The Black Swan Index Revisited

Dec. 19, 2019 5:38 PM ET 
Amplify ETF Trust - Amplify BlackSwan Growth & Treasury Core ETF (SWAN)
(After my previous article, I was asked to rethink my position.
I took a look at expanded data but come to the same conclusion.
SWAN is a balanced portfolio with a caveat.
There can be a place for SWAN for very risk-averse investors.
A few days back I posted an article, The Black Swan Index - A Balanced Portfolio in Hiding where I said I could not recommend Amplify BlackSwan Growth & Treasury Core ETF (SWAN). I could not recommend buying the ETF for 2 reasons.

2. An investor could replicate the index for very little, likely less than the fee on the ETF.
3. Further, I likened its performance to a balanced portfolio. A balanced portfolio that could be achieved for less in fees than the SWAN ETF.

Professor William Trainor, an author on the paper the index and ETF are based on, pushed back on the second point. He didn’t feel the portfolio should be compared to a balanced portfolio. We had an offline conversation and he pointed me to the backtested index returns dating from 2006 to present. I promised him an update, so here it is.
Still a Balanced Portfolio with a Caveat
There is no denying that the presence of call options in the portfolio reduces the downside risk of SWAN. No dynamic trading is required, the options have a floor beyond which you cannot lose money. This can be seen in the graph I posted on the original article.

Below a certain level, the payoff function turns flat and the option strategy cannot lose further value. The options are worthless, or near worthless, and all the value of the portfolio is in the bonds. At a high level, SWAN has a 10% holding in options and a 90% holding in bonds. Drops in the stock market can only wipe out value held in the options.
However, a balanced stock/bond portfolio has negatively correlated assets. We expect the value of bonds to rise when stocks fall. This, along with a not excessive stock exposure, will limit the downside of a balanced portfolio. That’s really the point of both strategies.
Using the index data available here, I calculated the daily returns for the index. Because the index is unmanaged, there are no trading costs or fees in the returns. I don’t have a good way to adjust for trading costs, but I expect them to be low. We do know that SWAN has a 0.49% annual fee. I broke this down into a daily fee and took that out of each day’s return.
I then used total return data from the S&P 500 ETF (SPY), the Short Treasury ETF (SHY), and the Long Treasury ETF (TLT) and I constructed a balanced portfolio. I used the same ratios as my article (55/22.5/22.5 – SPY/SHY/TLT) to approximately match the SWAN exposure. I label this “Balanced” in the following tables and graphs.
The table below shows the realized annual return, standard deviation, and Sharpe Ratio for SWAN, SPY and Balanced:

SWAN and Balanced have very similar annualized returns and risk.
However, risk is not just standard deviation. Behavioral research shows that investors are likely to sell after large drawdowns. Famous research by Kahneman and Tversky show that we feel the pain of loss much greater than the joy of winning. Therefore, we should look to REDUCE drawdown risk (exactly what SWAN attempts!).
Here are the top 3 drawdowns for each strategy:

During the global financial crisis, SPY famously fell over 50%. During that time, SWAN would have lost 13% while the Balanced Portfolio lost 27%.
Here is the caveat – in times of historic market drawdowns, SWAN will protect you from the largest drawdown.
However, look at the other drawdown periods, especially the 2018 bear market that saw SPY lose nearly 20%. SWAN lost 11% while Balanced lost 10%. Their drawdowns were nearly the same in a very bad market!
Let’s dig a bit further. Here is the total return of each strategy going back to 2006:

You can see the 2007-2009 period where SWAN and Balanced sidestep the epic crash. SWAN does better and that causes cumulative outperformance until Balanced and SPY catch up in the mid-2010s. SPY continues to pull away and we can see that huge drawdown at the end of 2018.
Here is the global financial crisis by itself. This graph is until the date that SPY breaks even, October 2007 - October 2012 – 5 years!

No surprise here. SWAN and Balanced look pretty good. But what if we look at the recovery out of the bottom (March 2009 – October 2012)?

SPY rockets off the bottom. That’s expected; it went down the most, so it had to grow the most to get back to even in 2012. Balanced outperforms off the bottom. Most of this occurs in 2009 where SWAN actually draws down while Balanced is growing.
Here is the 2018 drawdown (September 2018 – April 2019):

This graphs shows what we knew. SPY draws down about 20% which SWAN and Balanced drawdown about 10%. Again, Balanced grows out of the drawdown faster than SWAN.
Why does Balanced grow faster than SWAN off the bottom?
The reason is based on option pricing mechanics discussed in detail in the original article. At the bottom of the drawdown, SWAN and Balanced will have the lowest exposure to stocks. SWAN’s exposure will be less than that of Balanced. The DELTA of the option falls faster than the exposure in Balanced.
This makes sense. Remember the payoff graph above. The slope of that line is the exposure to stocks and the SWAN graph becomes flat. Balanced only has 0 exposure to stocks with stocks fall 100% (hopefully not something we see SPY do, ever).
Here is a chart of exposure to stocks during a drawdown:

So Balanced has more exposure and we can expect it to outperform SWAN during a recovery, purely on that fact alone.
The 2009 recovery starting in March was unfortunate for SWAN. The drop in stocks had wiped out all the value of the options position. SWAN was left with only bond exposure until it rebalanced in June. In the chart of the global financial crisis above, you can see that SWAN trades sideways to down (long bonds fell in value during this time) from March until June, when the rebalancing finally gives it exposure to SPY. The fact Balanced retained an exposure to equities is why it outperformed.
Takeaways
I reiterate that I cannot recommend SWAN. My reasoning stands as before, you can get similar performance in a balanced portfolio, for a smaller fee.
The one reason to hold SWAN is the outside chance we have a drawdown much like the global financial crisis. In that case, SWAN will better protect your assets. However, events with a super large drawdown are very rare. In the 13 years of data in this study, it happens once. In more normal market corrections, even large ones like 2018, you are better off in a balanced portfolio.
If you fear a 2008 style event, then SWAN is a completely viable option. You can run the strategy yourself, making trades twice a year with less expenses than SWAN. If you want someone to do it for you, then SWAN is your vehicle to do it.