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Math Matters: Rethinking Investment Returns & How Math Impacts Results8Exhibit 3Source: diyinvesting.orgNow imagine a large drawdown due to a bearmarket instead of the smooth, no volatility growthseen in Exhibit 3. Anything that causes a “reset”to a lower level, such as a large downturn in theportfolio, will weaken the eventual compoundreturns. This principle is strongly interconnectedwith the second factor, the value of avoiding largelosses. These two factors go hand in hand. Thepower of compounding, crucial to successfullong-term returns, can be better utilized whenavoiding large losses.2. The Value of Avoiding Large Losses“What do you call a market down 90%? It is amarket that was down 80%, and then got cut inhalf from there.” – Meb FaberLarge losses can be incredibly painful in the shortterm, but even more dramatic is the impact on thelong-term success of investment returns. Thereare many studies that show the value of avoidinglarge losses as well as studies that show howbehavioral bias contributes to people continuallyand frequently participating in large losses.Research has shown that most individuals arerisk avoiders when handling gains and risk takerswhen dealing with losses (Tversky and Kahneman,Judgment under Uncertainty: Heuristics andBiases, 1982). Tversky and Kahneman had peoplereceive 1,000 with the choice of a guaranteedgain of 500 or a 50% chance of a 1,000 gain.Over 80% chose the 500 guarantee, with fewwilling to take the risk of additional gain. On theother hand, in the second part of the experiment,people were given 2,000. They were then giventhe alternatives of a 50% chance of losing 1,000or a 100% chance of losing 500. Around 70%chose the chance of losing 1,000, with fewunwilling to avoid the risk of a larger loss. Theresults of the experiment indicated people tendto do the following when it comes to investing:Swan Global Investments 970-382-8901 swanglobalinvestments.com

Math Matters: Rethinking Investment Returns & How Math Impacts Resultsthey don’t let their profits run and they fail to cuttheir losses short. The reverse of this psychologyis necessary to be a successful trader or investor.As Warren Buffett once famously said regardingthe rules of investing: “Rule #1: Never lose money.Rule #2: Never forget rule #1.”It is of course challenging for investors to avoidlarge losses. It is hard-coded in our DNA. Thisbehavioral bias is called the disposition effect. Thedisposition effect is a behavioral bias wherein aninvestor exhibits reluctance to realize losses, asseen in the aforementioend experiment. Investorstend to sell winners too early and ride losers toolong, hoping that they might eventually turn intoa gain. Studies by Shefrin and Statman (1985),Barberis and Xiong (2009), Odean (1998), andWeber and Camerer (1998), to name a few, haveshown this disposition effect evident in investors’behavior. This is despite the fact that large lossescan occur much more quickly than large gains.9As the Oracle of Omaha once said: “It takes 20years to build a reputation and five minutes toruin it. If you think about that, you’ll do thingsdifferently.”In the same vein as Buffett’s quote, you couldreplace the word “reputation” with “portfolio”,since large losses can quickly and disastrouslywipe out years of investment growth. With thatin mind, you SHOULD do things differently andalways address and define risk in such a way thatlarge losses do not occur, or at least occur lessfrequently. For example; a solid 8% a year meansyou can double your money in 9 years (rule of72). But if you take a 50% loss in year 10, youwould be right back to where you started and theannualized return over those years would be 0%.Crestmont Research, in a thought provokingwhite paper entitled “Half & Half: Why RowingWorks”, graphically displayed the dynamic of theOne Really Bad Year Can Erase Many Good Years of Gains13%8% 8%8%8%8%8%8%8%8%0.0%0%-13%-25%-38%-50%-50%Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 Yr 6 Yr 7 Yr 8 Yr 9 Yr 10 AnnualizedExhibit 4Source: PIMCO and Swan Global Investmentsgains necessary to offset losses. As the lossesincrease, the required gain to recover your lossesexponentially increases. The exponential powerof large losses really starts to take effect after-30% to -40%, as seen in Exhibit 5.One key takeaway from this graph: avoidinga loss is the equivalent of capturing a gainof greater magnitude. This is why investorsshould consider the statistical measurementsof upside and downside capture for a strategy.Swan Global Investments 970-382-8901 swanglobalinvestments.com

Math Matters: Rethinking Investment Returns & How Math Impacts Results10THE IMPACT OF LOSSESWhy The First Rule Of Investing Is Also The Second Rule.1000%900%800%700%600%900%KEY POINTSAvoid Losses: the gain required to recover from a loss is exponential;likewise, a relatively smaller loss can erase big gains.Memorable Declines: what gain does it take to recover from these losses?Dow1929-1932 -89%NASDAQ 2000-2002 -78%S&P 500 1973-1974 -48%S&P 500 2007-2009 -57%S&P 500 2000-2002 -49%Next.-?%Note: "Dow" is the Dow Jones Industrial Average; Declines are peak to trough during the years 33%Gain Percent11%25%43%67%100%150%LOSSLoss ht 2009-2010, Crestmont Research (www.CrestmontResearch.com)Exhibit 5Source: Crestmont ResearchIn many cases, too much focus is mistakenly puton the upside capture statistic. Although upsidecapture is necessary, it is not nearly as importantas the downside capture of an investmentstrategy. Crestmont provides another graphic thatillustrates this key point incredibly well and tiestogether these first two factors of compoundingreturns and avoiding large losses:“The stock market is much more volatile thanmost investors realize. Two volatility gremlins– the disproportionate impact of losses and thefriction loss form the dispersion of returns –significantly reduce the compounding of egies recognize this dynamic and seekto enhance investors’ compounded returns byproviding a more risk-managed and consistentreturn profile. “Capture” is one way to measureand illustrate the effectiveness and benefit of thisapproach. Whereas the ‘relative return’ investor(tracking stock market indexes) will generallyexperience 100% of the downside and 100% of theupside to achieve market returns, the ‘absolutereturn’ investor only needs a fraction of the upsidewhen downside losses are limited. This graphillustrates just how little of the upside is neededSwan Global Investments 970-382-8901 swanglobalinvestments.com

Math Matters: Rethinking Investment Returns & How Math Impacts Resultsto match stock market returns over time and itdemonstrates the way that many absolute returnstrategies exceed stock market returns withouthaving to “beat-the-market” each year.”11What this graph indicates is that if you weresomehow able to miraculously avoid participationduring down months in the stock market, you wouldonly have needed to get 26% of the gains duringthe up months in order to match the market overCAPTURE!: "ACHIEVE RETURNS", NOT "BEAT-THE-MARKET"(percent of gains needed to meet market returns: 50 years 1966-2015)GAINS(this is the required % of gains in up monthsneeded to match stock market 6%20%10%0%0%20%40%LOSSES60%80%100%(if the portfolio experiences this % of losses in down months in the stock market)Copyright 2006-2016, Crestmont Research (www.CrestmontResearch.com)The stock market is much more volatile than most investors realize. Two volatility gremlins--the disproportionate impact ofExhibit6lossesand the friction loss from the dispersion of returns--significantly reduce the compounding of returns. Many absoluteSource:Crestmont Researchreturn-orientedinvestment strategies recognize this dynamic and seek to enhance investors' compounded returns byproviding a more risk-managed and consistent return profile. "Capture" is one way to measure and illustrate theeffectiveness and benefit of this approach. Whereas the 'relative return' investor (tracking stock market indexes) willgenerally experience 100% of the downside and 100% of the upside to achieve market returns, the 'absolute return' investora fractionof the upsidereturnwhen downsideThe graph aboveillustratesinvestingjust how littleisofnotthe trying tothat onlytimeneeds(9.48%annualizedfor thelossesDJIAare limited.to successfullong-termupside is needed to match stock market returns over time and it demonstrates the way that many absolute return strategiesTotalexceedReturnor 9.47%for thewithoutS&P 500TotalReturn).findyear.the hottest performer to get great up marketstockmarket returnshavingto "beat-the-market"eachIf participation in the down months was 40%, thenparticipation, but minimizing or avoiding losses!Copyright 2006-2016, Crestmont Research (www.CrestmontResearch.com)only capturing 55% in the up months would beHow big of a difference can avoiding large lossesneeded to match the market. This comes as anmake over the long-term?astonishing realization to most investors; a definiteExhibit 7 highlights the amazing impact avoidingreason to rethink the math behind investments. Solarge losses can have over time when comparedmany investors fall into the bad habit of hoppingto a buy and hold strategy. A 100,000 investmentfrom one investment to another, chasing marketin the Dow Jones Index in 1950, if left alone, wouldperformers trying to “beat the market”. The keySwan Global Investments 970-382-8901 swanglobalinvestments.com

Math Matters: Rethinking Investment Returns & How Math Impacts Results12Exhibit 7Source: WBI Investmentshave grown to an astounding 8.9mm by the endof 2014 (8900%). However, if only the ten worstquarters in the Index were avoided across the256 quarters over that time period, the final resultwould have been 612% more capital or 63.4mm(63,400% compared to 8900%)! Avoiding periodsof large decline can have an enormous impacton returns (and peace of mind). Although it isimpossible for any equity strategy to completelymiss the ten worst quarters in the market overa long timeframe, it is possible through properhedging or other various strategies to miss out onparticipating in some of the downside associatedwith the worst performing quarters in the market,and thus, in essence, “miss” some of thosequarters. Even if this means missing out on fullparticipation in some of the best quarters, missingthe worst quarters has a much greater impact onan investor’s bottom line. If all of the worst and bestquarters were completely missed, an investor stillends up with an amount 40% higher than a buyand hold investor ( 12.4mm). This is due to thepower of compounding and avoiding the power ofnegative compounding.By design, Swan’s Defined Risk Strategy wasmeant to minimize losses. This is especiallyimportant for those investors in the retirementstage who are drawing down their accounts tofund living expenses. And the DRS has beenable to minimize losses by always being hedged.Across 222 months of the DRS since its inceptionthrough the end of 2015, the S&P 500 has had 30months of losses greater than -3.5%, or around14% of the time. The DRS by comparison hashad only 14 or 6% of months with losses greaterthan -3.5% in a month, cutting the occurrencesin half. As it relates to the DRS’s capture ratio ofup/down quarters, the DRS has captured around52% of positive quarters in the S&P 500 and 13%of negative quarters. As seen in Exhibit 6, thisshould and did lead to better results than the S&P500 over the long-term and full market cycles.Exhibit8showshowthemarkethasperformed since the DRS’s inception in1997 versus the DRS and a hypotheticalinvestment that systematically captures 52%of up quarters and 13% of down quarters.Swan Global Investments 970-382-8901 swanglobalinvestments.com

Math Matters: Rethinking Investment Returns & How Math Impacts Results13S&P 500 TR vs Alternative Up/Down Capture 5,000,000 4,500,000 4,000,000 3,500,000 3,000,000 2,500,000 2,000,000 1,500,000 1,000,000 500,000 -S&P 500S&P 500 w 52% up and 13% downSwan DRSExhibit 8Source: Zephyr StyleAdvisor and Swan Global InvestmentsNotice this hypothetical shift in the mathematicalreturns nicely outperforms the S&P 500 most ofthe period after some underperformance during abull market in the early years. The DRS itself hasdone even better than the hypothetical example.The hypothetical case was calculated by applyinga 52% capture ratio to every up quarter and a 13%capture ratio to every down quarter, whereas inreality the DRS’s capture ratios vary on a quarterto quarter basis - sometimes better, sometimesworse - and this of course varies its path.largest calendar year loss over that sametimeframe was -37%. In fact, the S&P 500 had fouryears with annual returns worse than the DRS’sworst loss year over the same time period.Expanding the timeframe further out over its 18 years, the largest one-year calendar loss for theDRS equaled -5.38% (all results representedby the DRS Select Composite). The S&P 500’s“Too often, investors are so focused onthe task at hand that they can lose sight oftaking the actions that are necessary to bestMany times, the challenge with investors isgetting them to think of investments in relation totheir time horizon and goals. The longer the timehorizon, the more important these math principlesbecome. By the same token, emotions like fearand greed become less important. Crestmont’s EdEasterling states it this way:Swan Global Investments 970-382-8901 swanglobalinvestments.com

Math Matters: Rethinking Investment Returns & How Math Impacts Resultsachieve their goals. With investments, the goalis to achieve successful returns over time. Weshould not be distracted by a focus on this weekor month; we need successful returns over ourinvestment horizons—which often extend for adecade or two or more.”How can an investor know whether an investmentstrategy will truly be able to avoid large losses?Managers can call themselves “risk-managed” or“tactical”, but that does not mean their strategywill successfully avoid large losses. Managerscan either actively structure a strategy to seekto avoid large losses by defining risk through anon-correlated asset such as options, or theycan attempt to avoid large losses through markettiming or passive diversification (undefined risk).Based upon the examples discussed previously,it makes sense for the majority of an investor’sportfolio to be constructed of investmentsthat actively seek to avoid large losses. Moreaggressive strategies can be beneficial in theproper place, amount, and time, but the bulk of aninvestor’s portfolio should not be in investmentsthat can experience large losses. This is part ofthe shortcoming with today’s popular portfoliomanagement approaches based on ModernPortfolio Theory (the investment driving forcebehind fast-growing robo-advisors and target datefunds). These approaches seek to put investors ina majority of passive index investments or activeequity managers and another large percentagein fixed income investments, despite increasinglylow or negative yields around the globe. Althoughsome diversification is provided, both of theseasset classes have experienced large lossesin the past and likely will in the future. Thisapproach doesn’t take into consideration thesevarious factors behind growing long-term wealth;traditional investment management needs torethink the math and risk behind their investmentstrategies and think outside the (style) box.3. Variance Drain (Volatility)If someone were to tell you the market hasaveraged roughly 9.5% per year since 1928, youwould want that investment, right? But how manyyears did the market actually have a return in the149%-10% range? The answer might be surprising.Over the last 87 years, in only 2 years was themarket return near its long-term average returning9 or 10% and only 4 years within 2% (7.5-11.5).More often than not the market’s return in anygiven year was much greater or less than 9.5%and sometimes dramatically so. And that is theproblem with averages. Averages, by their verynature, mask volatility. And when it comes tocompounding returns, volatility and the sequenceof returns is very important to the final outcome.In reality, not everyone wants an investment thatgrows at an average 9.5% if it involves multiple-40% to -80% drawdowns and sometimes decadesof negative return in order to get it.This is another reason why defining downsiderisk is so important. Lowering volatility is key toachieving better compound growth as volatilitydiminishes the rate at which an investment growsover the long-term. Volatility has a measurablenegative effect on returns because of its impacton compounding.This impact is known as variance drain orvolatility drag. When two investments with thesame average return are compared, the one withthe greater volatility, or variance, all other thingsbeing equal, will have a lower compound return.This is due to the effect of negative compoundingon the more volatile investment.The concept of variance drain or volatility dragcomes from the term “arithmetic mean - geometricmean inequality” and was detailed in a 1995paper titled “Variance Drain - Is Your ReturnLeaking Down the Variance Drain?” by TomMessmore. Messmore observed that the morevariable a given asset’s return is, the greater thedifference between the arithmetic and geometricreturns. Arithmetic mean is the average of aset of numerical values, calculated by addingtogether and dividing by the number of terms inthe set. Geometric mean is defined as the valueof a set of numbers by using the product of theirvalues, as opposed to the arithmetic mean whichuses their sum.Swan Global Investments 970-382-8901 swanglobalinvestments.com

Math Matters: Rethinking Investment Returns & How Math Impacts ResultsA formula of variance drain looks like this:15 (100% - 50%) / 2The geometric return over 2 years is 0% or 100(final value) - 100 (starting value) In this example, the variance drain is 25% 25%(arithmetic average) - 0% (geometric average).This formula shows that the variance of returns“drains” the arithmetic average returns to producethe smaller, realized, compound returns (Source:Decker, Robert: The Variance Drain and Jensen’sInequality).Why should this matter for investors? In orderto optimally take advantage of the power ofcompounding, investors must avoid large lossesand the exponential growth needed to recoverfrom a loss. And in addition, investors must avoidthe negative power of compounding by seeking tolower volatility drag as best as possible. Exhibit 9shows this impact across various scenarios.rg geometric return, ra arithmetic return,its varianceAs an example, let’s say an investment ispurchased for 100. At the end of the first year,its value ha

rotation, and stock-picking through the benefits of a hedged equity strategy. However, there are a lot of misconceptions amongst investors as it relates to equity investment returns, hedged equity returns, and the math behind them. Many investors make their investment decisions based upon emotions like fear and greed. They