Insert not inserting in property : <p>Insert not adding to variable in property</p>

<pre><code>private string _DirectoryList = "";
public string DirectoryListAdd
        {
            get { return _DirectoryList; }
            set
            {
                    _DirectoryList.Insert(0, value + Environment.NewLine);
                    OnPropertyChanged("DirectoryListAdd");
            }
        }

public MainWindow()
        {
            InitializeComponent();
            DirectoryListAdd = "a";
            DirectoryListAdd = "b";
            Console.WriteLine(DirectoryListAdd);
        }
</code></pre>

<p>This is returning "". I wouldve expected it to return</p>

<pre><code>a
b
</code></pre>
