Tag: diversification Page 3 of 4

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Summary

Portfolio risk is often measured as the variance of returns over time. Another form of risk is the variance of terminal wealth that can arise from small variations in strategy inputs or asset returns.
Strategies or portfolios that are more sensitive to small changes in inputs are inherently “fragile.”
Fragile strategy design makes it difficult to rely upon backtests or historical results in setting forward expectations.
We explore how diversification across the “what,” “how,” and “when,” axes of portfolio construction can help reduce strategy fragility.

Introduction

At Newfound, we spend a lot less time trying to figure out how to be more right than we spend trying to figure out how to be less wrong. One area of particular interest for us is the idea of unintended bets: the exposures in a portfolio we may not even be aware of. And if we knew we had the exposure, we might not even want it.

For example, consider a portfolio that invests in either broad U.S., broad international, or broad emerging market equities based upon valuations. A significant tilt towards non-U.S. assets may be a valuation-driven decision, but for U.S. investors it creates significant exposure to fluctuations in the U.S. dollar versus foreign currencies.

Of course, exposures are not limited only to assets. Exposures may be broader macro-economic, stylistic, thematic, geographic, or even political factors.

These unintended bets can go far beyond explicit and implicit exposures. In our example, the choice of how to measure value may lead to meaningfully different portfolios, despite the same overarching thesis. For example, a naïve CAPE ratio versus adjusting for differences in relative sector composition dramatically alters the view of whether international equities are significantly cheaper than U.S. equities. These potential differences capture what we like to call “model specification risk.”

Finally, we can be subject to unintended bets based upon when the portfolio is re-evaluated and reconstituted. Evaluating valuations in January, for example, may lead to a different decision versus evaluating them in July.

How can we avoid these unintended bets? At Newfound, we believe that the answer falls back to diversification: not only in the traditional sense of what we invest in, but also across how we make decisions and when we make them.

When left uncontrolled, unintended bets can make a strategy incredibly fragile.

What, precisely, does it mean for a strategy to be fragile? A strategy is fragile when small variations of strategy inputs – be it asset returns or other measures – lead to meaningful dispersion in realized results.

Now we want to distinguish between volatility and fragility. Volatility is the dispersion of strategy returns across time, while fragility is the dispersion in end-of-period wealth across variations of the strategy.

As an example, a portfolio that invests only in the S&P 500 is very volatile but not particularly fragile. Given the last ten years of returns for the S&P 500, slight variations in annual returns would not lead to significant dispersion in end-of-period wealth. On the other hand, a strategy that flips a coin every December and invests for the next year in the S&P 500 when it lands on heads or short-term U.S. Treasuries when it lands on tails would have lower expected volatility than the S&P 500 but would be much more fragile. We need simply consider a few scenarios (e.g. all heads or all tails) to understand the potential dispersion such a strategy is subject to.

In the remainder of this commentary, we will demonstrate how diversification across the what, how, and when axes can reduce strategy fragility.

The Experiment Setup

Since a large degree of our focus at Newfound is on managing trend equity mandates, we will explore fragility through the lens of the style of measuring trends. For those unfamiliar with the approach, trend equity strategies aim to capture a significant portion of equity market growth while avoiding substantial and prolonged drawdowns through the application of trend following. A naïve implementation of such an idea would be to invest in the S&P 500 when its prior 12-month return has been positive and invest in short-term U.S. Treasuries otherwise.

To learn something about the fragility of a strategy, we are going to have to inject some randomness. After all, no amount of history will tell us about the fragility of a teacup that has spent its entire life sitting on a shelf; we will need to see it fall on the floor to actually learn something.

As with our recent commentary When Simplicity Met Fragility, we will inject randomness by adding white noise to asset returns. Specifically, we will add to daily returns a draw from a random normal distribution with mean 0% and standard deviation 0.025%. Using this slightly altered history, we will then run our investment strategy.

By performing this process a large number of times (10,000 in this commentary), we can explore how the outcome of the strategy is impacted by these slight variations in return history. The greater the dispersion in results, the more fragile the strategy is.

To demonstrate how diversification across the three different axes can affect fragility, we will start with a naïve trend equity strategy – investing in broad U.S. equities using a single trend model that is rebalanced on a monthly basis – and vary the three components in isolation.

The What

The “what” axis simply asks, “what are we invested in?”

How can our choice of “what” affect fragility? Consider a slight variation to our coin-flip strategy from before. Instead of flipping a single coin, we will now flip two coins. The first coin determines whether we invest 50% of the portfolio in either the S&P 500 or short-term U.S. Treasuries, while the second coin determines whether we invest the other 50% of the portfolio in either the Russell 1000 or short-term U.S. Treasuries.

In our single coin example, each year we expected to invest in the S&P 500 50% of the time and in short-term U.S. Treasuries 50% of the time. With two coins, we now expect to be fully invested 25% of the time, partially invested 50% of the time, and divested 25% of the time.

Let’s take this notion to further limits. Consider now flipping 100 coins where each determines the allocation decision for 1% of our portfolio, where heads leads to an investment in a large-cap U.S. equity portfolio and tails means invest in short-term U.S. Treasuries. Now being fully invested or divested is an infinitesimally small probability event; in fact, for a given year there is a 95% chance that your allocation to equities falls between 40-60%.¹

Even though we’ve applied the exact same process to each investment, diversifying across more investments has dramatically reduced the fragility of our coin-flipping strategy.

Now let’s translate this from the theoretical to the practical. We will begin with a simple trend following strategy that invests in the underlying asset when prior 12-1 month returns have been positive or invests in the risk-free rate, re-evaluating the trend at the end of each month.

To explore the impact of diversifying our what, we will implement this strategy five different ways:

A single in-or-out decision on broad U.S. equities.
Applied across 5 equally-weighted U.S. equity industry groups.
Applied across 12 equally-weighted U.S. equity industry groups.
Applied across 30 equally-weighted U.S. equity industry groups.
Applied across 48 equally-weighted U.S. equity industry groups.

The graph below plots the distribution of log difference in terminal wealth against the median outcome for each of these five approaches. Lines within each “violin” show the 25^th, 50^th, and 75^thpercentiles.

The graph clearly demonstrates that by increasing our exposure across the “what” axis, the dispersion in terminal wealth is dramatically reduced.

Source: Kenneth French Data Library. Calculations by Newfound Research.

But why is reduced dispersion in terminal wealth necessarily better?

It implies a greater consistency in outcome, which is not only important for setting forward expectations, but is also important for evaluating past performance (whether backtested or live). This evidence tells us that if we are evaluating a trend equity strategy that employs a single model to make in-or-out decisions on broad U.S. equities on a monthly basis, it will be nearly impossible to tell whether the realized results are in line with reasonable expectations or overly optimistic (we can probably guess that they aren’t overly pessimistic, as those sorts of returns typically aren’t marketed).

To justify a concentration in the “what” axis, we would have to demonstrate that the worst-case scenarios would still represent a meaningful improvement in expected terminal wealth versus a more diversified approach.

It should be noted that our experiment design prohibits dispersion from every being fully reduced, as we are injecting randomness into past returns. Even if no strategy is applied, there will be some inherent dispersion in final wealth. For example, below we plot the dispersion that occurs simply from adding randomness to past returns with a buy-and-hold approach.

Increasing the number of assets in the portfolio inherently reduces dispersion for buy-and-hold because diversification helps drive the expected impact of the injected randomness towards its mean: zero. With only one asset, on the other hand, outlier events are free to wreak havoc on results.

Source: Kenneth French Data Library. Calculations by Newfound Research.

Note that adding a strategy on top of buy-and-hold can exacerbate the fragility issue, making diversification that much more important.

The How

The “how” axis asks, “how are we making investment decisions.”

Many investors are already somewhat familiar with diversification along the “how” axis, often diversifying their active exposures across multiple managers who might have similar investment mandates but slightly different processes.

We like to call this “process diversification” and think of it as akin to the parable of the blind men and the elephant. Each blind man touches a different part of the elephant and pronounces his belief in what he is touching based upon his isolated view. The blind man touching the leg, for example, might think he is touching a sturdy tree while the blind man touching the tail might believe he is grabbing a rope.

None is correct in isolation but taken together we may gain a more well-rounded picture.

Similarly, two managers may claim to invest based upon valuations, but the manner in which they do so gives them a very different picture of where value can be found.

The idea of process diversification was explored in the 1999 paper “Do You Need More than One Manager for a Given Equity Style?” by Franklin Fant and Edward O’Neal. Fant and O’Neal found that while a multi-manager approach does very little for return variability across time (i.e. portfolio volatility), it does a lot for end-of-period wealth variability. They find this to be true across almost all equity style box categories. In other words: taking a multi-manager approach can reduce fragility.

Let us return to our prior coin flip example. Instead of making a choice to invest in the S&P 500 based upon a coin-flip, however, we will combine a number of different signals. For example, we might flip a coin, roll a die, measure the weather, and look at the second hand of a clock. Each signal gives us some sort of in-or-out decision, and we average these decisions together to get our allocation. As with before, as we incorporate more signals, we decrease the probability that we end up with extreme allocations, leading to a more consistent terminal wealth distribution.

Again, we should stress here that the objective is not just outright elimination of dispersion in terminal wealth. After all, if that were our sole pursuit, we could simply stuff our money under our mattress. Rather, assuming we will be implementing some active investment strategy that we hope has a positive long-term expected return, our aim should be to reduce the dispersion in terminal wealth for that strategy.

Of course, in investing we would not expect the processes to be entirely independent. With trend following, for example, most popular models are actually mathematically linked to one another, and therefore generate signals that are highly correlated. Nevertheless, even modest diversification can have meaningful benefits with respect to strategy fragility.

To explore the impact of diversification along the how axis, we implement our trend following strategy six different ways. Each invests in broad U.S. equities and rebalances monthly but differs in the number of trend-following models employed.²

The results are plotted below.

Source: Kenneth French Data Library. Calculations by Newfound Research.

Again, we can see that increased diversification across the how axis dramatically reduces dispersion in terminal wealth. Our takeaway is largely the same: without an ex-ante view as to which particular model (or group of models) is best (i.e. a view of how to be more right), diversification can lead to greater consistency in results. We will be less wrong.

A subtler conclusion of this analysis is that it should be very, very difficult to necessarily conclude that one model is better than another. We can see that if we risk selecting just one model to govern our process, seemingly minor variations in historical returns leads can lead to dramatically different terminal wealth results, as evidenced by the bulging distribution. Inverting this line of thinking, we should also be suspect of any backtest that seeks to demonstrate the superiority of a given model using a single backtest. For example, just because a 12-1 month total return model performs better than a 10-month moving average model on historical S&P 500 returns, we should be highly skeptical as to the robustness of the conclusion that the 12-1 model is best.

The When

Then “when” axis asks, “when are we making our investment decision?”

This is an oft overlooked question in public markets, but it is commonly addressed in the world of private equity and venture capital. Due to the illiquid nature of those markets, investors will often attempt to diversify their business cycle risk by establishing positions in multiple funds over time, giving them exposure to different “vintages.” The idea here is simple: the opportunity set available at different points in time can vary and if we allocate all of our earmarked capital to a particular year, we may miss out on later opportunities.

Consider our original coin-flipping example where we flipped a single coin every December to determine whether we would buy the S&P 500 or hold our capital in short-term Treasuries. But why was it necessary that we make the decision in December? Why not July? Or January? Or September?

While we would not expect there to be point-in-time risk for coin flipping, we can still consider the net effect of a vintage-based allocation methodology. Here we will assume that we flip a coin each month and rebalance 1/12^thof our capital based upon the result.

Again, the probability of allocating to the extremes (100% invested or 100% divested) is dramatically reduced (each has approximately a 0.02% chance of occurring) and we reduce strategy fragility to any specific coin flip.

But just how impactful is this notion? Below we plot the rolling 1-year total return difference between two 60% S&P 500 / 40% 5-year U.S. Treasury fixed-mix portfolios, with one being rebalanced in February and one in August. Even for this highly simplified example, we can see that the total return spread between the two portfolios blows out to over 700 basis points in March 2010 due to the fact that the February portfolio rebalanced back into equities at nearly the exact bottom of the crisis.

Source: Global Financial Data. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.

To increase diversification across the “when” axis, we want to increase the number of vintages we deploy. For our trend following example, we will assume that the portfolio allocates between broad U.S. equities and the risk-free rate based upon a single model, but with an increasing number of evenly-spaced vintages. Again, we will run 10,000 simulations that each slightly perturb historical U.S. equity market returns and compare the terminal wealth variation for approaches that employ a different number of vintages.

We can see in the graph below that, as with the other axes of diversification, as we increase the number of vintages employed, the variance decreases. While the 25^thand 75^thpercentiles do not decrease as dramatically as for the other axes, we can see that the extreme variations are reined in substantially when we move from 1 monthly tranche to 4 weekly tranches.

Source: Kenneth French Data Library. Calculations by Newfound Research.

Conclusion

We see two critical conclusions from this analysis:

To develop confidence in achieving our objective we have to consider our sensitivity to unintended bets that may be included within the portfolio.

Fragility makes it incredibly difficult to distinguish between luck and skill, particularly as strategy fragility increases. This is true for both backtested and live performance.

To conclude our analysis, below we present a graph that combines diversification across all three axes. We again run 10,000 samples, randomly perturbing returns. For each sample, we then run four variations:

A single, randomly selected model run in broad U.S. equities that is rebalanced monthly.
A random selection of 3 models run on 5 industry groups in 2 bi-weekly tranches.
A random selection of 6 models run on 12 industry groups in 4 weekly tranches.
A random selection of 9 models run on 30 industry groups in 20 daily tranches.

It should come as no surprise that as we increase the amount of diversification across all three axes, the dispersion in terminal wealth is dramatically reduced.³

Source: Kenneth French Data Library. Calculations by Newfound Research.

It is also important to note that while our analysis focused on trend following strategies, this same line of thinking applies across all investment approaches. As an example, consider a quantitative value manager who buys the top five cheapest stocks, as measured by price-to-book, in the S&P 500 each December and then holds them for the next year. Questions worth pondering are:

What does it say about our conviction when the 6^thstock in the list is incredibly close to the 5^thstock?
What happens if some of our measures of book value are incorrect (or even just outdated)?
How different would the portfolio look if we ranked on another value measure (e.g. price-to-earnings)?
How different would the opportunity set be if we ranked every June versus every December?

While low levels of diversification across the what, how, and when axes are not necessarily an indicator that a model is inherently fragile, it should be a red flag that more effort is required to disprove that it is not fragile.

Measuring the Benefit of Diversification

By Nathan Faber

On November 5, 2018

In Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

The benefits of diversification are often touted, but many investors feel disappointed in diversified portfolios because of the dispersion in performance of the individual holdings.
In the context of three different unconstrained sleeves, we look at a way to measure and visualize the benefit (or detriment) of diversification based on achieving different objectives.
Through this lens, we get a picture of how good or bad the results might have been, which can lead to confidence either in the robustness of the allocation or in the need to take a different approach.
Since we only experience one path of history, it is difficult to assess the benefit of diversification unless we consider what could have happened.
We believe that taking a systematic approach does not fully remove the art of the analysis but can remove some of the behavioral biases that make sticking with a portfolio difficult in the first place.

Introduction

Diversification is a standard risk management tool in any portfolio. Reducing the impact of idiosyncratic risks in individual investments by holding a suite of stocks, asset classes, strategies, etc. produces a smoother investment ride most of the time and reduces the risk of negative surprises.

But in a world where we only experience one outcome out of the multitude of possibilities, gauging the benefit of diversification is difficult. It is even hard to do in hindsight, not so much because we can’t but more often that we won’t. The results already happened.

Over a single time period with no rebalancing, a diversified portfolio will underperform the best asset that it holds. This is a mathematical fact when there is any dispersion in the returns of the assets and it is why we have said that diversification will always disappoint. Our natural behavioral tendencies can often get the better of us, despite the fact that diversification might be doing a great job, especially when examined through the appropriate lens and measured in the context of what could have happened.

Last summer, we published a presentation entitled Building an Unconstrained Sleeve. In it, we looked at ways to combine traditional and non-traditional assets and strategies to target specific objectives: equity hedging, absolute return, and equity-like with downside management.

Now that we have 15 months of subsequent data for all the underlying strategies, we want to revisit that piece and explore the benefit of diversification in the context of hindsight.

A Recap of the Process

As a quick refresher, we included seven strategies and asset classes in the construction of our unconstrained sleeves:

Long/flat trend-following equities
Minimum volatility equities
Macro trend-following (managed futures)
Macro risk parity
Macro value
Macro income
Intermediate U.S. Treasuries

While these strategies are surely not exhaustive, they cover a range of factors (value, momentum, low volatility, etc.) and a global set of asset classes (equities, bonds, commodities, and currencies) commonly included in unconstrained sleeves. They were also selected because many of these strategies are conveniently packaged as ETFs or mutual funds, making the resulting sleeves more easily implementable.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results. Index returns are total returns and are gross of all fees.

Over the 15 months, world equity was by far the best performer and the spread between best-performing and worst-performing positions exceeded 20 percentage points. If you wanted high returns – and going back to our statement about how diversification will always disappoint – you could have just held world equities and been quite content.

But putting ourselves back in June 2017, we did not know a priori that simply holding equities would have generated the highest returns. Looking at this type of chart in November 2008 would have led to a very different emotional conclusion.

The aim of our original study was to develop unconstrained sleeves that would meet their objectives regardless of how the future played out. Therefore, we employed a simulation-based method that aimed to preserve some of the unique correlation structure between the strategies across different market environments and reduce the risk of overfitting to a single realization of history. With this approach, we constructed portfolios that targeted three different objectives that investors might be interested in:

Equity hedge – designed to offset significant equity losses.
Absolute return – designed to create a stable and consistent return stream in all environments.
Equity-like – designed to capture significant equity upside with reduced downside.

(Note: Greater detail about portfolio construction process, strategy descriptions, and performance attributes of each strategy can be found in our original presentation.)

But were our constructed portfolios successful in achieving their objectives out-of-sample? To analyze this question, as well as explore the benefits/detractors of diversification for each objective, we will calculate the distribution of what could have happened. The hope is that, each strategy would perform well relative to all other possible portfolios that could have been chosen for the sleeve.

Saying exactly what portfolios we could have chosen is where a little art comes into play. For example, in the equity-like strategies, it is difficult to say that a 100% bond portfolio would have ever been a viable option and therefore may not be an apt out-of-sample comparison.

However, since our original process did not have any specific override for these intuitive constraints, and since we do not wish to assert after-the-fact which portfolios would have been rejected, we will allow the entire potential allocation space to be fair game in our comparison.

There are a number of ways to sample the set of allocations over the 7 asset classes that could have formed the portfolios for each sleeve. Perhaps the most obvious choice would be to sample uniformly over the possible allocations. The issue to balance in this case is coverage of the space (a 6-dimensional simplex) with the number of samples. To be 95% confident that we sampled an allocation above 95% for only a single asset class would require nearly 200 million samples. We have used modified Sobol sequences in the past to ensure coverage of more of the space with fewer points. However, in the current case, to mimic the rounding that is often found in portfolio allocations, we will use a lattice of points spaced 2.5% apart covering the entire space. This requires just under 10 million points in the simulations.

Equity Hedge

This sleeve was designed to offset significant equity losses by limiting downside capture. The resulting optimized portfolio was relatively concentrated in two main positions that historically have exhibited low-to-negative correlations to equities and exhibited potential crisis alpha during significant and prolonged drawdowns.Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

The down capture this portfolio during the out-of-sample period was 0.44. This result falls in the 70^th percentile (that is, better than 70% of the other sample portfolios and where lower down-capture is better) when compared to the 10 million possible other portfolios we could have originally selected. Not surprisingly, the 100% intermediate-term Treasury portfolio had the best down capture (-0.05) over the out-of-sample. Of the portfolios with better down capture, Intermediate Treasuries and Macro – Income were generally the highest allocations.

This does not come as much of a surprise to anyone who has followed the managed futures space for the last 15 months. The category largely remains in a multi-year drawdown (peaking in early 2014), but it has also done little to offset the rapid sell-offs seen in equities in 2018. Therefore, with the full benefit of hindsight, any allocation to Macro – Trend in the original portfolio would be a detriment realizing our out-of-sample objective.

Yet even with this lackluster performance, an out-of-sample realized 70^th percentile result over a short, 15-month horizon is a result to be pleased with.

Absolute Return

This sleeve was designed to seek a stable and consistent return stream in all market environments. We aimed to accomplish this by utilizing a risk parity approach. As expected, this sleeve holds all asset classes and is very well diversified across them.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

To measure the success of the risk parity over the live period, we will look at the Gini coefficient for each of the ten million potential portfolios we could have initially selected. The Gini coefficient quantifies the equality of the distribution, with a value of 1 representing 100% concentration and 0 representing perfect equality.

The Gini coefficient of the actual portfolio was 0.25 which was in the 99.8^th percentile of possible outcomes (i.e. highly diversified on a relative basis). Here, the percentile estimate is padded by the fact that many of the simulated portfolios (e.g. the 100% ones) would clearly not be close to equal risk contribution.

Did our original portfolio achieve its out-of-sample goal? Here, we can evaluate success as to whether the realized contribution to risk of each exposure was close to equivalent; i.e. did we actually achieve risk parity as desired? We can see below that indeed we did, with the main exception of Macro – Trend, which was the most volatile asset class over the period.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

Over the sample space of potential portfolios, the portfolio with the minimum out-of-sample Gini coefficient (0.08) was tilted toward the less volatile and more diversifying asset classes (Intermediate Treasuries and Macro – Income). Even so, due to the limited granularity of the sampled portfolios, the risk contribution of Macro – Income was still half of that for each of the other strategies.

It is also worth noting how similar this solution is – generated with the complete benefit of hindsight – to our originally constructed portfolio.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

Equity-like with Downside Management

This sleeve was designed in an effort to capture equity market growth while managing the risk of severe and prolonged drawdowns. It was tilted toward the equity-like exposures with a split among risk management styles (trend, minimum volatility, macro strategies, etc.). The allocation to U.S. Treasuries is very small.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

For this portfolio, we have two variables to analyze: the up capture relative to global equities and the Ulcer index, a measure of the severity and duration of drawdowns. In the construction of the sleeve, the target was to keep the Ulcer index less than 25% of the value for global equities. The joint distribution of these quantities over the live period is shown below with the actual values over the live period for the sleeve indicated.

The realized Ulcer level was 68% of that of world equity – a far cry from the 25% that the portfolio was optimized for – and was in the 42^nd percentile while the up capture of 0.60 was in the 93^rd percentile.

With the explicit goal of achieving a relative Ulcer level, a comparison against the entire potential allocation space of 10 million portfolios is not appropriate. Therefore, we reduce the set of 10 million comparative portfolios to only those that would have given a relative Ulcer index less than 25% compared to world equities, eliminating approximately 40% of possible portfolios.

The distributions of allocations to each of the strategies in the acceptable subset are shown below. We can see that the more diversifying strategies take on a larger range of allocations.

Interestingly, looking only over this subset of the original 10 million portfolios improves the out-of-sample up capture of our originally constructed portfolio to the 99^th percentile but does not change the percentile of the Ulcer index over the live period. Why is this?

The correlation of the relative Ulcer index over the live period with that over the historical period is only 0.1, indicating that the out of sample data did not line up with our expectations at first glance. However, this makes sense when we recall that the optimization was carried out using data from much more extreme market environments (think 2001 and 2008). It is a good reminder that, just because you optimize for a certain parameter value does not mean you will get it over the live data.

Higher up-capture typically goes hand-in-hand with a higher Ulcer index, as higher return often requires bearing more risk. Therefore, one way to standardize our measures across the potential set of portfolios is to calculate the ratio of up-capture to the Ulcer index. With this transformation, the risk-adjusted up capture falls in the 87^th percentile over the set of sample allocations, indicating a very high realized risk-adjusted return.

Conclusion

We only experience one path of the world and do not know the infinite alternate course history could have taken. But it is exactly this infinitude of alternate states that diversification is meant to address.

Diversification generally has no apparent benefit unless we envision what could have happened. Unfortunately our innate natures make this difficult. We do not often value our realized path in this context. After all, none of these alternate states actually happened, so it is difficult to picture what we did not experience.

A quantitative approach can yield a systematic way to evaluate the benefit (or detriment) of diversification. This way, we are not relying as much on intuition – how did our performance feel? – and are looking through a more objective lens at our initial decisions.

In the examples using the Unconstrained Sleeves, diversification focused on more than just returns. The objectives that initially went in to the portfolio construction were the parameters of interest.

Taking a systematic approach does not fully remove the art of the analysis, as was evident in the construction of the potential sample of portfolios used in the comparisons, but having a process can remove some of the behavioral biases that make sticking with a portfolio difficult in the first place.

Measuring Process Diversification in Trend Following

By Corey Hoffstein

On July 30, 2018

In Craftsmanship, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

We prefer to think about diversification in a three-dimensional framework: what, how, and when.
The “how” axis covers the process with which an investment decision is made.
There are a number of models that trend-followers might use to capture a trend. For example, trend-followers might employ a time-series momentum model, a price-minus moving average model, or a double moving average cross-over model.
Beyond multiple models, each model can have a variety of parameterizations. For example, a time-series momentum model can just as equally be applied with a 3-month formation period as an 18-month period.
In this commentary, we attempt to measure how much diversification opportunity is available by employing multiple models with multiple parameterizations in a simple long/flat trend-following process.

When investors talk about diversification, they typically mean across different investments. Do not just by a single stock, for example, buy a basket of stocks in order to diversify away the idiosyncratic risk.

We call this “what” diversification (i.e. “what are you buying?”) and believe this is only one of three meaningful axes of diversification for investors. The other two are “how” (i.e. “how are you making your decision?”) and “when” (i.e. “when are you making your decision?”). In recent years, we have written a great deal about the “when” axis, and you can find a summary of that research in our commentary Quantifying Timing Luck.

In this commentary, we want to discuss the potential benefits of diversifying across the “how” axis in trend-following strategies.

But what, exactly, do we mean by this? Consider that there are a number of ways investors can implement trend-following signals. Some popular methods include:

Prior total returns (“time-series momentum”)
Price-minus-moving-average (e.g. price falls below the 200-day moving average)
Moving-average double cross-over (e.g. the 50-day moving average crosses the 200-day moving average)
Moving-average change-in-direction (e.g. the 200-day moving average slope turns positive or negative)

As it turns out, these varying methodologies are actually cousins of one another. Recent research has established that these models can, more or less, be thought of as different weighting schemes of underlying returns. For example, a time-series momentum model (with no skip month) derives its signal by averaging daily log returns over the lookback period equally.

With this common base, a number of papers over the last decade have found significant relationships between the varying methods. For example:

	Evidence
Bruder, Dao, Richard, and Roncalli (2011)	Moving-average-double-crossover is just an alternative weighting scheme for time-series momentum.
Marshall, Nguyen and Visaltanachoti (2014)	Time-series momentum is related to moving-average-change-in-direction.
Levine and Pedersen (2015)	Time-series-momentum and moving-average cross-overs are highly related; both methods perform similarly on 58 liquid futures contracts.
Beekhuizen and Hallerbach (2015)	Mathematically linked moving averages with prior returns.
Zakamulin (2015)	Price-minus-moving-average, moving-average-double-cross-over, and moving-average-change-of-direction can all be interpreted as a computation of a weighted moving average of momentum rules.

As we have argued in past commentaries, we do not believe any single method is necessarily superior to another. In fact, it is trivial to evaluate these methods over different asset classes and time-horizons and find an example that proves that a given method provides the best result.

Without a crystal ball, however, and without any economic interpretation why one might be superior to another, the choice is arbitrary. Yet the choice will ultimately introduce randomness into our results: a factor we like to call “process risk.” A question we should ask ourselves is, “if we have no reason to believe one is better than another, why would we pick one at all?”

We like to think of it this way: ex-post, we will know whether the return over a given period is positive or negative. Ex-ante, all we have is a handful of trend-following signals that are forecasting that direction. If, historically, all of these trend signals have been effective, then there may be no reason to necessarily believe on over another.

Combining them, in many ways, is sort of like trying to triangulate on the truth. We have a number of models that all look at the problem from a slightly different perspective and, therefore, provide a slightly different interpretation. A (very) loose analogy might be using the collective information from a number of cell towers in effort to pinpoint the geographic location of a cellphone.

We may believe that all of the trend models do a good job of identifying trends over the long run, but most will prove false from time-to-time in the short-run. By using them together, we can potentially increase our overall confidence when the models agree and decrease our confidence when they do not.

With all this in mind, we want to explore the simple question: “how much potential benefit does process diversification bring us?”

The Setup

To answer this question, we first generate a number of long/flat trend following strategies that invest in a broad U.S. equity index or the risk-free rate (both provided by the Kenneth French database and ranging from 1926 to 2018). There are 48 strategy variations in total constructed through a combination of four difference processes – time-series momentum, price-minus-moving-average, and moving-average double cross-over– and 16 different lookback periods (from the approximate equivalent of 3-to-18 months).

We then treat each of the 64 variations as its own unique asset.

To measure process diversification, we are going to use the concept of “independent bets.” The greater the number of independent bets within a portfolio, the greater the internal diversification. Below are a couple examples outlining the basic intuition for a two-asset portfolio:

If we have a portfolio holding two totally independent assets with similar volatility levels, a 50% allocation to each would maximize our diversification.Intuitively, we have equally allocated across two unique bets.
If we have a portfolio holding two totally independent assets with similar volatility levels, a 90% allocation to one asset and a 10% allocation to another would lead us to a highly concentrated bet.
If we have a portfolio holding two highly correlated assets, no matter the allocation split, we have a large, concentrated bet.
If we have a portfolio of two assets with disparate volatility levels, we will have a large concentrated bet unless the lower volatility asset comprises the vast majority of the portfolio.

To measure this concept mathematically, we are going to use the fact that the square of the “diversification ratio” of a portfolio is equal to the number of independent bets that portfolio is taking.¹

Diversifying Parameterization Risk

Within process diversification, the first variable we can tweak is the formation period of our trend signal. For example, if we are using a time-series momentum model that simply looks at the sign of the total return over the prior period, the length of that period may have a significant influence in the identification of a trend. Intuition tells us that shorter formation periods might identify short-term trends as well as react to long-term trend changes more quickly but may be more sensitive to whipsaw risk.

To explore the diversification opportunities available to us simply by varying our formation parameterization, we build equal-weight portfolios comprised of two strategies at a time, where each strategy utilizes the same trend model but a different parameterization. We then measure the number of independent bets in that combination.

We run this test for each trend following process independently. As an example, we compare using a shorter lookback period with a longer lookback period in the context of time-series momentum in isolation. We will compare across models in the next section.

In the graphs below, L0 through L15 represent the lookback periods, with L0 being the shortest lookback period and L15 representing the longest lookback period.

As we might suspect, the largest increase in available bets arises from combining shorter formation periods with longer formation periods. This makes sense, as they represent the two horizons that share the smallest proportion of data and therefore have the least “information leakage.” Consider, for example, a time-series momentum signal that has a 4-monnth lookback and one with an 8-month lookback. At all times, 50% of the information used to derive the latter model is contained within the former model. While the technical details are subtler, we would generally expect that the more informational overlap, the less diversification is available.

We can see that combining short- and long-term lookbacks, the total number of bets the portfolio is taking from 1.0 to approximately 1.2.

This may not seem like a significant lift, but we should remember Grinold and Kahn’s Fundamental Law of Active Management:

Information Ratio = Information Coefficient x SQRT(Independent Bets)

Assuming the information coefficient stays the same, an increase in the number of independent bets from 1.0 to 1.2 increases our information ratio by approximately 10%. Such is the power of diversification.

Another interesting way to approach this data is by allowing an optimizer to attempt to maximize the diversification ratio. In other words, instead of only looking at naïve, equal-weight combinations of two processes at a time, we can build a portfolio from all available lookback variations.

Doing so may provide two interesting insights.

First, we can see how the optimizer might look to combine different variations to maximize diversification. Will it barbell long and short lookbacks, or is there benefit to including medium lookbacks? Will the different processes have different solutions? Second, by optimizing over the full history of data, we can find an upper limit threshold to the number of independent bets we might be able to capture if we had a crystal ball.

A few takeaways from the graphs above:

Almost all of the processes barbell short and long lookback horizons to maximize diversification.
The optimizer finds value, in most cases, in introducing medium-term lookback horizons as well. We can see for Time-Series MOM, the significant weights are placed on L0, L1, L6, L10, and L15. While not perfectly spaced or equally weighted, this still provides a strong cross-section of available information. Double MA Cross-Over, on the other hand, finds value in weighting L0, L8, and L15.
While the optimizer increases the number of independent bets in all cases versus a naïve, equal-weight approach, the pickup is not incredibly dramatic. At the end of the day, a crystal ball does not find a meaningfully better solution than our intuition may provide.

Diversifying Model Risk

Similar to the process taken in the above section, we will now attempt to quantify the benefits of cross-process diversification.

For each trend model, we will calculate the number of independent bets available by combining it with another trend model but hold the lookback period constant. As an example, we will combine the shortest lookback period of the Time-Series MOM model with the shortest lookback period of the MA Double Cross-Over.

We plot the results below of the number of independent bets available through a naïve, equal-weight combination.

We can see that model combinations can lift the number of independent bets from by 0.05 to 0.1. Not as significant as the theoretical lift from parameter diversification, but not totally insignificant.

Combining Model and Parameterization Diversification

We can once again employ our crystal ball in an attempt to find an upper limit to the diversification available to trend followers, as well as the process / parameterization combinations that will maximize this opportunity. Below, we plot the results.

We see a few interesting things of note:

The vast majority of models and parameterizations are ignored.
Time-Series MOM is heavily favored as a model, receiving nearly 60% of the portfolio weight.
We see a spread of weight across short, medium, and long-term weights. Short-term is heavily favored, with Time-Series MOM L0 and Price-Minus MA L0 approaching nearly 45% of model weight.
All three models are, ultimately, incorporated, with approximately 10% being allocated to Double MA Cross-Over, 30% to Price-Minus MA, and 60% to Time-Series MOM.

It is worth pointing out that naively allocating equally across all 48 models creates 1.18 independent bets while the full-period crystal ball generated 1.29 bets.

Of course, having a crystal ball is unrealistic. Below, we look at a rolling window optimization that looks at the prior 5 years of weekly returns to create the most diversified portfolio. To avoid plotting a graph with 48 different components, we have plot the results two ways: (1) clustered by process and (2) clustered by lookback period.

Using the rolling window, we see similar results as we saw with the crystal ball. First, Time-Series MOM is largely favored, often peaking well over 50% of the portfolio weights. Second, we see that a barbelling approach is frequently employed, balancing allocations to the shortest lookbacks (L0 and L1) with the longest lookbacks (L14 and L15). Mid-length lookbacks are not outright ignored, however, and L5 through L11 combined frequently make up 20% of the portfolio.

Finally, we can see that the rolling number of bets is highly variable over time, but optimization frequently creates a meaningful impact over an equal-weight approach.²

Conclusion

In this commentary, we have explored the idea of process diversification. In the context of a simple long/flat trend-following strategy, we find that combining strategies that employ different trend identification models and different formation periods can lead to an increase in the independent number of bets taken by the portfolio.

As it specifically pertains to trend-following, we see that diversification appears to be maximized by allocating across a number of lookback horizons, with an optimizer putting a particular emphasis on barbelling shorter and longer lookback periods.

We also see that incorporating multiple processes can increase available diversification as well. Interestingly, the optimizer did not equally diversify across models. This may be due to the fact that these models are not truly independent from one another than they might seem. For example, Zakamulin (2015) demonstrated that these models can all be decomposed into a different weighted average of the same general momentum rules.

Finding process diversification, then, might require moving to a process that may not have a common basis. For example, trend followers might consider channel methods or a change in basis (e.g. constant volume bars instead of constant time bars).

Failing Slow, Failing Fast, and Failing Very Fast

By Justin Sibears

On April 9, 2018

In Risk Management, Sequence Risk, Weekly Commentary

This post is available as a PDF download here.

Summary

For most investors, long-term “failure” means not meeting one’s financial objectives.
In the portfolio management context, failure comes in two flavors. “Slow” failure results from taking too little risk, while “fast” failure results from taking too much risk. In his book, Red Blooded Risk, Aaron Brown summed up this idea nicely: “Taking less risk than is optimal is not safer; it just locks in a worse outcome. Taking more risk than is optimal also results in a worse outcome, and often leads to complete disaster.”
A third type of failure, failing very fast, occurs when we allow behavioral biases to compound the impact of market volatility (i.e. panicked selling near the bottom of a bear market).
In the aftermath of the global financial crisis, risk management was often used synonymously with risk reduction. In actuality, a sound risk management plan is not just about reducing risk, but rather about calibrating risk appropriately as a means of minimizing the risk of both slow and fast failure.

On the way back from a recent trip, I ran across a fascinating article in Vanity Fair: “The Clock is Ticking: Inside the Worst U.S. Maritime Disaster in Decades.” The article details the saga of the SS El Faro, a U.S. flagged cargo ship that sunk in October 2015 at the hands of Hurricane Joaquin. Quoting from the beginning of the article:

“In the darkness before dawn on Thursday, October 1, 2015, an American merchant captain named Michael Davidson sailed a 790-foot U.S.-flagged cargo ship, El Faro, into the eye wall of a Category 3 hurricane on the exposed windward side of the Bahama Islands. El Faro means “the lighthouse” in Spanish.

The hurricane, named Joaquin, was one of the heaviest to ever hit the Bahamas. It overwhelmed and sank the ship. Davidson and the 32 others aboard drowned.

They had been headed from Jacksonville, Florida, on a weekly run to San Juan, Puerto Rico, carrying 391 containers and 294 trailers and cars. The ship was 430 miles southwest of Miami in deep water when it went down.

Davidson was 53 and known as a stickler for safety. He came from Windham, Maine, and left behind a wife and two college age daughters. Neither his remains nor those of his shipmates were ever recovered.

Disasters at sea do not get the public attention that aviation accidents do, in part because the sea swallows the evidence. It has been reported that a major merchant ship goes down somewhere in the world every two or three days; most ships are sailing under flags of convenience, with underpaid crews and poor safety records.

The El Faro tragedy attracted immediate attention for several reasons. El Faro was a U.S.-flagged ship with a respected captain – and it should have been able to avoid the hurricane. Why didn’t it? Add to the mystery this sample fact: the sinking of the El Faro was the worst U.S. maritime disaster in three decades.”

From the beginning, Hurricane Joaquin was giving forecasters fits. A National Hurricane Center release from September 29^th said, “The track forecast remains highly uncertain, and if anything, the spread in the track model guidance is larger now beyond 48 hours…” Joaquin was so hard to predict that FiveThirtyEight wrote an article about it. The image below shows just how much variation there was in projected paths for the storm as of September 30^th.

Davidson knew all of this. Initially, he had two options. The first option was the standard course: a 1,265-mile trip directly through open ocean toward San Juan. The second was the safe play, a less direct route that would use a number of islands as protection from the storm. This option would add 184 miles and six plus hours to the trip.

Davidson faced a classic risk management problem. Should he risk failing fast or failing slow?

Failing fast would mean taking the standard course and suffering damage or disaster at the hands of the storm. In this scenario – which tragically ended up playing out – Davidson paid the fatal price by taking too much risk.

Failing slow, on the other hand, would be playing it safe and taking the less direct route. The risk here would be wasting the company’s time and money. By comparison, this seems like the obvious choice. However, the article suggests that Davidson may have been particularly sensitive to this risk as he had been gunning for a captain position on a new vessel that would soon replace El Faro on the Jacksonville to San Juan route. In this scenario, Davidson would fail by taking too little risk.

This dichotomy between taking too little risk and failing slow and taking too much risk and failing fast is central to portfolio risk management.

Aaron Brown summed this idea up nicely in his book Red Blooded Risk, where he wrote, “Taking less risk than is optimal is not safer; it just locks in a worse outcome. Taking more risk than is optimal also results in a worse outcome, and often leads to complete disaster.”

Failing Slow

In the investing context, failing slow happens when portfolio returns are insufficient to generate the growth needed to meet one’s objectives. No one event causes this type of failure. Rather, it slowly builds over time. Think death by a thousand papercuts or your home slowly being destroyed from the inside by termites.

Traditionally, this was probably the result of taking too little risk. Oversized allocations to cash, which as an asset class has barely kept up with inflation over the last 90 years, are particularly likely to be a culprit in this respect.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

Take your average 60% stock / 40% bond investor as an example. Historically, such an investor would see a $100,000 investment grow to $1,494,003 over a 30-year horizon. Add a 5% cash allocation to that portfolio and the average end result drops to $1,406,935, an $87k cash drag. Double the cash bucket to 10% and the average drag increases to nearly $170k. This pattern continues as each additional 5% cash increment lowers ending wealth by approximately $80k.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

Fortunately, there are ways to manage funds earmarked for near-term expenditures or as a safety net without carrying excessive amounts of cash. For one example, see the Betterment article: Safety Net Funds: Why Traditional Advice Is Wrong.

Unfortunately, today’s investors face a more daunting problem. Low returns may not be limited to cash. Below, we present medium term (5 to 10 year) expected returns on U.S. equities, U.S. bonds, and a 60/40 blend from seven different firms/individuals. The average expected return on the 60/40 portfolio is less than 1% per year after inflation. Even if we exclude the outlier, GMO, the average expected return for the 60/40 is still only 1.3%. Heck, even the most optimistic forecast from AQR is downright depressing relative to historical experience.

Expected return forecasts are the views of the listed firms, are uncertain, and should not be considered investment advice. Nominal returns are adjusted by subtracting 2.2% assumed inflation.

And the negativity is far from limited to U.S. markets. For example, Research Affiliates forecasts a 5.7% real return for emerging market equities. This is their highest projected return asset class and it still falls well short of historical experience for the U.S. equity markets, which have returned 6.5% after inflation over the last 90 years.

One immediate solution that may come to mind is just to take more risk. For example, a 4% real return may still be technically achievable[1]. Assuming that Research Affiliates’ forecasts are relatively accurate, this still requires buying into and sticking with a portfolio that holds around 40% in emerging market securities, more than 20% in real assets/alternatives, and exactly 0% large-cap U.S. equity exposure[2].

This may work for those early in the accumulation phase, but it certainly would require quite a bit of intestinal fortitude. For those nearing, or in, retirement, the problem is more daunting. We’ve written quite a bit recently about the problems that low forward returns pose for retirement planning[3][4] and what can be done about it[5][6].

And obviously, one of the main side effects of taking more risk is increasing the portfolio’s exposure to large losses and fast failure, very much akin to Captain Davidson sailing way too close to the eye of the hurricane.

Failing Fast

At its core, failing fast in investing is about realizing large losses at the wrong time. Think your house burning down or being leveled by a tornado instead of being destroyed slowly by termites.

Note that large losses are a necessary, but not sufficient condition for fast failure[7]. After all, for long-term investors, experiencing a bear market eventually is nearly inevitable. For example, there has never been a 30-year period in the U.S. equity markets without at least one year-over-year loss of greater than 20%. 79% of historical 30-year periods have seen at least one year-over-year loss greater than 40%.

Fast failure is really about being unfortunate enough to realize a large loss at the wrong time. This is called “sequence risk” and is particularly relevant for individuals nearing or in the early years of retirement.

We’ve used the following simple example of sequence risk before. Consider three investments:

Portfolio A: -30% return in Year 1 and 6% returns for Years 2 to 30.
Portfolio B: 6% returns for Years 1 to 14, a -30% return in Year 15, and 6% returns for Years 16 to 30.
Portfolio C: 6% returns in Years 1 to 29 and a -30% return in Year 30.

Over the full 30-year period, all three investments have an identical geometric return of 4.54%.

Yet, the experience of investing in each of the three portfolios will be very different for a retiree taking withdrawals[8]. We see that Portfolio C fares the best, ending the 30-year period with 12% more wealth than it began with. Portfolio B makes it through the period, ending with 61% of the starting wealth, but not without quite a bit more stress. Portfolio A, however, ends in disaster, running out of money prematurely.

One way we can measure sequence risk is to compare historical returns from a particular investment with and without withdrawals. The larger this gap, the more sequence risk was realized.

We see that sequence risk peaks in periods where large losses were realized early in the 10-year period. To highlight a few periods:

The period ending in 2009 started with the tech bubble and ended with the global financial crisis.
The period ending in 1982 started with losses of 14.3% in 1973 and 25.9% in 1974.
The period ending in 1938 started off strong with a 43.8% return in 1928, but then suffered four consecutive annual losses as the Great Depression took hold.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

A consequence of sequence risk is that asset classes or strategies with strong risk-adjusted returns, especially those that are able to successfully avoid large losses, can produce better outcomes than investments that may outperform them on a pure return basis.

For example, consider the period from August 2000, when the equity market peaked prior to the popping of the tech bubble, to March 2018. Over this period, two common risk management tools – U.S. Treasuries (proxied by the Bloomberg Barclays 7-10 Year U.S. Treasury Index and iShares 7-10 Year U.S. Treasuries ETF “IEF”) and Managed Futures (proxied by the Salient Trend Index) – delivered essentially the same return as the S&P 500 (proxied by the SPDR S&P 500 ETF “SPY”). Both risk management tools have significantly underperformed during the ongoing bull market (16.6% return from March 2009 to March 2018 for SPY compared to 3.1% for IEF and 0.7% for the Salient Trend Index).

Data Source: CSI, Salient. Calculations by Newfound Research. Past performance does not guarantee future results. Returns include no fees except underlying ETF fees. Returns include the reinvestment of dividends.

Yet, for investors withdrawing regularly from their portfolio, bonds and managed futures would have been far superior options over the last two decades. The SPY-only investor would have less than $45k of their original $100k as of March 2018. On the other hand, both the bond and managed futures investors would have growth their account balance by $34k and $29k, respectively.

Failing Really Fast

Hurricanes are an unfortunate reality of sea travel. Market crashes are an unfortunate reality of investing. Both have the potential to do quite a bit of damage on their own. However, what plays out over and over again in times of crisis is that human errors compound the situation. These errors turn bad situations into disasters. We go from failing fast to failing really fast.

In the case of El Faro, the list of errors can be broadly classified into two categories:

Failures to adequately prepare ahead of time. For example, El Faro had two lifeboats, but they were not up to current code and were essentially worthless on a hobbled ship in the midst of a Category 4 hurricane.
Poor decisions in the heat of the moment. Decision making in the midst of a crisis is very difficult. The Coast Guard and NTSB put most of the blame on Davidson for poor decision making, failure to listen to the concerns of the crew, and relying on outdated weather information.

These same types of failures apply to investing. Imagine the retiree that sells all of his equity exposure in early 2009 and sits out of the market for a few years during the first few years of the bull market or maybe the retiree that goes all-in on tech stocks in 2000 after finally getting frustrated with hearing how much money his friend had made off of Pets.com. Taking a 50%+ loss on your equity exposure is bad, panicking and making rash decisions can throw your financial plans off track for good.

Compounding bad events with bad decisions is a recipe for fast failure. Avoiding this fate means:

Having a plan in place ahead of time.
If you plan on actively making decisions during a crisis (instead of simply holding), systematize your process. Lay out ahead of time how you will react to various triggers.
Sticking to your plan, even when it may feel a bit uncomfortable.
Diversify, diversify, diversify.

On that last point, the benefits of diversifying your diversifiers cannot be overstated.

For example, take the following four common risk management techniques:

Static allocation to fixed income (60% SPY / 40% IEF blend)
Risk parity (Salient Risk Parity Index)
Managed futures (Salient Trend Index)
Tactical equity with trend-following (binary SPY or IEF depending on 10-month SPY return).

We see that a simple equal-weight blend of the four strategies delivers risk-adjusted returns that are in line with the best individual strategy. In other words, the power of diversification is so significant that an equal-weight portfolio performs nearly the same as someone who had a crystal ball at the beginning of the period and could foresee which strategy would do the best.

Data Source: CSI, Salient, Bloomberg. Calculations by Newfound Research. Past performance does not guarantee future results. Returns include no fees except underlying ETF fees. Returns include the reinvestment of dividends. Blend is an equal-weight portfolio of the four strategies that is rebalanced on a monthly basis.

Achieving Risk Ignition

In the wake of the tech bubble and the global financial crisis, lots of attention has (rightly) been given to portfolio risk management. Too often, however, we see risk management used as a synonym for risk reduction. Instead, we believe that risk management is ultimately taking the right amount of risk, not too little or too much. We call this achieving risk ignition[9] (a phrase we stole from Aaron Brown), where we harness the power of risk to achieve our objectives.

In our opinion, a key part of achieving risk ignition is utilizing changes that can dynamically adapt the amount of risk in the portfolio to any given market environment.

As an example, take an investor that wants to target 10% volatility using a stock/bond mix. Using historical data going back to the 1980s, this would require holding 55% in stocks and 45% in bonds. Yet, our research shows that 20% of that bond position is held simply to offset the worst 3 years of equity returns. With 10-year Treasuries yielding only 2.8%, the cost of re-allocating this 20% of the portfolio from stocks to bonds just to protect against market crashes is significant.

This is why we advocate using tactical asset allocation as a pivot around a strategic asset allocation core. Let’s continue to use the 55/45 stock/bond blend as a starting point. We can take 30% of the portfolio and put it into a tactical strategy that has the flexibility to move between 100% stocks and 100% bonds. We fund this allocation by taking half of the capital (15%) from stocks and the other half from bonds. Now our portfolio has 40% in stocks, 30% in bonds, and 30% in tactical. When the market is trending upwards, the tactical strategy will likely be fully invested and the entire portfolio will be tilted 70/30 towards stocks, taking advantage of the equity market tailwinds. When trends turn negative, the tactical strategy will re-allocate towards bonds and in the most extreme configuration tilt the entire portfolio to a 40/60 stock/bond mix.

In this manner, we can use a dynamic strategy to dial the overall portfolio’s risk up and down as market risk ebbs and flows.

Summary

For most investors, failure means not meeting one’s financial objectives. In the portfolio management context, failure comes in two flavors: slow failure results from taking too little risk and fast failure results from taking too much risk.

While slow failure has typically resulted from allocating too conservatively or holding excessive cash balances, the current low return environment means that even investors doing everything by the book may not be able to achieve the growth necessary to meet their goals.

Fast failure, on the other hand, is always a reality for investors. Market crashes will happen eventually. The biggest risk for investors is that they are unlucky enough to experience a market crash at the wrong time. We call this sequence risk.

A robust risk management strategy should seek to manage the risk of both slow failure and fast failure. This means not simply seeking to minimize risk, but rather calibrating it to both the objective and the market environment.

[1] Using Research Affiliates’ asset allocation tool, the efficient portfolio that delivers an expected real return of 4% means taking on estimated annualized volatility of 12%. This portfolio has more than double the volatility of a 40% U.S. large-cap / 60% intermediate Treasuries portfolio, which not coincidently returned 4% after inflation going back to the 1920s.

[2] The exact allocations are 0.5% U.S. small-cap, 14.1% foreign developed equities, 24.6% emerging market equities, 12.0% long-term Treasuries, 5.0% intermediate-term Treasuries, 0.8% high yield, 4.5% bank loans, 2.5% emerging market bonds (USD), 8.1% emerging market bonds (local currency), 4.4% emerging market currencies, 3.2% REITs, 8.6% U.S. commercial real estate, 4.2% commodities, and 7.5% private equity.

[3] https://blog.thinknewfound.com/2017/08/impact-high-equity-valuations-safe-retirement-withdrawal-rates/

[4] https://blog.thinknewfound.com/2017/09/butterfly-effect-retirement-planning/

[5] https://blog.thinknewfound.com/2017/09/addressing-low-return-forecasts-retirement-tactical-allocation/

[6] https://blog.thinknewfound.com/2017/12/no-silver-bullets-8-ideas-financial-planning-low-return-environment/

[7] Obviously, there are scenarios where large losses alone can be devastating. One example are losses that are permanent or take an investment’s value to zero or negative (e.g. investments that use leverage). Another are large losses that occur in portfolios that are meant to fund short-term objectives/liabilities.

[8] We assume 4% withdrawals increased for 2% annual inflation.

[9] https://blog.thinknewfound.com/2015/09/achieving-risk-ignition/

Portable Beta: Making the Most of the Returns You’re Already Getting

By Corey Hoffstein

On December 4, 2017

In Podcast, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

Traditionally, investors have used a balance between stocks and bonds to govern their asset allocation. Expanding this palette to include other asset classes can allow them to potentially both enhance return and reduce risk, benefiting from diversification.
Modern portfolio theory tells us, however, that the truly optimal choice is to apply leverage to the most risk-efficient portfolio.
In a low expected return environment, we believe that capital efficiency is of the utmost importance, allowing investors to better capture the returns they are already earning.
We believe that the select application of leverage can allow investors to both benefit from enhanced diversification and capital efficiency, in a concept we are calling portable beta.

Diversification has been the cornerstone of investing for thousands of years as evidenced by timeless proverbs like “don’t put all your eggs in one basket.” The magic behind diversification – and one of the reasons it is considered the only “free lunch” available in investing – is that a portfolio of assets will always have a risk level less-than-or-equal-to the riskiest asset within the portfolio.

Yet it was not until Dr. Harry Markowitz published his seminal article “Portfolio Selection” in 1952 that investors had a mathematical formulation for the concept. His work, which ultimately coalesced into Modern Portfolio Theory (MPT), not only provided practitioners a means to measure risk and diversification, but it also allowed them to quantify the marginal benefit of adding new exposures to a portfolio and to derive optimal investment portfolios. For his work, Dr. Markowitz was awarded a Nobel prize in 1990.

What became apparent through this work is that the risk and expected reward trade-off is not necessarily linear. For example, in shifting a portfolio’s allocations from 100% bonds to 100% stocks, risk may actually initially decrease and expected return may increase due to diversification benefits. For example, in the hypothetical image below, we can see that the 60/40 stock-bond blend offers a nearly identical risk level to the 100% bond portfolio with significantly higher expected return.

Of course, these benefits are not limited solely to stock/bond mixes. Indeed, many investors focus on how they can expand their investment palette beyond traditional asset classes to include exposures that can expand the efficient frontier: the set of portfolios that represents the maximum expected return for each given risk level.

In the example graph below we can see this expectation labeled as the diversification benefit.

The true spirit of MPT suggests something different, however. MPT argues that in an efficient market, all investors would hold an identically allocated portfolio, which turns out to be the market portfolio. Holding any other portfolio would be sub-optimal. The argument goes that rational investors would all seek to maximize their expected risk-adjusted return and then simply introduce cash or leverage to meet their desired risk preference. This notion is laid out below.

In practice, however, while many investors are willing to expand their investment palette beyond just stocks and bonds, few ultimately take this last step of adding leverage. Conservative investors rarely barbell a riskier portfolio with cash, instead opting to be fully invested in fixed income centric portfolios. Aggressive investors rarely apply leverage, instead increasing their allocation to risky assets. Some argue that this leverage aversion actually gives rise to the low volatility / betting-against-beta anomaly.

This is unfortunate, as the prudent use of leverage can potentially enhance returns without necessarily increasing risk. For example, below we plot the hypothetical growth of a dollar invested in the S&P 500, a 60/40 portfolio, and a 60/40 portfolio levered to target the volatility level of the S&P 500.

	Ann. Return	Ann. Volatility	Max Drawdown
S&P 500	9.2%	14.1%	55.2%
60/40 Portfolio	8.0%	7.7%	29.8%
Levered 60/40 Portfolio	12.5%	14.9%	54.4%

Source: CSI. Calculations by Newfound Research. Results are hypothetical and backtested. Past performance is not an indicator of future results. Returns assume the reinvestment of all dividends and income and are gross of all fees except for underlying ETF expense ratios. The S&P 500 represented by SPDR S&P 500 ETF (”SPY”). 60/40 Portfolio is a 60% SPDR S&P 500 ETF (“SPY”) and 40% iShares 7-10 Year U.S. Treasury ETF (“IEF”) mix, rebalanced annually. Levered 60/40 applies 182% leverage to the 60/40 Portfolio by shorting an 82% position in the iShares 1-3 Year U.S. Treasury ETF (“SHY”). The leverage amount was selected so that the Levered 60/40 Portfolio would match the annualized volatility level of the S&P 500.

We can see that the Levered 60/40 portfolio trounces the S&P 500, despite sharing nearly identical risk levels. The answer as to why is two-fold.

First is the diversification benefits we gain from introducing a negatively correlated asset to a 100% equity portfolio. We can see this by comparing the annualized return and volatility of the S&P 500 versus the standard 60/40 portfolio. While the S&P 500 outperformed by 120 bps per year, it required bearing 640 bps of excess volatility (14.9% vs. 7.7%) and a realized drawdown that was of 2540 bps deeper (55.2% vs. 29.8%). Introducing the diversifying asset made the portfolio more risk-efficient. Unfortunately, in doing so, we were forced to allocate to an asset with a lower expected return (from equities to bonds), causing us to realize a lower return.

This lower return but higher risk-adjusted return is the thinking behind the common saying that “investors can’t eat risk-adjusted returns.”

That is where the benefits from leverage come into play. Leverage creates capital efficiency. In this example, we were able to treat each $1 invested as if it were $1.82. This allowed us to match the risk level of equities and benefit from the enhanced risk-efficiency of the diversified portfolio.

Efficiency Over Alpha

In a recent Barron’s roundtable[1], we were asked our thoughts on the future of ETFs. We receive this question fairly often when speaking on panels. The easy, obvious answers are, “more niche products,” or “an ETF for every asset class,” or even “smarter beta” (as if somehow beta has gone from high school to college and is now matriculating to graduate school).

In truth, none of these answers seem particularly innovative or even satisfactory when we consider that they will likely do little to help investors actually achieve their financial goals. This is especially true in a low expected return environment, where finding the balance between growth and safety is akin to sailing between Scylla and Charybdis[2]: too much exposure to risky assets can increase sequence risk and too little can increase longevity risk. Edging too close to either can spell certain financial doom.

With this in mind, our answer as of late has deviated from tradition and instead has focused on greater efficiency. Instead of trying to pursue excess returns, our answer is to maximize the returns investors are, largely, getting already. Here are a few examples of how this can be achieved:

Lower Costs. As expected excess returns go down, the proportion taken by fees goes up. The market may bear a 1% fee when expected excess returns are abundant, but that same fee may be the difference between retirement success and failure in a low return environment. Therefore, the most obvious way to increase efficiency for investors is to lower costs: both explicit (fees) and implicit (trading costs and taxes). Vanguard has led the charge in this arena for decades, and active managers are now scrambling to keep up. While simply lowering fees is the most obvious solution, more creative fee arrangements (e.g. flexible fees) may also be part of the solution.
Increased Exposure to Active Views. In a recent commentary, It’s Long/Short Portfolios All the Way Down[3], we explored the idea that an active investment strategy is simply a benchmark plus a dollar-neutral long/short portfolio layered on top. This framework implies that if the cost of accessing beta goes down, the implied cost for active necessarily goes up, creating a higher hurdle rate for active managers to clear. In our perspective, the way to clear this hurdle is for active managers to offer portfolios with greater exposure to their active views, with the most obvious example being be a high active share / active risk, concentrated equity portfolio. Such an approach increases the efficiency of exposure to active strategies.
Risk Management. Traditional risk management focuses exclusively on the use of capital diversification. Traditionally allocated portfolios, however, are often significantly dominated by equity volatility and can therefore carry around a disproportionate amount of fixed income exposure to hedge against rare tail events. We believe that diversifying your diversifiers – e.g. the incorporation of trend-following approaches – can potentially allow investors to increase their allocation to asset classes with higher expected returns without significantly increasing their risk profile.
Leverage. As we saw in our example above, leverage may allow us to invest in more risk-efficient, diversified portfolios without necessarily sacrificing return. In fact, in certain circumstances, it can even increase return. So long as we can manage the risk, increasing notional exposure to $1.50 for every $1 invested in a low return environment is effectively like increasing our returns by 1.5x (less the cost of leverage). For active strategies, a subtler example may be the return to a 130/30 style investment strategy (130% long / 30% short), which can allow investors enhanced access to a manager’s active views without necessarily taking on more beta risk. We expect that institutional investors may begin to re-acquaint themselves with ideas like portable alpha, where traditional portfolio exposures may be used as collateral for market-neutral, alpha-seeking exposures.[4]

Portable Beta Theory

We see lower costs as inevitable: Vanguard has made sure of that. We see increased exposure to active views as the only way for traditional active management (i.e. long-only stock pickers) to survive. A number of alternative diversifiers have already made their way to market, including defensive factor tilts, long/flat trend-following, options strategies, and managed futures. Leverage is where we really think new innovation can happen, because it allows investors to re-use capital to invest where they might not otherwise do so because it would have reduced their risk profile.

For example, for young investors the advice today is largely to invest predominately in equities and manage risk through their extended investment horizon. This has worked historically in the United States, but there are plenty of examples where such a plan would have failed in other markets around the globe. In truth, in almost no circumstance is 100% equities a prudent plan when leverage is available.[5]

As a simple example, let us constrain ourselves to only investing in stocks and bonds. Using J.P. Morgan’s 2018 capital market assumption outlook[6], we can create a stock-bond efficient frontier. In these assumptions, U.S. large-cap equities have an expected excess return of 4.4% with a volatility of 14.0%, while U.S. aggregate bonds have an expected excess return of 1.3% with a volatility of 3.8%. The correlation between the two asset classes is zero.

Plotting the efficient frontier, we can also solve for the portfolio that maximizes the risk-adjusted expected excess return (“Sharpe optimal”). We find that this mixture is almost exactly a 20% stock / 80% bond portfolio: a highly conservative mixture. However, this mix has an expected excess return of just 1.92%.

Source: J.P. Morgan. Calculations by Newfound Research.

However, if we are willing to apply 3.4-times leverage to this portfolio, so as to match the volatility profile of equities, the story changes. A levered maximum Sharpe ratio portfolio – 278% bonds and 66% stocks – would now offer an expected excess return of 6.6%: a full 2.2% higher than a 100% stock portfolio (again ignoring the spread charged above the risk-free rate in real world for accessing leverage).

What if an investor already has a 100% equity portfolio with significant capital gains? One answer would be to overlay the existing position with the exposure required to move the portfolio from its currently sub-optimal position to the optimal allocation. In this case, we could sell-short a 34% notional position in the S&P 500, use the proceeds to buy 34% in a core U.S. bond position, and then borrow to buy the remaining 244%. We would consider the -34% equity and +278% position in bonds our “portable beta.”

	Original Portfolio	Target Portfolio	Portable Beta
U.S. Equities	100%	66%	-34%
U.S. Aggregate Bonds	0%	278%	+278%

Portable Beta in Practice: Risk Cannot Be Destroyed, Only Transformed

In theory, the optimal decision is to lever a 20/80 stock/bond mix by 340%. In practice, however, volatility is not an all-encompassing risk metric. We know that moving from a portfolio dominated by equities to one dominated by bonds introduces significant sensitivity to interest rates. Furthermore, the introduction of leverage introduces borrowing costs and operational risks that are not insignificant.

Risk parity proponents would argue that this is actually a beneficial shift, creating a more diversified profile to different risk factors. In our example above, however, we can compare the results of a 100% stock portfolio to a 66% bond / 278% stock portfolio during the 1970s, when not only did interest rates climb precipitously, but the yield curve inverted (and remained inverted) on several occasions.

Source: Federal Reserve of St. Louis and Robert Shiller. Calculations by Newfound Research. Results are hypothetical and backtested. Past performance is not an indicator of future results. Returns assume the reinvestment of all dividends and income and are gross of all fees. The Levered 20/80 portfolio is comprised of a 66% position in U.S. equities and a 278% position in a 10-year constant maturity U.S. Treasury index and a -244% position in a constant maturity 1-year U.S. Treasury index. The period of 12/31/1969 to 12/31/1981 was used to capture an example period where interest rates rose precipitously.

While $1 invested on 12/31/1969 U.S. equities was worth $2.29 on 12/31/1981, the same dollar was worth only $0.87 in the levered portfolio. Of course, the outlook for stocks and bonds (including expected excess return, volatility, and correlation) was likely sufficiently different in 1969 that the Sharpe optimal portfolio may not have been a 20/80. Regardless, this highlights the significant gap between theory and practice. In modern portfolio theory, capital market assumptions are assumed to be known ex-ante and asset returns are assumed to be normally distributed, allowing correlation to fully capture the relationship between asset classes. In practice, capital market assumptions are a guess at best and empirical asset class returns exhibit fat-tails and non-linear relationships.

In this case in particular, an inverted yield curve can lead to negative expected excess returns for U.S. fixed income, correlation changes can lead to dramatic jumps in portfolio volatility, and the introduction of duration can lead to losses in a rising rate environment. Thus, a large, concentrated, and static portable beta position may not be prudent.

Traditional portfolio theory tells us that an asset should only be added to a portfolio (though, the quantity not specified) if its Sharpe ratio exceeds the Sharpe ratio of the existing portfolio times the correlation of that asset and the portfolio. We can use this rule to try to introduce a simple timing system to help manage risk.

When the trigger says to include bonds, we will invest in the Levered 20/80 portfolio; when the trigger says that bonds will be reductive, we will simply hold U.S. equities (labeled “Dynamic Levered 20/80” below). We can see the results below:

Source: Federal Reserve of St. Louis and Robert Shiller. Calculations by Newfound Research. Results are hypothetical and backtested. Past performance is not an indicator of future results. Returns assume the reinvestment of all dividends and income and are gross of all fees. The Levered 20/80 portfolio is comprised of a 66% position in U.S. equities, a 278% position in a 10-year constant maturity U.S. Treasury index and a -244% position in a constant maturity 1-year U.S. Treasury index. The period of 12/31/1969 to 12/31/1981 was used to capture an example period where interest rates rose precipitously.

Tactical timing, of course, introduces its own risks (including estimation risk, model risk, whipsaw risk, trading cost risk, reduced diversification risk, et cetera). Regardless, empirical evidence suggests that styles like value, momentum, and carry may have power in forecasting the level and slope of the yield curve.[7] That said, expanding the portable beta palette to include more asset classes (through explicit borrowing or derivatives contracts) may reduce the need for timing in preference of structural diversification. Again, risk parity argues for exactly this.

In practice, few investors may be comfortable with notional leverage exceeding hundreds of percentage points. Nevertheless, even introducing a modest amount of portable beta may have significant benefits, particularly for investors lacking in diversification.

For example, equity heavy investors may add little risk by introducing modest amounts of exposure to U.S. Treasuries. Doing so may allow them to harvest the term premium over time and potentially even benefit from flight-to-safety characteristics that may offset equity losses in a crisis. On a forward-looking basis (again, using J.P. Morgan’s 2018 capital market assumptions), we can see that using leverage to exposure to intermediate-term U.S. Treasuries is expected to both enhance return and reduce risk relative to a 100% equity portfolio.

Source: J.P. Morgan. Calculations by Newfound Research.

How would this more moderate approach have fared historically? Below we plot the returns of U.S. equities, a constant 100/50 portfolio (a 100% equity / 50% bond portfolio achieved using leverage), a dynamic 100/50 portfolio (100% equity portfolio that selectively adds a levered 50% bond position using the same timing rules discussed above).

	Ann. Return	Ann. Volatility	Max Drawdown
U.S. Equities	10.0%	15.7%	54.7%
100/50 Portfolio	10.7%	16.3%	51.1%
Dynamic 100/50 Portfolio	11.1%	15.8%	50.8%

Source: Federal Reserve of St. Louis and Robert Shiller. Calculations by Newfound Research. Results are hypothetical and backtested. Past performance is not an indicator of future results. Returns assume the reinvestment of all dividends and income and are gross of all fees. The Constant 100/50 portfolio is comprised of a 100% position in U.S. equities and a 50% position in a 10-year constant maturity U.S. Treasury index funded by a -50% position in a constant maturity 1-year U.S. Treasury index. The Dynamic 100/50 portfolio invests in either the U.S. Equity portfolio or the Constant 150/50 portfolio depending on the dynamic trade signal (see above). The period of 2/1962 to 10/2017 represents the full set of available data.

We can see that the Dynamic 100/50 strategy is able to add 110 bps in annualized return with only an added 10 bps in increased volatility, while reducing the maximum realized drawdown by 390 bps. Even naïve constant exposure to the Treasury position proved additive over the period. Indeed, by limiting exposure, the Constant 100/50 portfolio achieved a positive 95.7% total return during the 1969-1981 period versus the -13% return we saw earlier. While this still underperformed the 129.7% and 136.6% total returns achieved by U.S. equities and the Dynamic 100/50 portfolio respectively, it was able to add value compared to U.S. equities alone in 67% of years between 1981 and 2017. For comparison, the Dynamic 100/50 strategy only achieved a 60% hit rate.

Conclusion

We will be the first to admit that these ideas are neither novel nor unique. Indeed, the idea of portable beta is simply to take the theoretically inefficient exposure most investors hold and move it in the direction of a more theoretically optimal allocation through the prudent use of leverage. Of course, the gap between theory and practice is quite large, and defining exactly what the optimal target portfolio actually is can be quite complicated.

While the explicit concept of portable beta may be more palatable for institutions, we believe the concepts can, and should, find their way into packaged format. We believe investors can benefit from building blocks that enable the use of leverage and therefore allow for the construction of more risk- and capital-efficient portfolios. Indeed, some of these ideas already exist in the market today. For example:

Risk parity portfolios.
An alpha-generating fixed-income portfolio overlaid with equity futures.
The S&P 500 overlaid with a position in gold futures.
A strategic 60/40 allocation overlaid with a managed futures strategy.

We should consider, at the very least, how packed leverage applied to our traditional asset class exposures may allow us to free up capital to invest in other diversifying or alpha-seeking opportunities. The 100/50 portfolio discussed before is, effectively, a 66/34 portfolio levered 1.5 times. Thus, putting 2/3^rds of our capital in the 100/50 portfolio gives us nearly the same notional exposure as a 60/40, effectively freeing up 1/3^rd of our capital for other opportunities. (Indeed, with some mental accounting gymnastics, we can actually consider it to be the same as holding a 66/34 portfolio with 100% of our capital and using leverage to invest elsewhere.)

While “no derivatives, leverage, or shorting” may have been the post-2008 mantra for many firms, we believe the re-introduction of these concepts may allow investors to achieve much more risk-efficient investment portfolios.

[1] https://www.barrons.com/articles/whats-next-for-etfs-1510976833

[2] Scylla and Charybdis were monsters in Greek mythology. In The Odyssey, Odysseus was forced to sail through the Strait of Messina, where the two monsters presided on either side, posing an inescapable threat. To cross, one had to be confronted. The equivalent English seafaring phrase is, “Between a rock and a hard place.”

[3] https://blog.thinknewfound.com/2017/11/longshort-portfolios-all-the-way-down/

[4] https://en.wikipedia.org/wiki/Portable_alpha

[5] https://www.aqr.com/library/journal-articles/why-not–equities

[6] https://am.jpmorgan.com/us/institutional/our-thinking/2018-long-term-capital-market-assumptions

[7] See Duration Timing with Style Premia (Newfound 2017) and Yield Curve Premia (Brooks and Moskowitz 2017)

The Research Library of Newfound Research

Tag: diversification Page 3 of 4

What do portfolios and teacups have in common?

Summary

Introduction

The Experiment Setup

The What

The How

The When

Conclusion

Measuring the Benefit of Diversification

Summary

Introduction

A Recap of the Process

Equity Hedge

Absolute Return

Equity-like with Downside Management

Conclusion

Measuring Process Diversification in Trend Following

Summary

The Setup

Diversifying Parameterization Risk

Diversifying Model Risk

Combining Model and Parameterization Diversification

Conclusion

Failing Slow, Failing Fast, and Failing Very Fast

Summary

Failing Slow

Failing Fast

Failing Really Fast

Achieving Risk Ignition

Summary

Portable Beta: Making the Most of the Returns You’re Already Getting

Summary

Efficiency Over Alpha

Portable Beta Theory

Portable Beta in Practice: Risk Cannot Be Destroyed, Only Transformed

Conclusion

Tag: diversification Page 3 of 4

What do portfolios and teacups have in common?

Summary­

Introduction

The Experiment Setup

The What

The How

The When

Conclusion

Measuring the Benefit of Diversification

Summary­

Introduction

A Recap of the Process

Equity Hedge

Absolute Return

Equity-like with Downside Management

Conclusion

Measuring Process Diversification in Trend Following

Summary­

The Setup

Diversifying Parameterization Risk

Diversifying Model Risk

Combining Model and Parameterization Diversification

Conclusion

Failing Slow, Failing Fast, and Failing Very Fast

Summary

Failing Slow

Failing Fast

Failing Really Fast

Achieving Risk Ignition

Summary

Portable Beta: Making the Most of the Returns You’re Already Getting

Summary­­

Efficiency Over Alpha

Portable Beta Theory

Portable Beta in Practice: Risk Cannot Be Destroyed, Only Transformed

Conclusion

Summary

Summary

Summary

Summary