In a previous post, we discussed using Sharpe ratios, normally a metric of return efficiency, to evaluate loss probability.  Specifically, we discussed computing the probability adjusted average losses from Sharpe ratios as a methodology to compare downside risk in different strategies.

At Newfound, we’ve recently been working on a white paper that outlines a framework for determining whether including an a given alternative asset class, option strategy, or tactical model into our portfolio, with an eye towards loss mitigation, is worth the fee charged.  To put these varying strategies on an equal field, we consider the effective annual cost of an option strategy overlaid onto our original portfolio that would create an equivalent amount of risk management.  Specifically, we are interested in converging our probability adjusted average loss (P(x < 0) * CVaR(0)).  We deduce a formula that gives us the probability with which we should employ an ATM put option.

Below is an example monte-carlo simulation for monthly returns for three strategies.  The dark blue is the returns of our original portfolio.  The orange is our new portfolio.  The light blue is our original portfolio with our option overlaid.  Our computed probability of employing a the put option is 46.43% (i.e. choose a random number between 1 and 1000 every month; if the number is less than 4643, buy an ATM put option to cover 100% of our portfolio).

We find that the probability-adjusted average loss is -1.339%, -0.0477% , and -0.0402%, respectively, showing convergence in our new portfolio and the original portfolio with the option overlay.

In this specific example, we increased our Sharpe ratio from 0.3 to 0.7.  To achieve the same left-tail risk management that the Sharpe ratio provided, we would have to employ an option strategy that costs, on average, 3.19% a month.  So long as the strategy we are adding to our portfolio to achieve the new Sharpe level costs less, we would argue that from a risk management perspective, the purchase is worth it.

Look for our white paper in the next couple of weeks.

### Corey Hoffstein

Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients. Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of \$10bn. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.