Is diversifying your portfolio by adding volatility as an asset a good idea?

In portfolio theory we teach students that investing in different assets improves the performance of portfolios due to the diversification effect. This effect works best if the correlation between assets is low or even negative.

Unfortunately, the correlation between assets, especially stocks, is quite high nowadays making it difficult to benefit from diversification. One asset being highly negatively correlated with the stock market is volatility. The most famous volatility Index is the VIX® Index which “is a key measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices.” The correlation between the VIX and the S&P 500 is about -0.74 from the beginning of 2007 until today. So, it might be a good idea to add the VIX to your portfolio because of diversification, right?