How to get SELECT @@Identity to work, without generating the "String index out of bounds" error?

@@IDENTITY is not valid in Access. Is your db Access or SQL Server?  and where are you executing this statement from?
if you have an Access front end linked to SQL back end then you need to create a "pass through" query to SQL in order to use @@IDENTITY.
An Access query to linked tables in SQL will not work here.

Support for @@Identity was introduced to Access 2000 with Jet 4's ANSI SQL-92 extensions.
The attached snippet is a working example from Access 2003 using ADODB

I think that the problem you have might be a missing alias in your Select @@Autonumber, try this:

                // Fetch the new Rebalancing ID.
                SQLQuery = "SELECT @@IDENTITY AS RebalanceID"
                SQLrs = SQLStatement.executeQuery(SQLQuery) ;
                SQLrs.next() ;
                Long RebalancingID = SQLrs.getLong("RebalanceID") ;

Function InsertRecord(FirstName As String, LastName As String) As Long
 
Dim cn As ADODB.Connection
Dim cmd As New ADODB.Command
Dim rs As New ADODB.Recordset
 
Set cn = CurrentProject.Connection
 
With cmd
    Set .ActiveConnection = cn
    .CommandType = adCmdText
    .CommandText = "Insert INTO Employees(Lastname, FirstName) Values('" & LastName & "', '" & FirstName & "')"
    .Execute
    rs.Open "Select @@Identity as NewID", cn, Options:=adCmdText
    InsertRecord = rs("NewID")
End With
End Function

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>Support for @@Identity was introduced to Access 2000 with Jet 4's ANSI SQL-92 extensions.
oops, i had no idea. i take back what i posted earlier.

>>oops, i had no idea
That was something I learned here @ EE also.  I was quite surprised when I first read it -- and pleased!

"Select @@Identity" doesn't include a valid column name, so Access will create one - Expr1000 in the following example (again ADO in Access 2003):
     rs.Open "Select @@Identity", cn, Options:=adCmdText
     debug.print rs.Fields(0).Name
Expr1000
There is no automatic retrieval of the actual column name.

Trying to refer to this via any other field name will throw a "member not found in collection" error in VB.
"String Index Out of Range -1" sounds very much like the Java equivalent, which is why I suspect that the column name is the problem.
The alternative way of retrieving a field from a recordset is via its index (at least in ADO and DAO) as I did in the snippet above. Try this:

                Long RebalancingID = SQLrs.getLong(0) ;

One other comment:
>>>SQLrs.next() ;
DAO and ADO automatically position on the first record of a recordset, does JDBC not do that?

>>>Long RebalancingID = SQLrs.getLong(0) ;

The error condition "String index out of range -1" has already happened prior to the column-name reference.  It happens with the attempt to execute SQLrs = SQLStatement.executeQuery(SQLQuery) .  However, in my VB .NET 2007 code, I do have to execute the RebalancingID = CLng (drSQL.Item(0)) statement, where drSQL is declared as an OleDbDataReader.

Incidentally, the SQLrs.next() statement is definitely required to position at the first record of the result set in JDBC.

Ahh - I should have re-read your post after looking at the snippet, you did say that the execQuery statement had failed
Glad you found a work round :-)
Cheers,
Mike