Copulas and trading strategies

Reliance on linear correlation coefficients and joint normal distribution of returns in multi-asset trading strategies can be badly misleading. Such conventions often overestimate diversification benefits and underestimate drawdowns in times of market stress. Copulas can describe the joint distribution of multiple returns or price series more realistically. They separate the modelling of dependence structures from the marginal distributions of the individual returns. Copulas are particularly suitable for assessing joint tail distributions, such as the behaviour of portfolios in extreme market states. This is when risk management matters most. A critical choice is the appropriate marginal distributions and copula functions based on the stylized features of contract return data. Multivariate distributions based on these assumptions can be simulated in Python.

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Six ways to estimate realized volatility

Asset return volatility is typically calculated as (annualized) standard deviation of returns over a sequence of periods, usually daily from close to close. However, this is neither the only nor necessarily the best method. For exchange-traded contracts, such as equity indices, one can use open, close, high, and low prices and even trading volumes. These provide different types of information on the dispersion of prices and support the calculation of different volatility metrics. A recent paper illustrates the application of the volatility concepts of Parkinson, Garman-Klass, Rogers-Satchell, and Yang-Zhang, as well as intrinsic entropy, a method of econophysics. Intrinsic entropy seems to be more suitable for estimating short-term fluctuations in volatility.

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Predicting volatility with neural networks

Predicting realized volatility is critical for trading signals and position calibration. Econometric models, such as GARCH and HAR, forecast future volatility based on past returns in a fairly intuitive and transparent way. However, recurrent neural networks have become a serious competitor. Neural networks are adaptive machine learning methods that use interconnected layers of neurons. Activations in one layer determine the activations in the next layer. Neural networks learn by finding activation function weights and biases through training data. Recurrent neural networks are a class of neural networks designed for modeling sequences of data, such as time series. And specialized recurrent neural networks have been developed to retain longer memory, particularly LSTM (Long Short-Term Memory) and GRU (Gated Recurrent Unit). The advantage of neural networks is their flexibility to include complex interactions of features, non-linear effects, and various types of non-price information.

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How to construct a bond volatility index and extract market information

Volatility indices, based upon the methodology of the Cboe volatility index (VIX), serve as measures of near-term market uncertainty across asset classes. They are constructed from out-of-the-money put and call premia using variance swap pricing. Volatility indices for fixed income markets are of particular importance, as they allow inferring market expectations about discount factors and credit premia, which have repercussions on all assets and the broader economy. There is a step-by-step construction plan for building a bespoke index for any rates market with liquid futures and options. Such a volatility index supports asset management in two ways. First, it is a valid basis for portfolio risk management and volatility targeting. Second, it can be used for extracting forward-looking market information, including changing probability quantiles for prices and rates, probabilities of certain extreme events, and the skewness of expectations.

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Market dynamics: belief, risk, and ambiguity effects

To understand financial market dynamics, it is helpful to distinguish beliefs, attitudes towards risk, and attitudes towards ambiguity. Beliefs are subjective evaluations of future cash flows. Risk refers to uncertainty within a model of the asset’s return. And ambiguity means uncertainty about the model and probability distributions. Accordingly, one can separate price dynamics into three effects: changes in beliefs, changes in risk premia and changes in ambiguity premia. Ambiguity premia seem to be dominant, particularly when investors have little information about the nature of a particular risk. Traditional risk premia seem to be much less significant. Belief effects are negligible when ambiguity is high but increase as information accumulates. Often trading opportunities arise from the mean reversion of ambiguity premia and the “under-adjustment” of beliefs.

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Building a real-time market distress index

A new Fed paper explains how to construct a real-time distress index, using the case of the corporate bond market. The index is based on metrics that describe the functioning of primary and secondary markets and, unlike other distress measures, does not rely on prices and volatility alone. Thus, it includes issuance volumes and issuer characteristics on the primary side and trading volumes and liquidity on the secondary market side. Making use of a broad range of data on market functioning reduces the risk of mistaking a decline in asset values for actual market distress. Distress in a market that is critical for funding the economy and the financial system has predictive power for future economic dynamics and can be a valuable trading signal in its own right. It can be used for more advanced trend following and for detecting price distortions.

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Macro uncertainty as predictor of market volatility

Market volatility measures the size of variations of asset returns. Macroeconomic uncertainty measures the size of unpredictable disturbances in economic activity. Large moves in macroeconomic uncertainty are less frequent and more persistent than shifts in market volatility. However, macroeconomic uncertainty is an important driver of market volatility because it is related to future earnings and dividend discount rates. One proxy of macro uncertainty is a weighted average of forecasting errors over a wide set of macroeconomic indicators. Empirical evidence suggests that this proxy of latent macro uncertainty is a significant predictor of volatility and volatility jumps.

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Measures of market risk and uncertainty

In financial markets, risk refers to the probability distribution of future returns. Uncertainty is a broader concept that encompasses ambiguity about the parameters of this probability distribution. There are various types of measures seeking to estimate risk and uncertainty: [1] realized and derivatives-implied distributions of returns across assets, [2] news-based measures of policy and political uncertainty, [3] survey-based indicators, [4] econometric measures, and [5] ambiguity indices. The benefits for macro trading are threefold. First, uncertainty measures provide a basis for comparing the market’s assessment of risk with private information and research. Second, changes in uncertainty indicators often predict near-term flows in and out of risky asset classes. Third, the level of public and market uncertainty is indicative of risk premia offered across asset classes.

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Predicting volatility with heterogeneous autoregressive models

Heterogeneous autoregressive models of realized volatility have become a popular standard in financial market research. They use high-frequency volatility measures and the assumption that traders with different time horizons perceive, react to, and cause different types of volatility components. A key hypothesis is that volatility over longer time intervals has a stronger impact on short-term volatility than vice versa. This leads to an additive volatility cascade and a simple model in autoregressive form that can be estimated with ordinary least squares regression. Natural extensions include weighted least-squares estimations, the inclusion of jump-components and the consideration of index covariances. Research papers report significant improvement of volatility forecasting performance compared to other models, across equity, fixed income, and commodity markets.

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How loss aversion increases market volatility and predicts returns

Loss aversion means that people are more sensitive to losses than to gains. This asymmetry is backed by ample experimental evidence. Loss aversion is not the same as risk aversion, because the aversion is disproportionate towards drawdowns below a threshold. Importantly, loss aversion implies that risk aversion is changing with market prices. This means that the compensation an investor requires for holding a risky asset varies over time, giving rise to excessive price volatility (relative to the volatility of fundamentals), volatility clustering across time, and predictability of returns. All these phenomena are consistent with historical experience and form a useful basis for trading strategies, such as trend following.

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