In Part 1 of our series on risk-managed investing (RMI), we defined RMI as going beyond traditional diversification, asset allocation, and rebalancing to improve the risk/return profile of a portfolio by explicitly:
- Dampening its volatility; and/or
- Limiting its downside potential.
Both of these aspects of RMI lend themselves to direct quantification of their benefits.
If more stable returns — which enjoy both upside and downside volatility dampening — add demonstrable value as shown in Part 2, then it stands to reason that a return stream with strictly downside dampening should add even more value, as upside variations remain unimpeded. This proposition is dealt with in Part 3.
The immediate takeaway from this observation is that, in terms of percentage returns, it is more valuable to avoid a decline than it is to capture an advance of the same magnitude. Put another way, avoiding a loss is the economic equivalent of capturing a gain of even greater magnitude. This has major ramifications, which we explore below.
As the Appendix and Exhibit 5 below show, over the 78-year period from the beginning of 1936 through the end of 2013, there have been 29 separate, non-overlapping episodes of market declines that were each worse than -10%. Note that this equates to a frequency of once every 2.7 years (32 months), on average.
The average decline during those peak-to-trough periods (the red regions of Exhibit 5) has been approximately -21%, and the average length of those periods has been about seven months. Representatively, the subsequent trough-to-peak upswing (the combined light- and dark-green regions of the exhibit) has been roughly +68% cumulatively, and has lasted about 25 months (i.e., before the next -10%-or-worse downswing began). Assuming a $100.00 initial investment in this market at the beginning of a representative downdraft, it would decline to $79.00 over the first seven months, and then rebound to $132.72 over the next 25 months. Note, as a consistency check, that these figures are consistent with a long-term annual average return of approximately +11%, as cited above.
A Word about Downside Protection
Before we apply downside protection to this history and quantify its impact, it is useful to briefly discuss the nature of downside protection in a practical sense.
Typically, when downside protection is mentioned, most investors think in terms of put options. A 10% out-of-the-money put on the S&P 500 Total Return Stock Index, for example, will provide, for any loss in the index that exceeds the threshold defined by the put’s strike price (90% of the value of the index at the time the put was purchased in this case), 100% protection against the excess loss beyond that threshold. However, such a put will not provide 100% protection against the episodes we have defined above, because those episodes were defined in terms of drawdown, i.e., from peak to trough.
For a put to provide true peak-to-trough protection, the strike price would need to be continually adjusted upwards whenever the index reached a new peak, which is typically quite often. Furthermore, any time that the put was exercised (and, to provide true 100% protection, it would need to be exercised immediately on the day that the index falls -10% from its prior peak), it would need to be replaced seamlessly with another put, but this put would need to be at-the-money. The chance of needing to exercise that put in the near future is almost a certainty — at which point it would need to be replaced with another at-the-money put, and so on. This method of protection via puts (aside from being extremely expensive) is not feasible as a practical matter. So, to be realistic, we will examine forms of downside protection that provide less than 100% impact on a drawdown (peak-to-trough) basis.
Quantifying the Impact of Downside Protection
Now let us consider the impact if downside protection were applied to the episodes we identified from the return history of the S&P 500 Total Return Stock Index. Recall that the average peak-to-trough decline during those episodes has been approximately -21%, and the subsequent trough-to-peak upswing has been roughly +68%. Specifically, let us examine an RMI strategy that provides 50% downside protection against a decline threshold of -10%, that is, one that succeeds in modestly reducing the decline on the initial $100.00 investment, from -21% to -15.5% (i.e., by half the excess decline beyond -10%), net of the cost of the strategy. In this case, if the subsequent +68% upturn is unimpeded, the result after the full 32-month cycle would be $141.96, a much better result than $132.72, and one that would imply a long-term average annual return of +14% instead of +11%.
It is unrealistic to assume that an RMI strategy could successfully reduce the downside, however modestly, and not have some cost. It is useful to think of the cost in terms of a performance drag on the upside, as that is normally the way the investor would experience it. The simple 32-month model above gives us an excellent way to estimate how large that upside performance drag could be without negating the benefit of the downside protection. Specifically, if the 7-month decline on the $100.00 investment is -15.5% (net of the cost of the strategy) instead of -21%, then the subsequent 25-month bull market run need only be +57% cumulatively instead of +68% to achieve the “breakeven” value of $132.72, i.e., the value that would have been attained in the absence of the strategy.
What does the above result mean in terms of the annual tolerable cost? The annualized version of the +68% 25-month return is +28.3%, while the annualized version of the +57% return is +24.2%. The difference is 410 basis points. So, here is the result we have been seeking: an RMI strategy whose downside protection reduces only large declines in the equity markets (i.e., those worse than -10%), and reduces them only modestly (specifically, by half their excess beyond -10%), adds measurable value as long as its cost (i.e., its performance drag during bull markets) does not exceed 410 basis points per year. This kind of RMI strategy is not a stretch by any means — we believe it is quite realistically achievable. We believe that RMI strategies such as this are well worth pursuing.
To give some additional texture to this result, consider an RMI strategy that reduces the impact of portfolio downturns by 50% of the excess downturn beyond -10% (as in the example above) whose cost amounts to an annual performance drag during bull markets of 300 basis points — that is, 110 basis points better than the 410 basis point breakeven level derived above. And consider its impact over the investment horizon of a newly-married couple just leaving college. The probability of at least one spouse living into his/her late nineties is sizeable enough that prudent financial planning should consider a horizon of 75 to 80 years. If these years are anything like the last 78 years, every dollar invested by the newlyweds in the RMI portfolio will have grown to roughly 169% as much as it would have in a non-RMI portfolio over that horizon.
Generalizing the Results
Rounding out the analysis, below is a table (Exhibit 6) showing the tolerable cost of other theoretical RMI strategies that have varying levels of impact on mitigating downturns. To generate this table, we used the same simple 32-month model that we introduced in the previous section.
For example, according to this table, an RMI strategy whose downside protection reduces declines worse than -10% by three-quarters of their excess beyond -10% adds measurable value as long as its cost (i.e., its performance drag during bull markets) does not exceed 600 basis points per year.
It may seem less than rigorous to pin such an important conclusion on such a simple model of market reality. We agree. It can be dangerous to apply an operation to an average input and expect the result to be representative of what you are really after, which is the average result obtained by applying the operation to each input separately. This has been referred to as the “flaw of averages.” Therefore, in the Appendix, we take a much more painstaking approach to the issue, by building a detailed model using actual daily returns of the S&P index cited above. There, we apply the same RMI strategies as above to each of the 29 peak-to-trough-to-peak cycles in the S&P 500 Total Return Index history (each cycle with its own unique period and magnitude), and across a variety of investment horizons. Naturally, this approach leads to a range of tolerable costs for each RMI strategy. The resulting set of ranges is summarized in Exhibit 7 below.
As you can see, the results in Exhibit 7 are entirely consistent with those of Exhibit 6. In our judgment, therefore, the quantification in Exhibit 6 is robust and can be relied upon. Having said that, we want to remind readers that there were, in fact, outlier episodes with results beyond these ranges, and there is no guarantee that the next episode will not be another outlier.
It is possible to generalize the results further still. There are many ways to characterize the impact of an RMI strategy. We have chosen to use for illustration a measurement based on mitigating — to various degrees — an equity market decline beyond a -10% threshold. Other decline thresholds might be chosen and the quantification would proceed precisely along the lines we have outlined above. In Exhibit 8, below, we show the results for drawdown thresholds of -5% and -15%, in addition to the -10% threshold already discussed.
For example, by this table, an RMI strategy whose downside protection reduces declines worse than -5% by three-quarters of their excess beyond -5% adds measurable value as long as its cost (i.e., its performance drag during bull markets) does not exceed 1130 basis points per year! Some of the more effective RMI strategies we have seen fall somewhere in the lower left-hand segment of this table, i.e., they respond to declines somewhere between -5% and -10%, and they tend to offer protection of half to three-quarters of the decline beyond that point. This analysis implies that such RMI strategies could support a cost in the neighborhood of 700 basis points per year.
Some RMI techniques, however, may not lend themselves to measurement along the lines thus far described. For example, some may follow the same general risk management approach (i.e., protection beyond a threshold), but their impact may be more or less precise, or certain, than implied above. Those situations can easily be modeled following our example — that is, by applying the strategy directly to the relevant historical episodes and deriving the tolerable performance drag during the succeeding or preceding bull market period. Whichever way a particular RMI strategy may deliver its mitigating effect, we hope our quantification approach provides a useful roadmap to measuring the economic value of that effect.
Please note that the tolerable cost estimates derived through this analysis are conservative in that they focus solely on quantifying the benefits of downside protection, consistent with the focus of this section of the paper. Even RMI strategies that are aimed solely on downside protection also serve to provide a measure of volatility dampening (the focus of Part 2 of our paper) as well. But, in this section, we have not given any consideration to the additional beneficial effects outlined Part 2, such as sequence risk mitigation and tax effect considerations, nor have we reflected those outlined in Part 1, such as containment of fear, peace of mind, and quality of life. Explicitly considering these benefits would make the tolerable costs of RMI higher still. In particular, as we have noted, helping investors find the fortitude to stay true to their long-term allocation to risk assets during turbulent times may deliver the biggest benefit of all, and therefore support a tolerable cost well beyond those we have attempted to directly quantify here.
APPENDIX to Part 3 — Historical Model
To provide the raw data to support the quantitative analyses of downside protection, we compiled the history of one of the longest-recorded and most-closely-followed risk assets, U.S. large-cap stocks, as measured by the S&P 500 Total Return Index. In Exhibit 9, below, we reproduce the graph we introduced in Exhibit 5, and include below it a table which contains key information on each of the 29 non-overlapping episodes (shaded red in the graph) during which the index suffered a drawdown of -10% or worse. Specifically, for each episode, we note the date of the local peak of the index; the index value at that peak; the date of the subsequent local trough (i.e., after the -10%-or-worse decline); the index value at that trough; the length of drawdown (peak-to-trough) period; the percentage drawdown; the date of recovery (when the index re-achieves its prior peak); the length of that recovery period; the recovery percentage; the date of the next local peak (i.e., just prior to its beginning its next -10%-or-worse decline); the index value at that peak; the length of cyclical bull (trough-to-peak) period; and, finally, the percentage increase during the bull period. Note that the recovery period is a subset of the bull period (in terms of the graph, the recovery period is shaded light green, and the bull period is the combined light- and dark-green-shaded sections). Note also that the figures in red at the end of the table denote that the final bull period is not yet complete — we simply terminated the series at 12/31/2013.
The detailed table in Exhibit 9 allows the evaluation of any number of RMI strategies. We can apply a given RMI strategy to each episode separately, calculate its impact, summarize the results over several episodes, and draw conclusions.
Consistent with the main text, let us first focus on an RMI strategy that is successful in reducing the impact of a drawdown by half of its extent beyond -10%, net of the cost of the strategy. For example, a -30% drawdown would be reduced to -20%, a -20% drawdown would be reduced to -15.5%, and a -10% drawdown would be reduced not at all and remain at -10%. In Exhibit 10, we apply this strategy to each of the 29 episodes. It is a straightforward matter to then calculate the tolerable performance drag during the subsequent bull period of each episode, such that the resulting performance over the episode’s full cycle is no worse than would have been the case without the RMI strategy. These calculations are spelled out in the notes to Exhibit 10. Column H of the exhibit shows the tolerable performance drag for each episode in isolation. Since the length of each episode’s full cycle is generally much shorter than a typical investor’s investment horizon, we show the results of successive rolling-five-episode periods in column I. From column I, we derive the 25th and 75th percentiles shown in Exhibit 7 of the text.
We performed similar analyses for RMI strategies that provide different levels of protection (namely, 25% and 75%) of the drawdown below -10%, and for drawdown thresholds of degrees other than -10% (namely, -5% and -15%). These calculations are not reproduced here, but are straightforward versions of those just described, and the results are summarized in Exhibits 6, 7 and 8 of the text.
Note that we have not included an RMI strategy that protects 100% of the downside below -10% (or below any other threshold, for that matter). This is because we believe that 100% protection on a drawdown basis is not a practical possibility, for reasons cited in the main text.
In the text (and in Exhibits 6 and 8), we estimated that a particular RMI strategy — i.e., one that reduces equity market declines by half of the excess decline below -10% — adds value as long as its “cost” (performance drag during bull markets) does not exceed 410 basis points per annum.
Exhibit 11 shows the “payoff profile” of such an RMI strategy whose cost is precisely 410 basis points. On the left side of the graph, we plot — for each of the 29 drawdowns in our historical record — the net returns of a portfolio with this RMI strategy (in red), compared to the corresponding returns of the same portfolio without the strategy (in blue). On the right side of the graph, we plot — for each of the 29 subsequent bull periods — the annualized returns of the corresponding portfolios.
In our final graph, in Exhibit 12, we show the cumulative performance (on log scale) of the same two portfolios described immediately above.
Source: Giralda Advisors analysis of Bloomberg daily return data
- Columns A, C, and E are from Exhibit 9
- Column B is derived by applying the RMI strategy to column A
- Column D is calculated as (using Excel notation): (1+C)*((1+A)/(1+B))-1
- Columns F and G are annualized versions of columns C and D, respectively. E.g., column F is calculated as: (1+C)^(250/E), since there are approx. 250 trading days per annum
- Column H is the difference between columns F and G, expressed in terms of basis points per annum
- Column I is the rolling-five-episode average of column H
Disclosures: This document is for informational use only. Nothing in this publication is intended to constitute legal, tax, or investment advice. There is no guarantee that any claims made will come to pass. The information contained herein has been obtained from sources believed to be reliable, but Giralda Advisors (“Giralda”) does not warrant the accuracy of the information. Consult a financial, tax or legal professional for specific information related to your own situation.
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 In defining each non-overlapping episode, we first required the index to reach its prior peak. For example, the drawdown of -17% in July/August 2011 was not counted as a non-overlapping episode because the index had not yet reached its prior peak. If such overlapping episodes had been counted, there would have been even more than the 29 we examine, and the conclusions we reach in this paper would have still stronger support.
 Does the average 32-month term of the full cycle sound short? It initially did to us. But if it were any longer, there could not have been 29 of them in the last 78 years.
 Using Excel notation: ((1 - 0.21)*(1 + 0.68))^(12/32) - 1 ≈ 0.11
This is, in fact, how the representative trough-to-peak upswing of +68% was derived.
 There exist, in concept at least, such instruments as “Russian options” and “exotic look-back options” that are constructed along these lines but, to our knowledge, there do not exist viable liquid markets for such instruments. In contrast, RMI strategies that deliver protection of less than 100% are indeed feasible — examples include those described in our earlier writings such as “Dynamic Asset Allocation: Using Momentum to Enhance Portfolio Risk Management” (Journal of Financial Planning, February 2012) and “Integrated Tail Risk Hedging: The Last Line of Defense in Investment Risk Management” (Journal of Financial Planning, June 2012).
 Using Excel notation: (((1-0.155)*(1.283-0.03)^(25/12))/((1-0.21)*(1.283)^(25/12)))^29 = 1.69
 See, for example, The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty, Sam Savage, Wiley (2012), in which examples are cited such as how one can drown in a river with an average depth of three feet, and why a drunk staggering down the middle of a busy highway remains alive if you consider only his average position.
 For example, an episode with a shallow decline below -10% and an exceptionally long subsequent bull market period would lead to a tolerable cost that would be at the low end of the range.
 Source: Bloomberg
 The “payoff profile” graph is commonly used in visualizing various option strategies (calls, puts, collars, straddles, etc.), and we assume the reader is familiar with its interpretation.