This post is available as a PDF download here.

Summary­­

• Factor investing seeks to balance specificity with generality: specific enough to have meaning, but general enough to be applied broadly.
• Diversification is a key tool to managing risk in factor portfolios. Imprecision in the factor definitions means that unintended bets are necessarily introduced.
• This is especially true as we apply factors across securities that share fewer and fewer common characteristics. Left unmonitored, these unintended bets have the potential to entirely swamp the factor itself.
• By way of example, we explore a simple value-based country model.
• While somewhat counter-intuitive, constraints have the potential to lead to more efficient factor exposures.

In quantitative investing, we seek a balance between generality and specificity.  When a model is too specific – designed to have meaning on too few securities or in too few scenarios – we lose our ability to diversify.  When a model is too generic, it loses meaning and forecasting power.

The big quant factors – value, momentum, defensive, carry, and trend – all appear to find this balance: generic enough to be applied broadly, but specific enough to maintain a meaningful signal.

As we argued in our past commentary A Case Against Overweighting International Equity, the imprecision of the factors is a feature, not a bug.  A characteristic like price-to-earnings may never fully capture the specific nuances of each firm, but it can provide a directionally accurate roadmap to relative firm valuations.  We can then leverage diversification to average out the noise.

Without diversification, we are highly subject to the imperfections of the model.  This is why, in the same piece, we argued that making a large regional tilt – e.g. away from U.S. towards foreign developed – may not be prudent: it is a single bet that can take decades to resolve.  If we are to sacrifice diversification in our portfolio, we’ll require a much more accurate model to justify the decision.

Diversification, however, is not just measured by the quantity of bets we take.  If diversification is too naively interpreted, the same imprecision that allows factors to be broadly applied can leave our portfolios subject to the returns of unintended bets.

Value Investing with Countries

If taking a single, large regional tilt is not prudent, perhaps value investing at a country level may better diversify our risks.

One popular way of measuring value is with the Shiller CAPE: a cyclically-smoothed price-to-earnings measure.  In the table below, we list the current CAPE and historical average CAPE for major developed countries.

	CAPE	Mean CAPE	Effective Weight
Australia	18.5	17.2	2.42%
Belgium	25.0	15.4	0.85%
Canada	22.0	21.4	3.76%
Denmark	36.5	24.5	0.73%
France	20.9	21.9	4.85%
Germany	20.6	20.6	4.36%
Hong Kong	18.2	18.3	5.21%
Italy	16.8	22.1	1.33%
Japan	28.9	43.2	11.15%
Netherlands	23.5	14.8	1.45%
Singapore	13.9	22.1	1.09%
Spain	13.4	18.3	1.58%
Sweden	21.5	23.0	1.21%
Switzerland	25.9	21.9	3.15%
United Kingdom	16.5	15.3	6.55%
United States	30.5	20.3	50.30%

Source: StarCapital.de.  Effective weight is market-capitalization weight of each country, normalized to sum to 100%.  Mean CAPE figures use data post-1979 to leverage a common dataset.

While evidence[1] suggests that valuation levels themselves are enough to determine relative valuation among countries, we will first normalize the CAPE ratio by its long-term average to try to account for structural differences in CAPE ratios (e.g. a high growth country may have a higher P/E, a high-risk country may have a lower P/E, et cetera).  Specifically, we will look at the log-difference between the mean CAPE and the current CAPE scores.

Note that we recognize there is plenty to criticize and improve upon here.  Using a normalized valuation metric will mean a country like Japan, which experienced a significant asset bubble, will necessarily look under-valued.  Please do not interpret our use of this model as our advocacy for it: we’re simply using it as an example.

Using this value score, we can compare how over and undervalued each country is relative to each other.  This allows us to focus on the relative cheapness of each investment.  We can then use these relative scores to tilt our market capitalization weights to arrive at a final portfolio.

 

	Value Score	Relative Z-Score	Scaled Z-Score	Scaled Weights
Australia	-0.07	-0.13	0.88	2.31%
Belgium	-0.48	-1.50	0.40	0.37%
Canada	-0.03	0.02	1.02	4.15%
Denmark	-0.40	-1.22	0.45	0.36%
France	0.05	0.27	1.27	6.65%
Germany	0.00	0.11	1.11	5.24%
Hong Kong	0.01	0.13	1.13	6.37%
Italy	0.27	1.02	2.02	2.92%
Japan	0.40	1.45	2.45	29.59%
Netherlands	-0.46	-1.43	0.41	0.65%
Singapore	0.46	1.65	2.65	3.14%
Spain	0.31	1.15	2.15	3.68%
Sweden	0.07	0.33	1.33	1.75%
Switzerland	-0.17	-0.45	0.69	2.36%
United Kingdom	-0.08	-0.14	0.88	6.22%
United States	-0.41	-1.25	0.45	24.26%

Source: StarCapital.de.  Calculations by Newfound Research.  “Value Score” is the log-difference between the country’s Mean CAPE and its Current CAPE.  Relative Z-Score is the normalized value score of each country relative to peers.  Scaled Z-Score applies the following function to the Relative Z-Score: (1+x) if x > 0 and 1 / (1+x) if x < 0.  Scaled weights multiply the Scaled Z-Score against the Effective Weights of each country and normalize such that the total weights sum to 100%.

While the Scaled Weights represent a long-only portfolio, what they really capture is the Market Portfolio plus a dollar-neutral long/short factor tilt.

	Market Weight	+ Long / Short	= Scaled Weights
Australia	2.42%	-0.11%	2.31%
Belgium	0.85%	-0.48%	0.37%
Canada	3.76%	0.39%	4.15%
Denmark	0.73%	-0.37%	0.36%
France	4.85%	1.80%	6.65%
Germany	4.36%	0.88%	5.24%
Hong Kong	5.21%	1.16%	6.37%
Italy	1.33%	1.59%	2.92%
Japan	11.15%	18.44%	29.59%
Netherlands	1.45%	-0.80%	0.65%
Singapore	1.09%	2.05%	3.14%
Spain	1.58%	2.10%	3.68%
Sweden	1.21%	0.54%	1.75%
Switzerland	3.15%	-0.79%	2.36%
United Kingdom	6.55%	-0.33%	6.22%
United States	50.30%	-26.04%	24.26%

To understand the characteristics of the tilt we are taking – i.e. the differences we have created from the market portfolio – we need only look at the long/short portfolio.

Unfortunately, this is where our model loses a bit of interpretability.  Since each country is being compared against its own long-term average, looking at the increase or decrease to the aggregate CAPE score is meaningless.  Indeed, it is possible to imagine a scenario whereby this process actually increases the top-level CAPE score of the portfolio, despite taking value tilts (if value, for example, is found in countries that have higher structural CAPE values).  We can, on the other hand, look at the weighted average change to value score: but knowing that we increased our value score by 0.21 has little interpretation.

One way of looking at this data, however, is by trying to translate value scores into return expectations.  For example, Research Affiliates expects CAPE levels to mean-revert to the average level over a 20-year period.[2]  We can use this model to translate our value scores into an annualized return term due to revaluation.  For example, with a current CAPE of 30.5 and a long-term average of 20.3, we would expect a -2.01% annualized drag from revaluation.

By multiplying these return expectations against our long/short portfolio weights, we find that our long/short tilt is expected to create an annualized revaluation premium of +1.05%.

The Unintended Bet

Unfortunately, re-valuation is not the only bet the long/short portfolio is taking.  The CAPE re-valuation is, after all, in local currency terms.  If we look at our long/short portfolio, we can see a very large weight towards Japan.  Not only will we be subject to the local currency returns of Japanese equities, but we will also be subject to fluctuations in the Yen / US Dollar exchange rate.

Therefore, to achieve the re-valuation premium of our long/short portfolio, we will either need to bear the currency risk or hedge it away.

In either case, we can use uncovered interest rate parity to develop an expected return for currency.  The notion behind uncovered interest rate parity is that investors should be indifferent to sovereign interest rates.  In theory, for example, we should expect the same return from investing in a 1-year U.S. Treasury bond that we expect from converting $1 to 1 euro, investing in the 1-year German Bund, and converting back after a year’s time.

Under uncovered interest rate parity, our expectation is that currency change should offset the differential in interest rates.  If a foreign country has a higher interest rate, we should expect that the U.S. dollar should appreciate against the foreign currency.

As a side note, please be aware that this is a highly, highly simplistic model for currency returns.  The historical efficacy of the carry trade clearly demonstrates the weakness of this model.  More complex models will take into account other factors such as relative purchasing power reversion and productivity differentials.

Using this simple model, we can forecast currency returns for each country we are investing in.

	FX Rate	1-Year Rate	Expected FX Rate	Currency Return
Australia	1.2269	-0.47%	1.2546	-2.21%
Belgium	1.2269	-0.47%	1.2546	-2.21%
Canada	0.8056	1.17%	0.8105	-0.60%
Denmark	0.1647	-0.55%	0.1685	-2.29%
France	1.2269	-0.47%	1.2546	-2.21%
Germany	1.2269	-0.47%	1.2546	-2.21%
Hong Kong	0.1278	1.02%	0.1288	-0.75%
Italy	1.2269	-0.47%	1.2546	-2.21%
Japan	0.0090	-0.13%	0.0092	-1.88%
Netherlands	1.2269	-0.47%	1.2546	-2.21%
Singapore	0.7565	1.35%	0.7597	-0.42%
Spain	1.2269	-0.47%	1.2546	-2.21%
Sweden	0.1241	0.96%	0.1251	-0.81%
Switzerland	1.0338	-0.72%	1.0598	-2.46%
United Kingdom	1.3795	0.43%	1.3981	-1.33%
United States	1.0000	1.78%	1.0000	0.00%

Source: Investing.com, XE.com.  Euro area yield curve employed for Eurozone countries on the Euro.

Multiplying our long/short weights against the expected currency returns, we find that we have created an expected annualized currency return of -0.45%.

In other words, we should expect that almost 50% of the value premium we intended to generate will be eroded by a currency bet we never intended to make.

One way of dealing with this problem is through portfolio optimization.  Instead of blindly value tilting, we could seek to maximize our value characteristics subject to currency exposure constraints.  With such constraints, what we would likely find is that more tilts would be made within the Eurozone since they share a currency.  Increasing weight to one Eurozone country while simultaneously reducing weight to another can capture their relative value spread while remaining currency neutral.

Of course, currency is not the only unintended bet we might be making.  Blindly tilting with value can lead to time varying betas, sector bets, growth bets, yield bets, and a variety of other factor exposures that we may not actually intend.  The assumption we make by looking at value alone is that these other factors will be independent from value, and that by diversifying both across assets and over time, we can average out their impact.

Left entirely unchecked, however, these unintended bets can lead to unexpected portfolio volatility, and perhaps even ruin.

Conclusion

In past commentaries, we’ve argued that investors should focus on achieving capital efficiency by employing active managers that provide more pure exposure to active views.  It would seem constraints, as we discussed at the end of the last section, might contradict this notion.

Why not simply blend a completely unconstrained, deep value manager with market beta exposure such that the overall deviations are constrained by position limits?

One answer why this might be less efficient is that not all bets are necessarily compensated.  Active risk for the sake of active risk is not the goal: we want to maximize compensated active risk.  As we showed above, a completely unconstrained value manager may introduce a significant amount of unintended tracking error.  While we are forced to bear this risk, we do not expect the manager’s process to actually create benefit from it.

Thus, a more constrained approach may actually provide more efficient exposure.

That is all not to say that unconstrained approaches do not have efficacy: there is plenty of evidence that the blind application of value at the country index level has historically worked.  Rather, the application of value at a global scale might be further enhanced with the management of unintended bets.

 

---

 

[1] For example, Predicting Stock Market Returns Using the Shiller CAPE (StarCapital Research, January 2016) and Value and Momentum Everywhere (Asness, Moskowitz, and Pedersen, June 2013)

[2] See Research Affiliate’s Equity Methodology for their Asset Allocation tool.