Many people have asked me recently why interest rates continue to grind lower. As can be seen in Figure 1 below, when viewed over the course of 3 decades, interest rates have declined almost linearly since 1982. In fact, the same trend holds true for many western countries. Why might that be the case? .error { color: red; } (function(vegaEmbed) { var spec = {"

The Sharpe Ratio is one of the most common performance metrics for both individual stocks and portfolios. However, a more natural choice for a portfolio performance metric is the ratio of the expected return to some Value-at-Risk of the return distribution, which can be characterized as a Generalized Sharpe Ratio i.e., $$ GSR \equiv \lim_{\alpha \to 0} \frac{\mu}{V_\alpha(\mu=0,\sigma,s,k,…)} $$ where \(V_{\alpha}()\) is the Value-at-Risk, \(\alpha\) is the probability threshold and \(\mu\), \(\sigma\), \(s\), etc.

Introduction Traditional portfolio theory employs an optimization strategy that involves maximizing a expected portfolio’s Sharpe Ratio given asset Sharpe Ratios and a correlation matrix. Levy and Duchin (2009), however, demonstrate that optimal weights don’t significantly outperform a naive 1/N optimization strategy. The problem with weights is that they are heavily dependent on Sharpe Ratio estimatation. If a stock has a 0.99 correlation versus the market and has the highest Sharpe Ratio amongst all assets under consideration, then portfolio optimization would suggest that 100% of the portfolio should be in that single asset.

In Theory There are two common models of conceptualizing the risk associated with a stock: The Margin of Safety Principal popularized by Benjamin Graham Asset returns volatility The former can be characterized as a subjective assessment of how much downside risk is associated with a stock. In other words, it’s a consideration of the potential losses if an investor’s thesis is incorrect and/or if the worst case scenario is realized.