Summary U.S. small caps seem overvalued relative to international small caps. The dominate way to exploit this fact would likely be short VB and long GWX with a Sharpe ratio of 1.93. Given uncertainty about the underlying valuations of the ETFs, expected returns are between 22-42%. On Saturday, I stumbled across what I believe to be irregularity in the pricing of small-cap stocks, which I thought was worth exploring for a trade during my daily commutes. Since I generally operate under the assumption that I am wrong and the market is right and I am not much of a trader, I thought it was worth publishing the idea for critique before I put any real Helvetic francs to work. As we all know the major averages have taken a beating and the small-cap stocks have been hit harder than the large caps as one might expect. The international small-caps now seem undervalued relative to the United States where foreign capital continues to pour into small-cap companies to take advantage of the rising dollar, while at the same time be insulated against large-cap foreign earnings currency translation. Are (U.S.) Small-Caps Fundamentally Overpriced? Pitching my thesis, someone asked whether U.S. small-caps fundamentally overpriced. There are a number of ways of answering that question, in terms of growth, historical terms, GDP expectations, or using a model of international financial integration. In terms of growth the U.S. stocks now have a FW PEG ratio of about 1.25x, which is fundamentally overpriced, whereas the international stocks are about fair value with a FW PEG of about 1. In historical terms, stocks are pricey in general, but the international stocks are more in line with history. But in general, since stock prices often have little tether to their underlying claim on future profits, so we often look to analogous assets for guidance. Since I am a macro-economist, this article answers that question of fundamental valuation from an international capital mobility perspective, and the answer is, “Yes, U.S. small-caps are dear.” Under complete capital mobility, efficient exchange rate discovery, then U.S. small-caps are fundamentally misvalued . The U.S. has nigh perfect capital mobility, and we shall see below the exchange rate discovery is efficient. International investors prefer a cheaper claim on future profits for similar asset classes, ceteris paribus . The expected change in the dollar that drove international investors into small caps is likely overdone, meaning U.S. stocks are likely overpriced. Figure 1: Recent trend of the SPDR S&P International Small Cap ETF ( GWX) ((blue)) vs. the iShares Russell 2000 ETF ( IWM) (red). Source: Yahoo! Finance (click to enlarge) As one piece of evidence of this thesis, there seems to be a large discrepancy in the valuation levels between the Russell 2000, and the other major U.S. small-cap ETF holdings, and State Street’s GWX. The other international small-cap indices, the iShares MSCI EAFE Small-Cap ETF ( SCZ) and the Vanguard FTSE All-World ex-U.S. Small-Cap ETF ( VSS), are also a bit cheaper than IWM / the SPDR Russell 2000 ETF ( TWOK), but GWX seems to be the cheapest, and thus is the focus of this arbitrage. The ETF’s undervaluation is a bit surprising because GWX’s index, the S&P® Developed Ex-U.S. Under USD 2 Billion, does not seem terribly underpriced vis-à-vis the Russell 2000. Further evidence is exhibited in Table 1, which shows the standard valuation metrics of the major U.S. small-cap ETFs against GWX. Table 1: Fund and Index Characteristics ETF: Vanguard Small Cap ETF (NYSEARCA: VB ) SPDR S&P 600 Small Cap ETF (NYSEARCA: SLY ) SPDR Russell 2000 ETF ( TWOK)/IWM GWX Earnings Growth 3-5 Year Growth 14.87%* 14.61% 15% 16.67% Weighted Average Market Cap 2018 1714 1908 1248 Number of Holdings 1494 600 1963 2303 Price/Cash Flow 10.6 10.74 10.46 3.12** Price/Earnings 29.5 21.6 17.94 15.62 Price/Earnings ratio FY1 19.19 19.6 18.78 16.52 Return on equity 11.8% 11% 6.84% 9.40% Price/Book Ratio 2.5 2.03 2.07 1.37 Dividend Yield 1.43% 1.31% 1.62% 1.66% Price/Sales*** 1.17 1.16 1.15 0.74 * Average of SLY & IWM. Not all fund information is available. Some of the values are taken from the underlying index. **Still listed on their website as of this writing, but SSGA responded in an email stating the fund’s current P/CF is 8.55x. ***Source: macroaxis.com. Data as of Saturday, 15th August 2015. Based the fund information, most of the key metrics indicate that GWX is cheaper than its U.S. counterparts. That discount for an analogous asset class opens up the possibility of a pair trade by going long GWX and short one of the small-cap U.S. ETFs. ETFs have been a great financial innovation allowing retail and institutional investors to cheaply invest. Yet, I do think they have a few weaknesses that became more apparent in this exercise. The first is that all the characteristics needed to rationally evaluate the ETF holdings are not entirely reported, nor are they comparably reported across providers. Moreover, the entire holdings lists are often not reported in a way that allows one to match with external data to fill that gap. A glaring example is that State Street reports a 3.12x cash flow for its benchmark index on its website for GWX, but the index provider reports 14.12. It is hard to know whether this is typo (doubtful because attributes are reported daily and hence are likely automated), or some value-factor “optimized sampling” (a term of art in the ETF industry), which the State Street uses to juice returns when selecting the 2303 stocks from the 3571 stocks from the benchmark index, or how negative cash flows are accounted for. All these small differences make a pure arbitrage play more difficult because the margin of error is slim already given the relative efficiency of the market. The other thing that became clear is that the funds often trade at a premium to NAV and their holdings seem to be slightly bid up vis-à-vis their benchmark (i.e. NAV premium drag on top of ETF drag on top of indexing drag). Both likely have some drag on returns; depending how you leg into the long and short side you might already be down 100 bps before commissions. Not a trade breaker, but an additional complication. As an additional caution for our investors outside the U.S., please be aware that this arbitrage strategy poses additional risks because foreign versions of these ETFs exist in highly fragmented regulatory environments, which are essentially legalized scalping operations with mile-wide bid-ask spreads, implied local currency premia, higher expense ratios, and stronger departures from NAV. Étude d’Arbitrage Now that we have a trading thesis in hand, the question is how to best operationalize it. While the spark of a trading idea came from the price of the Russell 2000, alternate ways to implement the strategy might be to short Vanguard’s VB or State Street’s IWM, two widely held small-cap ETFs. We thus need to ascertain the concomitant risk-return profiles for each possible implementation (a tedious feat, and why most arbitrage is done with computers). Since we are dealing with percentages, there are a few ways to calculate the returns depending on whether you think the trade will lean to one side. The assumption here is both legs will eventually regress toward their mean netting profit on both sides. Rather than rely on a single indicator like price to book, I calculate the average of them all in order to estimate the expected arbitrage for a leg. Table 2 shows the expected gains for each leg, which are calculated off the center point values of the legs. Table 2: Arbitrage ALTERNATE SHORT LEGS LONG LEG GWX AGAINST: VB SLY TWOK/IWM VB SLY TWOK/IWM Price/Cash flow* 12.5% 11.1% 12.7% -9% -9% -10% Price/Earnings -36.9% -13.8% -6.5% 19% 19% 7% Price/Earnings ratio FY1 -5.9% -7.9% -6.0% 9% 9% 7% Return on equity 18% 6% -16% -6% -6% 16% Price/Book ratio -32.0% -16.3% -16.9% 24% 24% 26% Dividend yield convergence -3.5% -11.8% -1.2% 11% 11% 1.2% Price/Sales -23.2% -22.1% -21.7% 28% 28% 28% 5-Year growth convergence -3.5% -4.7% -3.5% 4% 4% 3% Ex{Center point arbitrage on leg} 9.3% 7.4% 7.4% 10.1% 10.1% 9.7% Ex{Total gain} (3.12x CF) 19% (42%) 17.5% (39.7%) 17.1% (39%) *Assumed to be 13.12x not 3.12x. See text. Since, the expected gains may be sensitive to the cash/flow outlier, I conservatively assume the cash flow to be 13.12x rather than 3.12. Being short the U.S. small-caps and long foreign small-caps implies being short dollars and long foreign currency, which means currency is a concern. A fair assumption might that the spot rate is the correct rate, but currency translation has been a major headache for me this year (thank you SNB…), so I am especially cautious. In order to estimate FX effects, I use the standard economist’s model that domestic net interest and inflation rates equal net inflation interest and inflation rates abroad, where “abroad” I define as Japan and the Eurozone. Currency Risk USD (EUR+JPY) /2 Spread Inflation (IMF 2016 forecast) 1.49% 1.10% 0.39% Interest (forward 6-month LIBOR) 0.56% 0.24% -0.32% Net spread: 0.07% Estimated USD appreciation needed to eliminate spread: 0.29% What amount of currency appreciation would U.S. rates into line? About 0.3%, assuming an inflation/currency elasticity of -0.24 (Kim 1998, pg. 617). Bond and currency traders seem to be doing their job extremely well, so we probably should not worry about currency. Since the strategy is equally long and short, it should be market-neutral. Yet, despite the proposed trade having an expected beta of zero, it entails risk. Therefore, I estimate the portfolio standard deviation using 2 years of adjusted price return data from Yahoo! Finance as a proxy for the portfolio risk. Strategy Profiles Table 3 shows the strategy implemented either using 2 or 3 ETFs. Using more than one short leg held out the possibility of reducing risk. Table 3: Strategy Implementation Profiles Three Asset Two Asset -VB/+GWX -SLY/+GWX -IWM/+GWX -SLY/+GWX -VB/ +GWX -IWM/ +GWX -TWOK/ +GWX -SLY/ +GWX Ex{Sharpe}* (3.12x CF) [+ lending] 1.54 (3.57) [4.15] 1.40 (3.39) [3.61] 1.93 (4.31) [4.99] 1.43 (3.44) [4.01] 0.68 (2.54) [3.07] 0.82 (2.00) [2.34] Ex{Equity Arbitrage} 23.51% 22.15% 25.05% 22.32% 22.32% 21.97% Ex{Currency Delta} -0.29% -0.29% -0.29% -0.29% -0.29% -0.29% Ex{Borrow Costs} -1.24% -1.48% -1.00% -1.48% -9.11% -1.47% Ex{Lending Income} 6.29% 6.29% 6.29% 6.29% 6.29% 6.29% Ex{SD Portfolio} 10.9% 11.1% 9.4% 11.0% 11.9% 18.6% *Returns calculated without lending income and 13.12xCF. See text. I present 3 different Sharpe values. The most conservative version assumes a price to cash flow of 13.12x. The second uses the provider’s index information. And the third includes the market rate security lending income. If you are able to collect the market rate for lending GWX, the trade becomes almost a pure arbitrage play. With an expected Sharpe of 1.93, the dominant operationalization would appear to be short VB and long GWX. Conclusion It would therefore seem, even based on conservative calculations, the proposed long-short strategy dominates a long position in the S&P500, which has an expected Sharpe of about 0.47. All of the trades seem to meet the first test of rationality, and thus a decent risk-adjusted trading opportunity. For this reason, I like to know what you think. Is the data wrong? Have I made an error in calculation? Is there a problem with my deduction and/or conclusion? If not, how would you implement the trade and when? Based on your feedback I shall make a determination to open a small position. Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. (More…) I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.