java secure client socket authentication

For secure server sockets in order to send the server certificate, all I do is initialize SSLContext with a KeyManagerFactory.getKeyManagers() that has been initialized with my keystore.
But how can I do this in client side?
I.e. for client I do:

System.setProperty("javax.net.ssl.keyStore", "clientKeystore.keystore");
System.setProperty("javax.net.ssl.keyStorePassword", "secret");
System.setProperty("javax.net.ssl.trustStore", "clientKeystore.keystore");
System.setProperty("javax.net.ssl.trustStorePassword", "secret");
SSLSocketFactory factory = (SSLSocketFactory) SSLSocketFactory.getDefault();
SSLSocket socket = (SSLSocket) factory.createSocket("localhost", 7890);

I use the same keystore as trust store. I assume that just for looking arround JSSE it is ok.
Problem is that I get in the server part (I have setNeedClientAuth in the serversocket to true).

Exception in thread "main" javax.net.ssl.SSLHandshakeException: null cert chain

So how am I supposed to configure the client side to send a certificate?Isn't the system properties a correct approach?
Because I do not see how the SSLContext can be used in client side.

Thank you!