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 Portfolio Construction Based on Management of Tail Risk
4.1.1 Case Study: SPY vs Bitcoin MDDs
To showcase the importance of looking at risks and rewards in context of one-another, we compare GEV- modeled 90- day MDDs of SPY to those of Bitcoin (BTC). Figure 11 shows that BTC is far more likely to incur large MDDS than SPY is, with the largest observed BTC MDDs approaching 70%, nearly double the largest SPY MDD of approximately 35%.
4.1.2 Case Study: SPY vs 60/40
The classic 60/40 portfolio – composed of 60% large- cap equities and 40% bonds – is a classic investment strategy that has been employed for decades, partic- ularly for long-term investments such as retirement funds. The 60/40 rule-of-thumb very nearly maximizes the Sharpe ratio over the last twenty years when com- pared to other passive strategies containing these two asset classes. It minimally sacrifices the expected re- turn of an all-equities portfolio while greatly reducing volatility.
We compare SPY against a 60/40 portfolio of SPY and TLT, an ETF providing exposure to long-term (20+ year) U.S. Treasury bonds, modelling the 90-day MDD distributions of these two strategies with using historical data from 2002 to 2020. As we can see from Figure 13, 60/40 is able to successfully manage the risk of small MDDS, which is in line with its ability to reduce bulk fluctuations in the form of volatility. While the largest realized MDD of the 60/40 portfolio is much smaller than that of SPY, there is insufficient evidence that the 60/40 portfolio is able to reduce the tail risk of extremely large MDDs. This is indicated by the significant overlap between our confidence bands in this region.
Figure 13: GEV-modeled 90-day MDDs of SPY and the 60/40 portfolio. 60/40 is able to reduce the occurrence rate of small MDDs, but significant overlap of the confidence intervals in the tails indicates that 60/40 may not be able to reduce the risk of these extreme drawdowns.
Re-scaling the 90-day MDDs by the 90-day expected return of each portfolio, the differences between their risk/reward profiles further disappears. Figure 14 still shows some ability of 60/40 to manage small MDDs, but the confidence bands begin to overlap even in this region. This analysis reinforces our claim that optimizing the volatility-reward trade-off is an insufficient approach to risk management. Volatility-minimizing portfolios may be able to manage some short-term risks, but we find insufficient evidence of their ability to man- age long- term tail risks. These tail risks are particularly relevant to the retirement investors that a 60/40 strategy may be marketed towards: we note that MDDs at the 1% probability level are expected to occur once in any 100 90-day periods, or approximately once in every 25 years.
 Figure 11: GEV-modeled 90-day (quarterly) MDDs for SPY and BTC. BTC appears far more risky, exhibiting larger MDDs with far higher probability.
To put this risk in context, we examine the same graph, but we now re-scale the 90-day MDDs by the 90-day expected return of each portfolio, simply estimated by their historical averages. Historical averages are independently computed for each block-bootstrap sample, allowing the confidence bands to accurately reflect the additional variability due to fluctuations in quarterly return rates over the historical period. In this case, BTC in fact looks favorable to SPY, rarely exhibiting 90-day MDDs more than twice the 90-day average return rate, while SPY 90- day MDDs are frequently more than four times its 90-day average returns. This analysis is not entirely conclusive due to the significant overlap in confidence bands, but in contrast to examining we certainly cannot conclude that BTC is more “risky" than SPY when contextualized in this manner.
  Figure 12: GEV-modeled 90-day (quarterly) MDDs for SPY and BTC, re-scaled by average 90-day returns. This re-scaling shows that SPY has larger drawdowns relative to its average realized rate of return over the same periods. We note that the
overlapping confidence bands indicates a degree of uncertainty in this comparison.
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