Overloading the class subscript operator to access elements of a member std::vector object

I am parsing a text based file to read variables from it. Existence of variables in the file is important, so I decided to write a template class which will hold both value of the variable (Value) and its existence flag (Exists).

template<class Type>
class MyVariable
{
    public:
        Type    Value;
        bool    Exists;
        MyVariable()
            : Value(Type()), Exists(false)
        {
        }
        MyVariable(const Type & Value)
            : Value(Value), MyVariable()
        {
        }
        MyVariable(const Type && Value)
            : Value(std::move(Value)),  MyVariable()
        {
        }
        MyVariable(const Type & Value, bool Existance)
            : Value(Value), Exists(Existance)
        {
        }
        MyVariable(const Type && Value, bool Existance)
            : Value(std::move(Value)), Exists(Existance)
        {
        }
        size_t size() const
        {
            return Value.size();
        }
        const MyVariable & operator=(const MyVariable &  Another)
        {
            Value   = Another.Value;
            Exists  = true;
        }
        const MyVariable & operator=(const MyVariable && Another)
        {
            Value   = std::move(Another.Value);
            Exists  = true;
        }
        const Type & operator[](size_t Index) const
        {
            return Value[Index];
        }
              Type & operator[](size_t Index)
        {
            return Value[Index];
        }
        const   Type & operator Type() const
        {
            return Value;
        }
                Type & operator Type()
        {
            return Value;
        }
};

The stored variable type will occasionally be std::vector, so I overloaded the subscript operator operator[] to directly access the elements of the vector. So that I can make the Value and Exists members private.

I use this class like this in the code:

const MyVariable<std::vector<int>> AVector({11, 22, 33, 44 ,55});
for (size_t i=0; i<AVector.size(); i++)
{
    std::wcout << L"Vector element #" << i << L" --> " << AVector.Value[i]  << std::endl;   // Works okay.
    std::wcout << L"Vector element #" << i << L" --> " << AVector[i]        << std::endl;   // Gives error.
}

I get the following error message:

Error C2679 binary '<<': no operator found which takes a right-hand operand of type 'const std::vector>' (or there is no acceptable conversion)

What am I doing wrong here?