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发表于 2011-6-27 14:45:37
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Macros to estimate value at risk
From Dapangmao's blog on sas-analysis
<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-O21RdjGq6KU/TfoqFt0CkqI/AAAAAAAAAnY/i-p_8SFbS90/s1600/plot2.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="300" width="400" src="http://1.bp.blogspot.com/-O21RdjGq6KU/TfoqFt0CkqI/AAAAAAAAAnY/i-p_8SFbS90/s400/plot2.jpg" /></a></div><br />
Value-at-risk (VaR) measures the risk of loss on a specific portfolio of financial asset. Jon Danielsson introduced how to apply the nonparametric(historic simulation) and parametric methods to estimate univariate and multivariate VaRs [Ref. 1]. And the simplest parametric ways are probably to imagine the daily returns as a normal distribution (or t-distribution) and therefore find the locations by probability. Then following his steps, for a single asset portfolio, I used Google’s adjusted returns since 2006; for a two-asset account, I used Google and Apple with a 0.3:0.7 weight ratio. The probabilities are both 1% and the money value sets at $1000. For the example below, parameters of the t-distribution were inferred by a routine of Proc NLMIXED in the first macro for univariate VaR [Ref. 2]; in the second macro, variance-covariance matrix was obtained again by the Cov() function of Proc IML for bi-variate VaRs. <br />
<br />
SAS actually has two components for matrix computation: Proc IML and Proc FCMP. My personal experience is: <br />
-- if code porting from VBA to SAS is needed, Proc FCMP should be the No.1 choice, because Proc FCMP is exactly built on the logic of EXCEL/VBA; <br />
-- if code porting from Matlab or R to SAS is needed, Proc IML should be the preference, because they speak the same language. <br />
<br />
Generally, Proc IML is more efficient than Proc FCMP for either programmer or machine (I was driven crazy by the nested loops of Proc FCMP). Of course, SAS/IML has a higher learning curve. For those who are willing to learn SAS/IML, Rick Wicklin’s new book is classical [Ref. 3]. I learned a lot by reading the free 2nd chapter online and the author’s blog. And I ordered one from Amazon and am waiting for it. Hope with it, I can delve into SAS/IML more. <br />
<br />
References:<br />
1. Jon Danielsson. ‘Financial Risk Forecasting’. Wiley, 2011<br />
2. Steven Gilbert and Ling Chen. ‘Using SAS Proc NLMIXED for Robust Regression’. SAS Global 2007<br />
3. Rick Wicklin. ’ Statistical Programming with SAS/IML Software’. SAS Publishing, 2010<br />
<br />
<pre style="background-color: #ebebeb; border: 1px dashed rgb(153, 153, 153); color: #000001; font-size: 14px; line-height: 14px; overflow: auto; padding: 5px; width: 100%;"><code>
/*******************READ ME*********************************************
* - Macros to estimate value at risk -
*
* SAS VERSION: 9.2.2
* DATE: 17jun2011
* AUTHOR: <!-- e --><a href="mailto:hchao8@gmail.com">hchao8@gmail.com</a><!-- e -->
*
****************END OF READ ME******************************************/
****************(1) MODULE-BUILDING STEP********************************;
%macro univar(data = , var = , p = , value = , filepath = );
proc sort data = &data out = _tmp01;
by &var;
run;
data _tmp02;
set _tmp01 nobs = nobs;
if _n_ = round(%sysevalf(&p)* nobs);
run;
ods select none;
proc nlmixed data = _tmp01;
parms mu 0 sigma2 1 dft 1;
y = &var;
pi = arcos(-1);
z = (y-mu)/sqrt(sigma2);
logl = lgamma(.5*(dft+1))-.5*log(sigma2)-.5*log(dft*pi)-lgamma(dft/2)
-( (dft+1)/2 )* log(1+ (1/dft)*z**2);
model y ~ general(logl);
ods output ParameterEstimates = _tmp03;
run;
proc sql;
select std(&var) into: std from _tmp01;
select estimate into :dft from _tmp03 where parameter = 'dft';
select estimate into :sigma2 from _tmp03 where parameter = 'sigma2';
quit;
ods select all;
data _tmp04;
length var_desc $30;
set _tmp02; var_value = - &var * &value; var_desc = 'Historical simulation VaR'; drop &var date;
output;
var_value = - &std * probit(&p) * &value; var_desc = 'Normal VaR';
output;
var_value = -sqrt(&sigma2) * tinv(&p, &dft) * &value; var_desc = 't-distribution VaR';
output;
run;
ods html file = "&filepath\&data..xls" gpath = "&filepath\" style = money;
title; footnote;
proc report data = _tmp04 nowd;
col var_desc var_value ;
define var_desc / 'VaR type' style(column) = [foreground=lime just=center];
define var_value / 'Value' format = dollar8.2 style(column) = [font_weight=bold] ;
run;
proc sgplot data = &data;
histogram &var;
density &var;
density &var / type = kernel;
run;
ods html close;
%mend univar;
%macro mulvar(data =, var1 =, var2 =, p =, value =, firstweight =, filepath = );
%let secondweight = %sysevalf(1 - &firstweight) ;
data _tmp01;
merge &data;
by date;
sum = &var1*&firstweight + &var2*&secondweight;
if missing(&var1) + missing(&var2) > 0 then delete;
run;
proc sort data = _tmp01 out = _tmp02;
by sum;
run;
data _tmp02;
set _tmp02 nobs = nobs;
if _n_ = round(%sysevalf(&p)* nobs);
run;
proc iml;
start Cov(A);
n = nrow(A);
C = A - A[:,];
return( (C` * C) / (n-1) );
finish;
use _tmp01;
read all var{&var1 &var2};
y = &var1 || &var2;
w = {&firstweight , &secondweight};
sigma = sqrt(t(w)* Cov(y)* w);
call symput('sigma', left(char(sigma)));
quit;
data _tmp03;
length var_desc $30;
set _tmp02; var_value = - sum * &value; var_desc = 'Historical simulation VaR'; keep var_:;
output;
var_value = - &sigma * probit(&p) * &value; var_desc = 'Normal VaR';
output;
run;
ods html file = "&filepath\%sysfunc(compress(&data)).xls" gpath = "&filepath\" style = money;
title; footnote;
proc report data = _tmp03 nowd;
col var_desc var_value ;
define var_desc / 'VaR type' style(column) = [foreground=lime just=center];
define var_value / 'Value' format = dollar8.2 style(column) = [font_weight=bold] ;
run;
ods graphics on;
ods select ContourPlot BivariateHistogram;
proc kde data = _tmp01;
bivar &var1 &var2 / plots= all;
run;
ods graphics off;
ods html close;
%mend mulvar;
****************(2) TESTING STEP****************************************;
%getr(startday = '01jan2006'd, squote = goog, filepath = c:\tmp,
rpath = c:\Program Files\R\R-2.13.0\bin);
%getr(startday = '01jan2006'd, squote = aapl, filepath = c:\tmp,
rpath = c:\Program Files\R\R-2.13.0\bin);
%univar(data = goog, var = goog_r, p = 0.01, value = 1000, filepath = c:\tmp );
%mulvar(data = goog aapl, value = 1000, p = 0.01, var1 = goog_r, var2 = aapl_r,
firstweight = 0.3, filepath = c:\tmp);
****************END OF ALL CODING***************************************;
</code></pre><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/3256159328630041416-210846694184229165?l=www.sasanalysis.com' alt='' /></div><img src="http://feeds.feedburner.com/~r/SasAnalysis/~4/gwESYyzuMc8" height="1" width="1"/> |
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