#Quant Invest Chicago: Make diversification your beta

Steve Sapra, Managing Director at TOBAM North America, gave this presentation at Quant Invest Chicago. He spoke on breaking down all aspects of diversification. Portfolio weights are a function of beliefs in expected returns; however, in the absence of conviction, the only solution is to diversify. The Anti-Benchmark is an approach that seeks maximum diversification. Using volatility and correlations, we calculate the most diversified portfolio and the global minimum variance portfolio. Calculate the correlation between the assets and the portfolios. The MDP is unbiased towards any factors.

The diversification ratio measures the diversification of a portfolio across sources of risk, not individual stocks, calculated by dividing the weighted average of the stock’s volatilities by the portfolio volatilities. The higher the DR, the more diversified the portfolio. If you buy the S&P 500, you are buying  2 risk factors, based upon the calculation of DR for the index. Maximizing the number of degrees of freedom in the portfolio via DR brings us closer to the tangency portfolio.  Traits of the process include: the MDP is exposed to the largest number of risk factors possible and the MDP is more correlated to the stocks it does not hold than to those it does.

The Anti-Benchmark is the tangency portfolio; we assume all expected Sharpe ratios are the same.  If all expected returns are the same, then the GMV portfolio is the tangency portfolio. Cap weighted indices, while generally accepted as a proxy for owning the market, is a biased allocator of risk, not neutral, due to the bias towards the largest stocks. Alpha of the market index is negative when measured vs a neutral risk allocation.

For more information, check out Quant Invest Chicago.