'Missing required input arguments Mu, Sigma, or T.');
end
[n, i] = size(Mu);
if (n > 1) || (i > 1)
error('Finance:emaxdrawdown:InvalidInputArg', ...
'Argument Mu must be a scalar.');
end
[n, i] = size(Sigma);
if (n > 1) || (i > 1)
error('Finance:emaxdrawdown:InvalidInputArg', ...
'Argument Sigma must be a scalar.');
end
T = T(:);
[n, i] = size(T);
if i > 1
error('Finance:emaxdrawdown:InvalidInputArg', ...
'Argument T must be a vector.');
end
if ~isfinite(Mu) || ~isfinite(Sigma) || (Sigma < 0)
error('Finance:emaxdrawdown:InvalidInputArg', ...
'Invalid argument values. Requires finite Mu, Sigma >= 0, T >= 0.');
end
for i = 1:n
if ~isfinite(T(i)) || (T(i) < 0)
error('Finance:emaxdrawdown:InvalidInputArg', ...
'Invalid argument values. Requires finite T >= 0.');
end
end
if Sigma < eps
if Mu >= 0.0
EDD = zeros(n,1);
else
EDD = - Mu .* T;
end
return
end
EDD = zeros(n,1);
for i = 1:n
if T(i) < eps
EDD = zeros(n,1);
else
if abs(Mu) <= eps
EDD(i) = (sqrt(pi/2) * Sigma) .* sqrt(T(i));
elseif Mu > eps
Alpha = Mu/(2.0 * Sigma * Sigma);
EDD(i) = emaxddQp(Alpha * Mu * T(i))/Alpha;
else
Alpha = Mu/(2.0 * Sigma * Sigma);
EDD(i) = - emaxddQn(Alpha * Mu * T(i))/Alpha;
end
end
end
function Q = emaxddQp(x)
A = [ 0.0005; 0.001; 0.0015; 0.002; 0.0025; 0.005;
0.0075; 0.01; 0.0125; 0.015; 0.0175; 0.02;
0.0225; 0.025; 0.0275; 0.03; 0.0325; 0.035;
0.0375; 0.04; 0.0425; 0.045; 0.0475; 0.05;
0.055; 0.06; 0.065; 0.07; 0.075; 0.08;
0.085; 0.09; 0.095; 0.1; 0.15; 0.2;
0.25; 0.3; 0.35; 0.4; 0.45; 0.5;
1.0; 1.5; 2.0; 2.5; 3.0; 3.5;
4.0; 4.5; 5.0; 10.0; 15.0; 20.0;
25.0; 30.0; 35.0; 40.0; 45.0; 50.0;
100.0; 150.0; 200.0; 250.0; 300.0; 350.0;
400.0; 450.0; 500.0; 1000.0; 1500.0; 2000.0;
2500.0; 3000.0; 3500.0; 4000.0; 4500.0; 5000.0 ];
B = [ 0.01969; 0.027694; 0.033789; 0.038896; 0.043372; 0.060721;
0.073808; 0.084693; 0.094171; 0.102651; 0.110375; 0.117503;
0.124142; 0.130374; 0.136259; 0.141842; 0.147162; 0.152249;
0.157127; 0.161817; 0.166337; 0.170702; 0.174924; 0.179015;
0.186842; 0.194248; 0.201287; 0.207999; 0.214421; 0.220581;
0.226505; 0.232212; 0.237722; 0.24305; 0.288719; 0.325071;
0.355581; 0.382016; 0.405415; 0.426452; 0.445588; 0.463159;
0.588642; 0.668992; 0.72854; 0.775976; 0.815456; 0.849298;
0.878933; 0.905305; 0.92907; 1.088998; 1.184918; 1.253794;
1.307607; 1.351794; 1.389289; 1.42186; 1.450654; 1.476457;
1.647113; 1.747485; 1.818873; 1.874323; 1.919671; 1.958037;
1.991288; 2.02063; 2.046885; 2.219765; 2.320983; 2.392826;
2.448562; 2.494109; 2.532622; 2.565985; 2.595416; 2.621743 ];
if x > 5000
Q = 0.25*log(x) + 0.49088;
elseif x < 0.0005
Q = 0.5*sqrt(pi*x);
else
Q = interp1(A,B,x);
end
function Q = emaxddQn(x)
A = [ 0.0005; 0.001; 0.0015; 0.002; 0.0025; 0.005;
0.0075; 0.01; 0.0125; 0.015; 0.0175; 0.02;
0.0225; 0.025; 0.0275; 0.03; 0.0325; 0.035;
0.0375; 0.04; 0.0425; 0.045; 0.0475; 0.05;
0.055; 0.06; 0.065; 0.07; 0.075; 0.08;
0.085; 0.09; 0.095; 0.1; 0.15; 0.2;
0.25; 0.3; 0.35; 0.4; 0.45; 0.5;
0.75; 1.0; 1.25; 1.5; 1.75; 2.0;
2.25; 2.5; 2.75; 3.0; 3.25; 3.5;
3.75; 4.0; 4.25; 4.5; 4.75; 5.0 ];
B = [ 0.019965; 0.028394; 0.034874; 0.040369; 0.045256; 0.064633;
0.079746; 0.092708; 0.104259; 0.114814; 0.124608; 0.133772;
0.142429; 0.150739; 0.158565; 0.166229; 0.173756; 0.180793;
0.187739; 0.194489; 0.201094; 0.207572; 0.213877; 0.220056;
0.231797; 0.243374; 0.254585; 0.265472; 0.27607; 0.286406;
0.296507; 0.306393; 0.316066; 0.325586; 0.413136; 0.491599;
0.564333; 0.633007; 0.698849; 0.762455; 0.824484; 0.884593;
1.17202; 1.44552; 1.70936; 1.97074; 2.22742; 2.48396;
2.73676; 2.99094; 3.24354; 3.49252; 3.74294; 3.99519;
4.24274; 4.49238; 4.73859; 4.99043; 5.24083; 5.49882 ];
if (x > 5.0)
Q = x + 0.5;
elseif x < 0.0005
Q = 0.5*sqrt(pi*x);
else
Q = interp1(A,B,x);
end
@akaniklaus Sorry for the late response, but I believe that the max drawdown is implemented here:
https://github.com/quantopian/empyrical/blob/master/empyrical/stats.py#L315
@eigenfoo Thanks but expected max drawdown (for a brownian motion) is different than max drawdown