This is the second post in the series I’m writing to introduce the VIX Portfolio Hedging (VXH) Strategy. I am discussing the problems with conventional portfolio hedging methods first – before getting into the details of the VXH strategy – because if widely-known conventional methods are suitable, then there’s little reason why anyone should consider a novel method. The two conventional hedging methods I’ll review are diversification (Modern Portfolio Theory), and portfolio insurance using long put options and option collars. I’ll conclude with a comment about some of the recent portfolio hedging offerings from major banks and other institutions.
1. Diversification (Modern Portfolio Theory)
The promise of diversification and Modern Portfolio Theory (MPT) was that we could increase our expected returns by diversifying capital among non-correlated assets. Why risk everything on one or two stocks, when you can hold five hundred? By contemporary standards, Markowitz’s intuition may seem quaint, but despite the explosion in specialized fund and ETF offerings, not much has changed since 1952. Sure, whereas your grandfather diversified by buying both IBM and GE, you would be scandalized to find a portfolio without emerging markets exposure. But maybe that’s because large-cap U.S. stocks stopped moving quite so independently, and diversification had to be sought elsewhere. The investment product industry entered its baroque period at the peak of the credit bubble (PowerShares Lux Nanotech, anyone?), is probably now on the decline, and the credibility of MPT seems to have fallen in tandem.
There are plenty of critiques to choose from, but to me the most general one seems best, which is that there are more things in heaven and earth than are dreamt of in the expected return variables of MPT and CAPM. Measurements of variance are all right if they cover the real distribution of possible outcomes, but in a world fortunate enough to have had David Hume, why would anyone ever think that they do? Empirically, the rates at which assets will change relative to one another are unstable, with correlations most famously “going to one” in a crisis. The time series 2007-2008 does most of the work for critics of MPT, and I can’t improve on these charts from Doug Short (click to enlarge):
When the protection sought from diversification by sector, size, and geography fares so poorly under crisis conditions, investors can be forgiven for doubting whether diversification is worth the trouble at all. They would be wrong, I think, as the only alternative to diversification would appear to be picking assets on their own individual merits, without regard for portfolio effects. And having a concentrated portfolio could easily have yielded the same tragic consequences in 2008, as Markowitz et al. pointed out in a recent response to critics. But even if there’s no obvious alternative to diversification, we can still look for non-correlated components (like volatility-qua-asset) that will perform well when everything else falls together.
But why focus only on the crisis? The high correlations across assets during the reflationary rally of 2009 are just as problematic for friends of diversification, and perhaps more so. Crises are occasional, and as upsetting as they are, we know generally what they look like. But the idea of a “new normal” in which everything is one big correlated risk-on / risk-off trade flattens the efficient frontier into a linear function of your leverage.
It’s because of the rebound – not just the crisis – that I suspect that the addition of volatility as an asset class may be much more than an incremental revision to the reigning dogma. If stocks, commodities, and real estate can all conceivably move together as a matter of course, they function ultimately as one giant bet that Modern Portfolio Theory is true. A steady allocation to long volatility positions is an (at the very least, implicit) admission that something beyond the ken of CAPM-generated prices will have a significant impact on the performance of a conventional portfolio – it hardly matters whether that something is the irrationality studied by behavioral psychologists, the tectonic rumblings noted by keen macroeconomists, or the end of cheap, dense energy projected by the handful of uncompromised industry analysts.
Markowitz et al.’s response to all of this is that if you’re worried about something unforeseen happening, you should reduce your risk:
At any time we should make our best estimates for “the next spin of the wheel,” and then choose an appropriate point from the implied risk-return trade-off curve. [...] If the market goes up dramatically, those with high beta portfolios will be happy; if it goes down they will be sad. “You pays your money and you takes your choice!”
I’m not trying to disrespect a Nobel prize-winner, but this strikes me as unresponsive, avuncular tripe. The problem is not that prices sometimes fall; it’s that, for many investors, the diversified portfolios they held in 2007 fared far worse in 2008 than they had reason to expect, and that the persistently high correlations among equities give rational investors serious pause about the value of diversification in the future. Back-slapping assurances about the proper distribution of eggs in baskets do nothing to alleviate those concerns.
2. Portfolio Insurance – Puts and Collars
Portfolio insurance strategies were developed in the late 1970s and early 1980s to provide institutional investors with a guaranteed return and reduced uncertainty, and coincided with the creation of options exchanges. See Bouyé 2009 for an overview of the history and types of portfolio insurance. I’ve tested three such strategies here:
- Long ATM 1-year puts: Given a starting $500,000 portfolio allocated to the SPDR S&P 500 ETF (SPY), buy at-the-money (ATM) put options expiring in one year and hold through expiration. Rebalance the SPY shares after expiration to account for any realized gains or losses, and re-hedge.
- Long 10% OTM puts: Given a starting $500,000 portfolio allocated to the SPDR S&P 500 ETF (SPY), buy 3-month put options with a strike price 10% below the current SPY price and hold through expiration. Rebalance the SPY shares after expiration to account for any realized gains or losses, and re-hedge.
- Zero-cost collars: Given a starting $500,000 portfolio allocated to the SPDR S&P 500 ETF (SPY), buy 3-month zero-cost collars with a long put strike price 10% below the current SPY price and a short call strike price set at the highest level that brings in sufficient credit to offset the price of the put. Hold through expiration. Rebalance the SPY shares after expiration to account for any realized gains or losses, and re-hedge.
Option trades included commissions of $1.25 per contract per side. Options were sold at the bid and bought at the offer, i.e. slippage is already included. Option profits and losses were recorded at expiration and divided retroactively among each day of the period (this allowed for smoother and more realistic equity curves than if profits or losses were simply recorded at expiration). SPY prices were not adjusted for dividends. I selected the first strategy to examine the value of the simplest hedging strategy I could conceive. For the last two strategies, I selected the 10% OTM put strike price as hopefully marking a realistic balance between likely investor sensitivity to hedging costs and willingness to realize large portfolio losses over any three-month period. I realize that more sophisticated strike selection criteria are obvious and desirable. But even strategies this simple are probably optimistically defined as “conventional”: quarterly put-buying and option collars are still out of reach for many investors, who have neither the time, skills, or discipline to create and manage their own portfolio insurance.
Equity curves are shown below for SPY and for the hedged portfolios (click to enlarge). Data are from CSI and thinkorswim.
The quarterly 10% OTM put-hedged portfolio had the worst performance overall, with lower returns during rising markets and surprisingly little benefit from hedging during the financial crisis. The zero-cost collar, as one might expect, substantially reduced the costs of hedging in most situations while offering lower portfolio volatility and a smaller maximum drawdown. The simplest strategy – the 1Y ATM long puts – performed the best, offering some substantial protection during the crisis. Relevant statistics are provided in the table below.
It is safe to conclude that simply buying 10% OTM puts each quarter is a non-starter. However, even the collar strategy and one-year puts provided little more than a smoothing effect. We could modify the zero-cost collar by selecting a put strike that is closer to the money, but to retain the zero-cost structure a nearer short call strike would also be required, and this would have the predictable effect of forcing the hedged portfolio to sit out a larger share of strong bull markets.
Despite their protective advantage, long-dated at-the-money put options are very expensive, and the 1Y ATM put-hedged portfolio was actually the worst performer through the end of 2007; notably, it has also given up nearly all of its relative gains versus the other portfolios during 2010, confirming (in my view) that despite its superior performance in this test, this strategy will underperform the others significantly in the absence of crisis conditions. The principal disadvantages of longer-term options as portfolio hedges are that 1) they are more expensive, since the implied volatility of options increases with time, and 2) they introduce more path or strike dependence into the hedge, meaning that there is increased uncertainty about the effectiveness of the hedge at preserving capital and profits. The choice between short- and long-dated options should be viewed on a continuum, with short-term options imposing higher transaction costs and greater time decay and long-term options imposing higher implied volatility costs and increased path dependence. The nature of the underlying portfolio to be hedged may have some bearing on the appropriate hedge duration, but I would expect these relative disadvantages to equal out over time, such that varying the time to expiration will be no panacea.
3. Structured Offerings
Deutsche Bank, PIMCO, and numerous smaller firms are now offering hedge funds and structured products to satisfy the demand for tail risk insurance. While no strategist is going to disclose key program details, I don’t get the sense from any of the coverage I’ve seen that this new crop of tail risk funds is doing anything particularly nuanced when it comes to capital allocation. If that’s the case, investors who are prepared to pay a small premium for protection each year might need to reset their expectations, since buying the same amount of insurance at the inception of a bull market that you might buy at the start of a bear market will create a substantial drag on returns. If the problem with MPT and conventional option strategies is that they are cheap to implement but don’t work well enough, these new offerings may work, but will probably not be cheap to implement. There is also a hidden and difficult-to-calculate disadvantage to any expensive portfolio hedging method: the probability that some human decision-maker will halt an otherwise effective hedging method increases with the cost of the method.
For some recent media coverage of the turn toward tail risk insurance, see:
Preparing for the Next ‘Black Swan’ – WSJ, 8/21/10
The Big Boys Discover Options – Barron’s, 9/4/10
Taleb’s Pessimism Lures CIC – WSJ, 8/22/10
China Eyes the Black Swan Protection Protocol – Felix Salmon, 8/24/10
After reviewing the performance of Modern Portfolio Theory-inspired and options-hedged portfolios over the last several years, I see little reason for investors to be content with conventional hedging strategies. Diversification offered no protection against the financial crisis of 2007-2008, and as more markets become fully exposed to international capital flows, the search for non-correlated assets will only become more difficult. Conventional options strategies were able to provide significant downside protection, or minimal lag during bull markets, but not both. To achieve effective protection without incurring undue costs in normal market environments, a strategy with a little more sophistication is required.