In SharePoint 2013 the Sign in as a Different user menu item is not default present. Here is how to configure it back within five minutes:

Go to the welcome.ascx file in ‘”15Hive”\TEMPLATE\CONTROLTEMPLATES’:

Add the code below to the welcome.ascx file in whichever place you prefer (i.e., in what order you want the link to appear).
<SharePoint:MenuItemTemplate runat="server" ID="ID_LoginAsDifferentUser"
Text="<%$Resources:wss,personalactions_loginasdifferentuser%>"
Description="<%$Resources:wss,personalactions_loginasdifferentuserdescription%>"
MenuGroupId="100"
Sequence="100"  UseShortId="true" /> 

Refresh and voila: