Statistical learning and macro trading: the basics

February 5, 2022

The rise of data science and statistical programming has made statistical learning a key force in macro trading. Beyond standard price-based trading algorithms, statistical learning also supports the construction of quantamental systems, which make the vast array of fundamental and economic time series “tradable” through cleaning, reformatting, and logical adjustments. Fundamental economic developments are poised to play a growing role in the statistical trading and support models of market participants. Machine learning methods automate the process and are a basis for reliable backtesting and efficient implementation.

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How to estimate factor exposure, risk premia, and discount factors

January 22, 2022

The basic idea behind factor models is that a large range of assets’ returns can be explained by exposure to a small range of factors. Returns reflect factor risk premia and price responses to unexpected changes in the factors. The theoretical basis is arbitrage pricing theory, which suggests that securities are susceptible to multiple systemic risks. The statistical toolkit to estimate factor models has grown in recent years. Factors and exposures can be estimated through various types of regressions, principal components analysis, and deep learning, particularly in form of autoencoders. Factor risk premia can be estimated through two-pass regressions and factor mimicking portfolios. Stochastic discount factors and loadings can be estimated with the generalized method of moments, principal components analysis, double machine learning, and deep learning. Discount factor loadings are particularly useful for checking if a new proposed factor does add any investment value.

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Variance risk premia for patient investors

January 8, 2022

The variance risk premium manifests as a long-term difference between option-implied and expected realized asset price volatility. It compensates investors for taking short volatility risk, which typically comes with a positive correlation with the equity market and occasional outsized drawdowns.
A recent paper investigates a range of options-related strategies for earning the variance risk premium in the long run, including at-the-money straddle shorts, strangle shorts, butterfly spread shorts, delta-hedged shorts in call or put options, and variance swaps. Evidence since the mid-1990s suggests that variance is an attractive factor for the long run, particularly when positions take steady equal convexity exposure. Unlike other factor strategies, variance exposure has earned premia fairly consistently and typically recovered well from its intermittent large drawdowns.

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Classifying market regimes

December 25, 2021

Market regimes are clusters of persistent market conditions. They affect the relevance of investment factors and the success of trading strategies. The practical challenge is to detect market regime changes quickly and to backtest methods that may do the job. Machine learning offers a range of approaches to that end. Recent proposals include [1] supervised ensemble learning with random forests, which relate the market state to values of regime-relevant time series, [2] unsupervised learning with Gaussian mixture models, which fit various distinct Gaussian distributions to capture states of the data, [3] unsupervised learning with hidden Markov models, which relate observable market data, such as volatility, to latent state vectors, and [4] unsupervised learning with Wasserstein k-means clustering, which classifies market regimes based on the distance of observed points in a metric space.

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The risk-reversal premium

December 10, 2021

The risk reversal premium manifests as an overpricing of out-of-the-money put options relative to out-of-the-money call options with equal expiration dates. The premium apparently arises from equity investors’ demand for downside protection, while most market participants are prohibited from selling put options. A typical risk reversal strategy is a delta-hedged long position in out-of-the-money calls and an equivalent short position in out-of-the-money puts. Historically, the returns on such a strategy have been positive and displayed little correlation with the returns of the underlying stocks. The strategy does incur gap risk with a large downside, however. The long-term profit of risk-reversal strategies reflects implicit market subsidies related to “loss aversion”.

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Fundamental value strategies

November 13, 2021

Value opportunities arise when market prices deviate from contracts’ present values of all associated entitlements or obligations. However, this theoretical concept is difficult and expensive to apply. Instead, simple valuation ratios, such as real interest rates or equity earnings yields with varying enhancements, have remained popular. Moreover, value strategies can take a long time to pay off and positive returns may be concentrated on episodes of “critical transitions”.
Historically, it has been easier to predict relative value between similar contracts rather than absolute value. Also, simple valuation ratios become more meaningful when combined with related economic indicators. Thus, long-term bond yields are plausibly related to inflation expectations and the correlation of bond prices with economic cycles and market trends. Equity earnings yields can be enhanced by economic trends and market information. And effective exchange rates become a more meaningful metric when combined with inflation differentials and measures of competitiveness of a currency area.

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Equity factor timing with macro trends

October 30, 2021

Plausibility and empirical evidence suggest that the prices of equity factor portfolios are anchored by the macroeconomy in the long run. A new paper finds long-term equilibrium relations of factor prices and macro trends, such as activity, inflation, and market liquidity. This implies the predictability of factor performance going forward. When the price of a factor is greater than the long-term value implied by the macro trends, expected returns should be lower over the next period. The predictability seems to have been economically large in the past.

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Measuring the value-added of algorithmic trading strategies

October 16, 2021

Standard performance statistics are insufficient and potentially misleading for evaluating algorithmic trading strategies. Metrics based on prediction errors mistakenly assume that all errors matter equally. Metrics based on classification accuracy disregard the magnitudes of errors. And traditional performance ratios, such as Sharpe, Sortino and Calmar are affected by factors outside the algorithm, such as asset class performance, and rely on the normal distribution of returns. Therefore, a new paper proposes a discriminant ratio (‘D-ratio’) that measures an algorithm’s success in improving risk-adjusted returns versus a related buy-and-hold portfolio. Roughly speaking, the metric divides annual return by a value-at-risk metric that does not rely on normality and then divides it by a similar ratio for the buy-and-hold portfolio. The metric can be decomposed into the contributions of return enhancement and risk reduction.

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The emotion beta of stocks

October 2, 2021

Stock markets cater to both the financial and emotional needs of investors. In particular, integral emotions, which are caused by decisions themselves, are useful personal experiences. However, they compromise conventional valuation criteria and can lead to market inefficiency. A new paper estimates the emotional ‘glitter’ of stocks as an ’emotion beta’, i.e. the statistical sensitivity of returns to a market-level emotion index. The index is based on the difference between excitement and anxiety word counts in newspaper articles. Emotion betas significantly and positively predict subsequent return differentials across stocks. Tracking emotional attraction seems to make investor behavior partly foreseeable. High-emotion portfolios have historically outperformed low-emotion portfolios significantly.

Bin Hasan Shehub, Alok Kumar and Richard Taffler (2021), “Anxiety, Excitement, and Asset Prices”

The below quotes are from the paper. Headings, cursive text, and text in brackets has been added.
This post ties in with this site’s summary on implicit subsidies, particularly the section on equity.

The importance of emotions in investment decisions

“Stock market participation meets both emotional and financial needs of investors. Investors are likely to enter into emotional relationships with stocks…The role of emotions in decision-making is a dominant theme in the psychology literature. Financial economists have… recognized the importance of incidental emotions such as weather, sentiment, and mood in investment decisions and financial market outcomes…In contrast, the potential impact of integral or fundamental emotions (e.g., excitement, anxiety, fear, panic, anger, guilt, etc.) on financial decisions and aggregate market outcomes has received relatively less attention…Integral emotions…are fundamental and often unconscious, and at sufficient levels of intensity can strongly affect cognitive processing.”

“As opposed to incidental emotions, integral emotions are emotions that are caused by the decision itself. They arrive, for example, when you think about the parameters of the decision or its implications. And these emotions can actually be pretty useful. If thinking through a decision causes you some anxiety, that is useful information: it might be a sign that you need to be very cautious, and that you should potentially be more risk-averse rather than risk-seeking with the decision.” [Cote]

“The effects of integral emotions are difficult to avoid and they are influential even in the presence of cognitive information. The intensity of such fundamental emotions progressively takes over and overrides rational courses of action. Consequently, investors are likely to make sub-optimal decisions”

“The intensity of investor-firm emotional relation adds to the conventional asset valuation criteria. In particular, investors’ expectations of future gain, both as individuals and as a group, create excitement, but with the associated anxiety of future loss. We demonstrate that such an uncertainty-driven emotional process is an important driver of asset prices.”

How to measure emotion beta

“We introduce the concept of emotional utility and posit that investors enter into emotionally-charged relationships with the stocks they invest in. Investors are likely to experience different emotions such as excitement and anxiety and enter into ambivalent object relationships with stocks of a ‘love’ and ‘hate’ nature affecting their investment preferences…Investors create a set of attractive stocks that grab their attention before making the final investment decision. In the same way, we conjecture that investors are attracted to stocks that have emotional ‘glitter’, i.e., high emotional utility. Once such an emotional bond exists, investors are likely to derive emotional utility from their investments.”

“We measure the time-varying emotional utility of stocks for investors in terms of the feelings of excitement and anxiety that they generate. We estimate each stock’s emotional utility to investors, and examine whether this firm-level measure of sensitivity to changes in market-level emotional state (i.e., emotion beta) can explain cross-sectional patterns in stock returns.”

“To measure an individual stock’s emotional utility to investors, we first construct a market-level emotion index. We construct this index using a standard bag-of-words technique with keyword dictionaries made up of 134 excitement-related words and 161 anxiety-related words. For each month during the January 1990 to December 2018 sample period, we use the ratio of difference between excitement and anxiety word counts in newspaper articles to the total number of excitement and anxiety words to derive the market emotion index…Media coverage keeps individual stocks and the market alive in investors’ minds, and in the spotlight of public discussion…This index is designed to capture the emotional engagement of investors with the overall stock market.”

“To capture the cross-sectional variation in emotional utility across individual firms, we estimate individual firm-level stock emotion betas using 60-month rolling regressions of excess stock returns on the market emotion index. These betas are our proxy for the emotional connections between investors and firms. In particular, the returns of a firm with high emotion beta exhibits greater sensitivity to the variation in the emotional state of the overall market.”

“We transform the monthly emotion betas into conditional emotion-sensitive betas by taking their absolute values. We focus on the magnitude of the conditional emotion beta for several reasons. First, emotional intensity represents ‘arousal’ in the circumplex model of affect increases with absolute value of valence. Arousal represents the power of the emotions individuals experience that we expect to impact investor decision making in a predictable manner. Second, strength of investor emotion is more salient than its valency. At sufficient levels of intensity emotion overwhelms cognitive processing and directs behavior in directions different from those predicted by rational decision-making.”

“Specifically, we posit that investors are more attracted to stocks with high emotion beta, which in turn could affect its pricing. The more powerful the investor ‘arousal’, the greater the propensity to invest and higher are the prices in the near future. Conversely, the weaker a firm’s emotional utility to investors, the lower would be the appeal of the stock to investors, and lower would be the stock price in the short-term.”

How emotion beta is related to subsequent returns

“Our main objective is to quantify the emotional attraction individual stocks have for investors and how this can be used to predict the cross-section of stock returns.”

“To examine the relation between stock emotion betas and cross-sectional patterns in stock returns, we first sort stocks into quintile portfolios based on previous month emotion beta, and measure the monthly returns of the resulting portfolios. We find that the high emotion beta portfolio outperforms the low emotion beta portfolio. During the January 1995 – December 2018 sample period, the high-minus-low portfolio earns an abnormal return of 0.41% per month (t-statistic = 5.23) on a risk-adjusted basis. Similarly, the characteristic-adjusted average excess return is 0.54% per month (t-statistic = 3.80).”

“The economic significance of the alpha estimates persists for up to four months and then becomes insignificant. This evidence indicates that the alpha estimates of emotion beta portfolios capture mispricing of stocks with high emotional sensitivity, which eventually gets corrected over the next few months.”

“In additional tests, we estimate monthly Fama and MacBeth regressions and find that emotion beta is economically significant. It has a coefficient estimate of 0.55 with tstatistic of 4.06. In economic terms, this estimate implies that a one standard deviation shift in conditional emotion beta is associated with a 0.55 × 2.43 = 1.34% shift in stock return in the following month. Consistent with the factor model estimate, we find that the predictive ability of emotion beta remains strong for up to several months ahead.”

“We investigate whether our integral emotion beta predictability is distinct from the known predictive ability of incidental emotions such as seasonal mood, valence such as sentiment, positivity/negativity-based textual tone and [the] economic policy uncertainty index…Evidence indicates that the emotion beta effect is distinct from the other related determinants of future stock returns.”

Risk premia in energy futures markets

September 18, 2021

Energy futures markets allow transferring risk from producers or consumers to financial investors. According to the hedging pressure hypothesis, net shorts of industrial producers and consumers bias futures prices towards the low side. According to the theory of storage, inventory and supply shortages bias spot and front futures’ prices to the high side relative to back futures. Under both popular hypotheses, “backwardated” futures curves are – all other influence being neutral– indicative of premia paid to longs in back futures. A new paper finds sizeable hedging pressure premia. Long-short positions across a range of energy futures based on hedging pressure and term structure factors seem to have produced significant returns. A promising approach is to integrate various factors into a single long-short portfolio across the spectrum of energy futures.

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Macrosynergy is a London based macroeconomic research and technology company whose founders have developed and employed macro quantamental investment strategies in liquid, tradable asset classes, across many markets and for a variety of different factors to generate competitive, uncorrelated investment returns for institutional investors for two decades. Our quantitative-fundamental (quantamental) computing system tracks a broad range of real-time macroeconomic trends in developed and emerging countries, transforming them into macro systematic quantamental investment strategies. In June 2020 Macrosynergy and J.P. Morgan started a collaboration to scale the quantamental system and to popularize tradable economics across financial markets.

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