Moving averages are well-understood and easily calculated – they take into account one asset at a time and produce one value for each time period.  Moving correlations, unlike moving averages,  must take into account multiple assets and produce a matrix of values for each time period.  In the simplest case, we care about the correlation between two assets – for example, the S&P 500  (SPY) and the financial sector (XLF).  In this case, we need only pay attention to one value in the matrix.  However, if we were to add the energy sector (XLE), it becomes more difficult to efficiently calculate and represent these correlations.  This is always true for 3 or more different assets.

I’ve written the code below to simplify this process (download).  First, you provide a matrix (dataMatrix) with variables in the columns – for example, SPY in column 1, XLF in column 2, and XLE in column 3.  Second, you provide a window size (windowSize).  For example, if dataMatrix contained minutely returns, then a window size of 60 would produce trailing hourly correlation estimates.  Third, you indicate which column (indexColumn) you care about seeing the results for.  In our example, we would likely specify column 1, since this would allow us to observe the correlation between (1) the S&P and financial sector and (2) the S&P and energy sector.

The image below shows the results for exactly the example above for last Friday, October 1st, 2010.

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I normally don’t delve too much into the programmatic details of my work, but I’ve seen enough interest in this topic that I figured I’d lend a helping hand to those fellow frustrated souls.

There are a few awkward, non-native MEX implementations of various database interfaces.  However, Matlab has its own database toolbox built around ODBC/JDBC, and when developing distributable software, one always hopes to minimize third-party library usage.  As a result, I’ve put a good deal of effort into integrating Matlab with both MySQL and SQLite.  In fact, the data for every post on this site is stored in a 2GB MySQL database server running on my laptop.

As you can see, this requires only that you distribute the platform-independent JAR.  No DLLs, no MEX compilation.

% Database Server
host = 'localhost';

% Database Username/Password
user = 'user';
password = 'password';

% Database Name
dbName = 'assets'; 

% JDBC Parameters
jdbcString = sprintf('jdbc:mysql://%s/%s', host, dbName);
jdbcDriver = 'com.mysql.jdbc.Driver';
% Set this to the path to your MySQL Connector/J JAR
javaaddpath('mysql-connector-java-5.1.6-bin.jar')
% Create the database connection object
dbConn = database(dbName, user , password, jdbcDriver, jdbcString);
% Check to make sure that we successfully connected
if isconnection(dbConn)
    % Fetch the symbol, market cap, and last close for the 10 largest
    % market cap ETFs
    result = get(fetch(exec(dbConn, 'SELECT info.symbol,info.marketcap,series.close FROM info, series WHERE info.type=''ETF'' AND info.id = series.symbolid AND series.date = ''2008-04-11'' ORDER BY marketcap DESC LIMIT 10')), 'Data');
    disp(result);

% If the connection failed, print the error message
else
    disp(sprintf('Connection failed: %s', dbConn.Message));
end

% Close the connection so we don't run out of MySQL threads
close(dbConn);

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Kaplan and Knowles, extending the original work of Shadwick and Keating as well as that of Kazemi, Schneeweis, and Gupta, describe a generalized downside risk-adjusted measure Kappa.  By design, the Omega and Sortino measures are special cases of the Kappa measure, and, as such, the Kappa function is capable of calculating both easily.

So that this very helpful function can be used by those in the community who are having difficulty with the original works, I am publishing a single-line Kappa function for Matlab.

% D : return series vector
% r : return threshold
% n : Kappa order
function k = kappa(D, r, n)
k = (mean(D) - r) ./ nthroot(mean((D < r) .* (r-D).^n), n);

To calculate the Omega measure, put n=1 and add 1 to the result, i.e. kappa(D, r, 1) + 1.

To calculate the Sortino ratio, put n=2, i.e. kappa(D,r,2).

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