Graham | Research Papers

A couple of days in mid-March 2023 will enter records as some of the most volatile times for fixed income returns. Whether measured in yield change or change in futures prices, the sudden bond appreciation starting on March 10 represented moves of the order of multiple standard deviations. Historically, the closest event in terms of market moves dates back to Black Monday in 1987. Turbulent markets often lead to a large dispersion in performance for systematic traders. In this note we investigate how different execution paths following the market shock of March 10 would have resulted in wildly different PnL outcomes, over a period of less than a week.

Successful systematic trading strategies depend on some element of predictability of market behavior, however small. When trading futures, signals seek to predict market returns, while predictions of market volatility and correlations are made to allow for risk management of the portfolio. In this note we take a brief look at how easily each of these market variables is predicted and what implications this has for systematic trading.

The first half of 2022 was an arduous stretch for markets, as the reflation risks of 2021 shifted to full-blown inflation coming into the year. Amid the resultant dispersion in active management styles, trend-following has been a notable winner. But given the capricious nature of global events, it's reasonable to ask how trend portfolios might fare under a sudden reversal of recent moves. In this note, we show that volatility-targeting trend-following portfolios would not per se draw down badly, even in an extreme scenario.

Inflation levels have recently reached highs not seen in decades, causing concern amongst investors over the impact this may have on their investment returns, especially for portfolios with large exposures to equities and bonds. With traditional inflation hedges such as TIPS having an uncertain outlook, and commodities only just having experienced a strong rally, we explore trend-following as a suitable investment strategy to provide inflation protection in a more risk-controlled and consistent way.

Trend-following profits from timing markets, which leads to the question whether trend-following itself can be timed. This note examines performance statistics for a trend-following benchmark, suggesting that timing the entry or exit from trend-following will not yield consistent performance.

If trend-following can successfully time asset returns, can we apply the strategy to its own NAV to boost performance? In this research note we introduce a simplified model that preserves the nature of generic trend-following strategies, reducing them to an analytically tractable form. We then deduce some mathematical characteristics from trend-following P&L returns that are distinct from asset returns, showing that the former is less amenable to being trend-followed again. Our results cast doubt upon the ability of an allocator to time strategies to enhance portfolio performance.

Trend-following strategies offer diversification benefits with their inherent low correlation to equities. Their potential to be long equities when markets rally can pose challenges for asset owners, however, who can only accomodate limited equity exposure. Other investors may even seek trend-following strategies with negative correlation to equities in the hope of added protection in negative equity markets. In this note we address ways of modifying equity exposure to achieve such goals.

This paper surveys the nascent but fast-growing universe of ESG equity index futures by contract, volume, and open interest. We estimate the tradeable portfolio size, replacing standard equity index futures with ESG index futures in our core trend-following strategies. We find that, in simulation, such a substitution would not be to the detriment of the portfolio overall.

We seek to develop a quantitative framework to assess how macro-economic shocks impact the stock-bond correlation. In particular, we examine how these shocks drive long periods of either positive or negative bond-stock correlation. We find that the positive correlation observed from 1972 to 1999 is attributable to high inflation shocks coupled with a hawkish Fed policy. The negative correlation observed from 2000 to 2020 can be attributed to recurring negative growth shocks and concerns over economic strength. Accordingly, our findings cast doubt on the conventional wisdom that one can always trust bonds to hedge losses in stocks. Instead, we find that the hedging property of bonds is highly dependent on the source of macroeconomic shocks driving losses in stocks.

Over the last couple of decades, bonds have been a reliable investment, added to portfolios to generate consistent long-term returns and provide crisis protection. Looking ahead and against the backdrop of meager yields that effectively cannot drop much lower, it is far from certain that their return potential and ability to offer protection will carry forward. With this in mind, we explore whether we can achieve a bond-like return profile via a suitable combination of different assets.

Correlation is widely used as a measure of the expected efficacy of portfolio diversifiers, despite the fact that it has many limitations. This note examines its shortfalls when used as a single measure and suggests supplementary methods of assessing the expected benefit that diversifying portfolio components can bring, specifically with regards to preventing or softening losses in tail scenarios. Being aware of the 'type' of diversification one seeks, an investor can purposefully choose portfolio components that fulfill the desired role. While there may be no single perfectly reliable tail loss diversifier - other than paying a significant premium for insurance in the form of options - a combination of a variety of well-chosen diversifiers can offer downside protection whilst still achieving a positive expected return.

In this paper we highlight some of the mechanics, nuances, and pitfalls unique to OTC FX trading and propose that building a bespoke FX Aggregator is a way to overcome some of these challenges. We also highlight some of the considerations that are needed in such an endeavor.

In this research note, we explore the effect of volatility on compound returns. We start with the so-called volatility drag, which refers to the well-known, but sometimes counterintuitive, difference between the arithmetic and geometric mean returns of a portfolio. We then present some results that show the effect of leverage on terminal wealth.

Portfolio protection against sharp declines in equity markets is an important allocation consideration for investors, and has been highlighted amidst the recent crisis. In this brief note we take a closer look at the effectiveness of bonds to deliver a hedge during equity drawdowns, and find that while historically they may have performed well, it is not clear they will do so going forward.

The health crisis that started its grip on the world at the beginning of 2020 shook the financial markets in February and March, leading to sudden and massive declines in the equity markets. Investors with long equity exposure saw gains that had accrued over years wiped out in mere weeks. While the markets have recouped a significant amount of these losses in the medium term since, the crisis has brought renewed interest to investments and investment strategies that can offer effective portfolio protection in such tail risk events. In this note we compare and contrast several investment approaches by assessing their long-run and crisis performance. We find that all of them deliver protection to some extent, allowing an investor to determine which approach is most suited as an addition to their particular portfolio.

Trend-following strategies experienced a wide range of performance outcomes during February and March 2020. In this paper, we illustrate how the precise sequence of events that occurred led to some strategies performing unexpectedly poorly, while others performed unexpectedly well. Our results suggest that should we see a similar situation replay again, where markets fall the same amount in the same period, but along a slightly different path, we would generally expect to see broadly positive performance and a narrower range of outcomes.

Interpretability is an increasingly vital issue in machine learning. Computerized statistical modeling has become the de facto paradigm for quantitative decision-making in any number of fields, including healthcare, advertising, investing, and more. And yet, the relative opacity of many of these techniques can pose a real issue in sensitive applications. Furthermore, the inability to interpret a model's behavior removes an essential part of the feedback loop for the practitioner, who needs to have a good understanding of the model to know when it's bound to fail, or where it can be improved. In this note, we first review the canonical statistical machine learning problem, before describing the issue of model interpretability and some of the recent developments. We list some examples of both interpretable and non-interpretable models and explain some of the differences.