This article analyzes why the S&P 500 Index is not a self-financed or a tradable portfolio and why it cannot be replaced with a mimicking portfolio, such as the SPDR, when applying the standard arbitrage pricing theory. In particular, we show that the nonlinear and extreme risk dynamics of the mimicking portfolio are very different from that of the S&P 500 Index. The tracking errors on the S&P 500 Index can explain the violations of the spot-futures parity and the put-call parity by the index and its derivatives, which are encountered in practice. These properties also imply that the standard pricing methods that assume the underlying asset is tradable cannot be used to evaluate derivatives written on the S&P 500 Index.
XU, P. (2014). Is the S&P 500 Index Tradable? Journal of Index Investing, 5(3), pp. 10-20.