The Power of Math + Time

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The Power of Math + Time

2019-11-15T12:35:54-05:00By |

Two of the most common themes in intelligent investing are the difficulty of “beating the market” and the folly of setting that as your investment goal. The troupe is so ubiquitous it’s almost cliché. The message goes like this: Start investing early and the power of compounding returns over time will build wealth. It won’t be “getting rich quick” and it almost assuredly will not “beat the market”, but you will benefit from that consistent approach – because the powerful forces of math and time are on your side.

In this world view, you don’t know when the market will go up/down – but to the extent that the technology/productivity in the world economy is increasing, over a long enough timeframe the expectation is that the market will go up and you will benefit from being invested. So, if this is the winning formula, why devote all this time to reading/learning about investing, much less writing/educating about it? An article by Meb Faber caught my attention with an intuitive message, wrapped in a title evocative enough to jump off the page and smack me in the face – ‘Nobody Wants to Invest in Your Shit’.

Human emotions like Fear and Greed make it difficult for investors to stay the course and be content with Market returns. My “AHA!” moment from the article was the distillation that readers only care to devote their time to your work, if you provide guidance on one or more of the below questions.

  1. Does the new fund improve the absolute returns of my portfolio?
  2. Does the new fund reduce the risk of my portfolio?
  3. Does the new fund improve the chances of my sticking to my plan?
  4. Does the new fund reduce the cost or [increase] tax efficiency of my portfolio?

Therefore this is no longer an article I’m writing, it’s a pact. In return for the attention you are investing, it’s incumbent on me to address the above questions in a way that delivers value.

Challenge Accepted.

The Difficulty of Beating The Market

The 2017 SPIVA U.S. scorecard (which is the defacto scorekeeper of active vs passive debate) reported that the S&P 500 (The index I am referring to when I say “The Market”) outperformed 92.3% of Large Cap US managers over a 15-year period. A staggering number to be sure and gives credence to the notion that in absence of non-public data, low cost ETF exposure to the market is an attractive way to invest. But what makes the S&P 500 so hard to beat? The answer is not cut and dry – most likely a combination of fees, trading costs and the double edge sword of human discretion; relative to the clinical efficiency of a Cap Weighted Index which happens to perform exceptionally well when leaning into the momentum of paradigm shattering companies/industries – with long runs of outperformance. When the efficiency of Cap Weighted investing is referenced, it is referring to operational efficiency and while that contributes to keeping trading costs and taxes low, allocating capital to companies simply because they are large (essentially Buying High and Selling Low) should create some offsetting investment inefficiency which can be exploited.

Exploiting Inefficiencies

The S&P 500 Equal Weight Index (SPEW) was originally launched in 2003 with the official S&P DJI back-test to 12/31/1996. Over that time period (see Exhibit 1) an Equal Weighted Index of the same 500 companies, provided significant outperformance of SPX – alongside some additional volatility. The SPIVA information demonstrated the difficulty of actively picking subsets of a universeto consistently outperform the whole. Here is a situation in which selling the winners/buying the losers to parity across the entire benchmark universe on a quarterly basis, provided enough relative excess investment return to more than make up for the additional operational cost associated with rebalancing.

Exhibit 1

Note: S&P EWI has an index launch date of 1/8/2003 and is licensed and calculated by S&P Dow Jones Indices and all information for the Indices prior to its Launch Date is back-tested by S&P DJI, based on the methodology that was in effect on the Launch Date. Standardized performance can be found by clicking S&P EWI

What accounts for this consistent overperformance? Well herein lies the dirty little secret of Cap Weighting – it definitionally and systematically over-weights, overvalued companies. It is impossible to know ahead of time which companies are the overvalued ones, but over time the investor takes the mathematical loss.

When viewed through this lens, it’s apparent that exploiting the allocation inefficiency of Cap Weighting through Equal Weighting is only a half measure.

The opposite of “Cold” isn’t “Room Temperature”, it’s “Hot”.

Reverse Cap Weighted Index (Reverse), which as the name implies – reverses the order of the S&P 500 through weighting by 1/Mkt Cap, takes exploiting that inefficiency one step further. In direct contrast to Cap Weighting, Reverse definitionally and systematically over-weights, undervalued companies. Again, it’s impossible to know ahead of time which companies are the undervalued ones, but over time the investor gets the mathematical win. More information on Reverse Cap Indexing can be found here.

What Drives This Phenomenon?

Exhibit 2

To explore this effect, we can look at constituent level comparisons between the Cap Weighted and Reverse Cap Weighted S&P 500. The bars to the left of the vertical red line (in Exhibit 2 above) represent the number of S&P 500 constituents (over two thirds!) that contributed more profit (or less loss) to Reverse (vs SPX) while a member the S&P 500 between 2008 and 2017. The area in which SPX excelled, was through continued outsized performance from a relatively small number of very large companies, depicted in that skinny tail on the right. However, the pool of companies that performed better when Reverse Weighted was over twice as large, more than making up for those handful of “Big Winners”. All contribution data for this study (including the annualized risk/return figure above) was pulled from Morningstar. While difficult to predict ahead of time which companies were overvalued and which were undervalued, Exhibit 2 quantifies the mathematical Win/Loss associated with the two strategies over time.

Cumulative and Annualized Results

Exhibit 3

Note: S&P EWI has an index launch date of 1/8/2003 and Reverse has an Index launch date of 10/23/2017. Both Indices are licensed and calculated by S&P Dow Jones Indices and all information for the Indices prior to its Launch Date is back-tested by S&P DJI, based on the methodology that was in effect on the Launch Date. Standardized performance for S&P 500, S&P EWI, and REVERSE can be found by clicking the respective link.

Exhibit 3 shows the annualized risk/return of the three S&P weighting iterations we discussed and not surprisingly, the relationship holds – The more one tilts the math to overweighting, undervalued companies across the S&P universe, historically resulted in additional return alongside some additional volatility. The relationship between these three is key, each index is licensed and calculated by S&P DJI and always holds the same 500 underlying stocks. In environments in which SPEW outperforms SPX, we would expect Reverse to outperform both and in environments in which SPX is the best performing, we would expect Reverse to be the weakest.

Below is a cumulative chart of the three indices from 12/31/96 to 2/28/19.

Exhibit 4

Note: S&P EWI has an index launch date of 1/8/2003 and Reverse has an Index launch date of 10/23/2017. Both Indices are licensed and calculated by S&P Dow Jones Indices and all information for the Indices prior to its Launch Date is back-tested by S&P DJI, based on the methodology that was in effect on the Launch Date. Standardized performance for S&P 500, S&P EWI, and REVERSE can be found by clicking the respective link.

The above chart is just another demonstration of the systematic differences resulting from overweighting over/undervalued companies in the relative weighting schemes, and how drastic the compounded effects can be over time.

So with all this information, why is Cap Weighting still thought of as the gold standard of passive investing? My sense is that allocators feel like going into a Cap Weighted Index is the default and any alternative weighting scheme is therefore an active decision. Our first instinct is to avoid decisions, because the fear of loss often stings more than the joy of gain. To a rational investor it should be clear that allocating via Cap Weighting is just as much a choice as any other method and in accepting that, take time to understand the benefits/drawbacks of other available options. Ultimately the investment case for alternatively weighted S&P 500’s, relies on capturing investment efficiencies that outweigh the operational efficiencies provided by Cap Weighting. Being able to do so while utilizing the same universe of securities to which most investors benchmark and with systematic rebalances through the nature of the index itself, increases the chances of successfully sticking to the plan. Investing to secure one’s financial future can feel overwhelming, but alternatively weighting S&P 500 exposure as a piece of one’s US Large Cap allocation can be a simple way to leverage the power of Math and Time in your favor.

 

Disclosure: The Reverse Cap Weighted U.S. Large Cap Index (Reverse) is a rules-based reverse capitalization weighted index comprised of the 500 leading U.S.-listed companies as measured by their free-float market capitalization contained within the S&P 500 universe. The Index has an inception date of October 23, 2017, with a back tested time-series inception date of December 31, 1996. You cannot invest directly in an index.

The S&P 500 Index is a widely recognized capitalization-weighted index of 500 common stock prices in U.S. companies. You cannot invest directly in an index.

The S&P 500 Equal-Weight Index is the equal-weight version of the widely-used S&P 500. The index includes the same constituents as the capitalization weighted S&P 500, but each company in the S&P 500 EWI is allocated a fixed weight – or 0.2% of the index total at each quarterly rebalance. You cannot invest directly in an index.

The Reverse Cap Weighted U.S. Large Cap Index (the “Index”) is the property of Exponential ETFs, which has contracted with S&P Opco, LLC (a subsidiary of S&P Dow Jones Indices LLC) to calculate and maintain the Index. The Index is not sponsored by S&P Dow Jones Indices or its affiliates or its third-party licensors (collectively, “S&P Dow Jones Indices”). S&P Dow Jones Indices will not be liable for any errors or omissions in calculating the Index. “Calculated by S&P Dow Jones Indices” and the related stylized mark(s) are service marks of S&P Dow Jones Indices and have been licensed for use by Exponential ETFs. S&P® is a registered trademark of Standard & Poor’s Financial Services LLC (“SPFS”), and Dow Jones® is a registered trademark of Dow Jones Trademark Holdings LLC (“Dow Jones”).

Past performance of an index is not a guarantee of future results, which may vary. The value of investments may go down as well as up and potential investors may not get back the amount originally invested. Performance figures contained herein contain both hypothetical and live returns; results, hypothetical or otherwise, are intended for illustrative purposes only. Index performance returns do not reflect any management fees, transaction costs, or expenses, which would reduce returns. Inclusion of a security within an index is not a recommendation by to buy, sell, or hold such security, nor is it considered to be investment advice. It is not possible to invest directly in an index.

The Index, strategy, and performance returns discussed are for informational purposes only and do not represent an offer to buy or sell a security and should not be construed as such.

Posted By: Josh Blechman 03/14/19

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