A Blast From The Past
Hey Fellow Slopers,
Early last year, I posted about a hedged portfolio investing method we developed at Portfolio Armor. The basic idea was to find securities that had high expected returns over the next six months and were also relatively cheap to hedge, and then to buy and hedge a handful of those names every six months. One of you asked if I had backtested this method, and I hadn’t. So, I took a break from posting for a bit while I did that. The backtesting turned out to be a lot more time consuming than I anticipated, but it’s done and now I can share with you the results. First, a quick recap of the hedged portfolio method.
The Hedged Portfolio Method
In broad strokes, this is the process for creating a hedged portfolio:
- Calculate a potential return for every hedgeable security in your universe (the Portfolio Armor universe consists of the 3,000+ hedgeable stocks and exchange traded products traded in the U.S.).
- Calculate the cost of optimally hedging each security.
- Subtract 2. from 1. to get potential returns net of hedging costs, or net potential returns.
- Rank the securities in order of their net potential returns.
- Pick a handful of the securities with the highest net potential returns to populate a concentrated portfolio and hedge them according to the investor’s risk tolerance.
There are a few additional steps we employ to minimize cash levels and maximize potential returns, but that’s the basic idea. Below is an example of what a hedged portfolio looks like.
[image of hedged portfolio]
That one was created on August 11th, 2015, and was designed for an investor who wanted to invest $1,000,000 while limiting his downside risk to a drawdown of no more than 18% over the next six months. That portfolio includes the stocks with highest potential returns in Portfolio Armor’s universe as of that date.
It’s clear that the first step in creating a hedged portfolio, calculating potential returns, is crucial, for two reasons: first, if you can’t select securities with the potential to generate alpha, your hedged portfolio returns will lag; second, in order to know if it’s worth the cost of hedging the securities, you need to have an idea of how accurate your potential returns are. So, before backtesting the hedged portfolio method as a whole, first we backtested our security selection method.
Backtesting Our Security Selection Method
Every trading day, Portfolio Armor generates high-end estimates of how more than 3,000 stocks and exchange traded products will perform over approximately the next six months. These estimates are based on analysis of historical returns as well as option market sentiment (determined by the cost of hedging each security in various ways), which provides a forward-looking element. We call this high-end estimate a security’s potential return. Essentially, it’s how the security might perform over the next six months in a bullish scenario.
We backtested this method by running our analysis every trading day from 1/2/2003 to 10/31/2013 and then looking at the actual returns of the securities with the highest potential returns on our daily scans over the next six months. Over that 11-year period, we conducted 25,412 comparisons of our calculated potential returns to actual returns, an average of 9.4 top-ranked securities each trading day. The average potential return we calculated was 22.4%. The average actual return over the next six months, unhedged, was 6.84%. Since the average actual return was 0.3x the average potential return, we use that 0.3x multiple to derive expected returns from our potential returns. While a potential return represents a bullish upside, an expected return is the more likely result.
A subset of our top-ranked securities – 5,202 of them, or about 20% of them – had an even higher average actual return: 9.35%. All of our top-ranked securities were hedgeable with optimal collars, but the securities in this subset were also hedgeable with optimal puts (we call these AHP securities, for short). There aren’t always AHP securities available, but when there are, our portfolio construction algorithm gives preference to them proportional to their higher average returns in our tests. Specifically, we increase their potential returns by 37%, since 9.35% is 1.37x 6.84%.
The security returns mentioned above were unhedged; we also tested gross returns (i.e., not net of hedging costs) of our security selection method while hedging against greater-than-9% declines. When doing so with optimal puts, the average gross return was 12.08% over six months. The average gross return for the same securities when hedged with optimal collars capped at their potential returns was about half as much, 6.25%. This illustrates to what extent the average actual returns of the securities hedged with optimal puts were driven by outliers – securities that appreciated beyond our calculated potential returns. We adjust for the impact of potential outliers during the portfolio construction process, by only hedging with optimal collars when the net potential return is greater than 1.93x that of the same security when hedged with an optimal put (since 12.08/6.25 = 1.93).
Backtesting The Hedged Portfolio Method
To backtest the hedged portfolio method, we started searching for a hedged portfolio at each threshold on 1/2/2003. Hedged portfolios were run for six months, or until all positions had been exited, whichever came first, and then the ending dollar amount of the first portfolio was used as the starting dollar amount of the second sequential portfolio, and so on, until the end of our data series on 4/30/2014.
When there were no securities available with positive net potential returns (usually, because hedging costs were too high), the last portfolio ending dollar amount was held as cash until the start of the next hedged portfolio. During those periods, we treated the cash as if it were held in a non-interest bearing account, so the dollar amount invested remains constant until the start of the next hedged portfolio. Within hedged portfolios, residual cash positions were treated as if they were invested in a money market fund, earning the yield prevailing at the time (during much of this time period, that yield was negligible).
Within hedged portfolios, positions in underlying securities were entered at their unadjusted closing prices, with trading commissions of $7.95 deducted. To facilitate performance tracking, the dollar amounts allocated to these underlying securities were converted to the equivalent numbers of each security at its adjusted closing price on the start date of the portfolio. Underlying security positions were exited at their adjusted closing prices, with trading commissions of $7.95 deducted.
During the simulation, to be conservative, puts were purchased at the closing ask price, and calls were sold at the closing bid price; options were exited at the midpoint of the closing bid-ask spread or their intrinsic value, whichever was higher (“last” prices weren’t used because in many cases with options, the last price might be weeks old). Each time options positions were entered or exited, a trading fee of $7.95 + $0.75 per option contract was deducted (the trading fees were the ones charged by Fidelity at the time).
Results of the Hedged Portfolio Backtests
In general, the higher the threshold was, the higher the CAGR was. CAGRs ranged from 3.26% at a 2% threshold, to 11.06% at a 22% threshold. Results at those thresholds and three other thresholds in between, and interactive graphs showing hedged portfolio holdings (both underlying securities and options) at each threshold during the backtesting period, can be found at this link if you scroll down: https://portfolioarmor.com/boosting-potential-returns
Note that, to avoid survivorship bias, our universe of securities for the backtests included stocks that didn’t survive to the present, such as Lehman Brothers, Bear Stearns, etc. In fact, if you go to the 2% threshold backtest interactive graph at the link above, click to show positions, and then move your mouse pointer over the graph to 6/22/2006, you’ll see Lehman Brothers (LEH) was a holding in a hedged portfolio then.