[c#] Binding ComboBox SelectedItem using MVVM

I have a problem with the SelectedItem in my ComboBox.

<ComboBox Name="cbxSalesPeriods"
        ItemsSource="{Binding SalesPeriods}"
        DisplayMemberPath="displayPeriod"
        SelectedItem="{Binding SelectedSalesPeriod}"
        SelectedValuePath="displayPeriod"
        IsSynchronizedWithCurrentItem="True"/>

If I open the ComboBox, I see the values.

If I select an item, the selected Item won't be shown.

Has anybody an idea?

In my ViewModel I have these two properties:

public ObservableCollection<SalesPeriodVM> SalesPeriods { get; private set; }

private SalesPeriodVM selectedSalesPeriod;
public SalesPeriodVM SelectedSalesPeriod
{
    get { return selectedSalesPeriod; }

    set 
    {
        if (selectedSalesPeriod != value)
        {
            selectedSalesPeriod = value;
            RaisePropertyChanged("SelectedSalesPeriod");
        }
    }
}

These are a few properties from the class :

public SalesPeriodVO Vo
{
    get { return period; }
}

public int Year
{
    get { return period.Year; }
    set
    {
        if (period.Year != value)
        {
            period.Year = value;
            RaisePropertyChanged("Year");
        }
    }
}

public int Month
{
    get { return period.Month; }
    set
    {
        if (period.Month != value)
        {
            period.Month = value;
            RaisePropertyChanged("Month");
        }
    }
}

public string displayPeriod { 
    get
    {
        return this.ToString();
    }
}

public override string ToString()
{
    return String.Format("{0:D2}.{1}", Month, Year);
}

EDIT: The Following happens If I remove the Property DisplayMemberPath:

<!-- xaml code-->
    <Grid>
        <ComboBox Name="cmbData"    SelectedItem="{Binding SelectedstudentInfo, Mode=OneWayToSource}" HorizontalAlignment="Left" Margin="225,150,0,0" VerticalAlignment="Top" Width="120" DisplayMemberPath="name" SelectedValuePath="id" SelectedIndex="0" />
        <Button VerticalAlignment="Center" Margin="0,0,150,0" Height="40" Width="70" Click="Button_Click">OK</Button>
    </Grid>



        //student Class
        public class Student
        {
            public  int Id { set; get; }
            public string name { set; get; }
        }

        //set 2 properties in MainWindow.xaml.cs Class
        public ObservableCollection<Student> studentInfo { set; get; }
        public Student SelectedstudentInfo { set; get; }

        //MainWindow.xaml.cs Constructor
        public MainWindow()
        {
            InitializeComponent();
            bindCombo();
            this.DataContext = this;
            cmbData.ItemsSource = studentInfo;

        }

        //method to bind cobobox or you can fetch data from database in MainWindow.xaml.cs
        public void bindCombo()
        {
            ObservableCollection<Student> studentList = new ObservableCollection<Student>();
            studentList.Add(new Student { Id=0 ,name="==Select=="});
            studentList.Add(new Student { Id = 1, name = "zoyeb" });
            studentList.Add(new Student { Id = 2, name = "siddiq" });
            studentList.Add(new Student { Id = 3, name = "James" });

              studentInfo=studentList;

        }

        //button click to get selected student MainWindow.xaml.cs
        private void Button_Click(object sender, RoutedEventArgs e)
        {
            Student student = SelectedstudentInfo;
            if(student.Id ==0)
            {
                MessageBox.Show("select name from dropdown");
            }
            else
            {
                MessageBox.Show("Name :"+student.name + "Id :"+student.Id);
            }
        }

I had a similar problem where the SelectedItem-binding did not update when I selected something in the combobox. My problem was that I had to set UpdateSourceTrigger=PropertyChanged for the binding.

<ComboBox ItemsSource="{Binding SalesPeriods}" 
          SelectedItem="{Binding SelectedItem, UpdateSourceTrigger=PropertyChanged}" />