The St. Petersburg Paradox: To Hedge or Not to Hedge

As SPX bounced back from the bear territory, the market is split about the future. Yardeni is already seeing a bottom while Roubini calls that ‘delusional’. Thus the question: to hedge or not now? Mark Spitznagel from Universa provides interesting insights in his latest book Safe Haven, investing for financial storms: safe haven investing not only lowers risk but also LIFTS wealth and the Buffett-esque value effect of buying during/after crash is not statistically significant. In this light, seeking protection now seems advisable, both strategically and tactically. A simple safe haven strategy is examined for main street investors.

Bulls and bears getting further apart

Since the previous two publications, SPX dipped into bear market territory in June and bounced back this month. And bulls and bears become increasingly vocal.

Dr. Yardeni, who nailed the market bottom in 1982 and 2009, is already calling a bottom. Dr. Roubini, who predicted the 2008 Global Financial Crisis, calls that ‘delusional’ and sees a ‘stagflationary debt crisis’ instead. JPMorgan bets inflation has peaked and a Fed pivot can help market rebound in H2 2022. Morgan Stanley considers it too early for Fed to stop tightening. Bears see ‘recession’ from two negative GDP prints. Bulls respond ‘who-cares’ with eyes on hot labor market and healthy consumers.

To hedge or not to hedge

Hence the dilemma: to seek safe haven before/during a Roubini-type crisis? Or to leave the safe haven to catch the Yardeni-type rebound? Security has to at the cost of investment return, right?

This is not new. Back at the bottom of the 2020 pandemic, CALPERS made the headline by exiting a portfolio hedge managed by Universa just a few weeks before the pandemic hit and missing the $1 billion payout. CALPERS justified it by the constant fee drag, which cost $140 million (or 0.04%) of total returns in FY 2019.

The debate continued. Mark Spitznagel runs the above Universa and argues in his 2021 book, Safe Haven: investing for financial storms, that safe haven investing can lower lower risks and INCREASE wealth. Very intriguing indeed: no alpha sacrifice necessarily.

St. Petersburg Paradox: standalone loss can lead to wholistic gain

Spitznagel illustrate the point via the St. Petersburg Paradox. Simplified details here:

A merchant buys commodities in Amsterdam to sell in St. Petersburg for a profit.

- beginning saving = 3,000 rubles

- net profit from the trade if successful = 10,000 rubles

- net profit from the trade if experiencing accidents (pirates/weather/etc) = 0 rubles

- probability of accidents = 5%

- insurance premium against accidents = 800 rubles/ trip

On a standalone basis, the insurance is not worth it:

expected value of insurance = 95% * (-800) + 5% * (10,000-800) = -300

However, buying this loss-making insurance actually increases the expected ending wealth in the long term:

Expected ending wealth without insurance = (3,000+10,000)^(95%)*(3,000)^(5%) = 12,081 rubles

Guaranteed ending wealth with insurance = 3,000 + 10,000 – 800 = 12,200 rubles

As Spitznagel points out there is nothing magical but everything mathematical:

- focus on geometric average rather than arithmetic average when forming expectations

- focus on the severe damage from disastrous returns when compounding

- focus on the whole rather than the summing parts

Therefore, safe havens may cost investors on a standalone basis but can INCREASE long term wealth with lower risks, in principle at least.

Warrent-Buffett-Effect: buying during/after the crash?

Now we have experienced a bear market in June, is it too late to seek safe havens? Spitznagel did a simple test in his book: the conditional average 1-year, 5-year, 10-year SPX returns following any year that SPX is down 15% or more are not statistically different from the corresponding unconditional 1-year, 5-year and 10-year returns.

This suggests that the need for safe haven is not weakened after the current market correction, esp. if we are investing for the long term.

From the theory to the real world: what safe haven to seek?

Spitznagel examines many of the popular safe havens. Though most show up as not cost effective, gold and US 20-year treasury bonds seem the best among them with caveats. Gold stands out mainly because of the 1970-80s and 20-year Treasury is barely cost-effective. Readers are free to follow the same methodology to test their own preferred safe haven universe.

Safe haven for the main street

If there is one thing that both bulls and bears would agree, it is that market volatility will probably stay elevated. It follows that any outsized market selloffs, even if recovered, will make wealth appreciation more challenging. Because that requires more outsized (arithmetic) gains to compensate. This alone makes the need for safe havens evident.

At the same time, any cost-effective (lowering risk while adding return) safe havens are unlikely to be accessible to main street investors. What is the second-best option?

Here we examine a simple safe haven investing strategy: fully invest in S&P 500 and hide in Treasury bills during storms.

- stay fully invested during normal times

- hide in 3-month treasury bills when things look stormy. ‘Stormy’ periods are the time when the drawdown from market high-water-mark (as defined by rolling 5-year total return index) exceeds 15%

- rebalance portfolio monthly

Scoreboard:

Key findings:

Not surprisingly, this is not a ‘cost-effective’ safe haven (without using leverage): it lowers risks but at the expense of lower returns. However, for the main street investors with limited resources, the trade-off may be worthwhile.

Return sacrifice amounts to 1.2% a year, but the risk mitigation is much more impactful: worst drawdown is cut by more than half, from 82% to 33.9%. Volatility comes down more than return does and Sharpe ratio is improved. (Not to mention investors sleep better as well.)

A technical note. Transaction cost is ignored, and the 3-month T-bill data starts only from 1954. The former overstates Simple Haven performance while the latter understates. Net-net, Simple Haven may do even better than in the above experiment.

Investing is about making trade-offs, intelligently preferably.