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 manage systemic risk in asset management

Systemic crises are rare but critical for long-term performance records. When the financial system fails, good trades become bad trades and many sensible investment strategies incur outsized losses due to deleveraging and liquidation pressure. Managers have two principal sets of tools to address systemic risk. The first is estimation and control of tail risk. The second is a contingency plan for systemic events. Estimating tail risk can make use of extreme value models, Bayesian risk forecasting, bubble indicators, and conditional value-at-risk models. Action plans for systemic crises can be based on research of systemic pressure points, guidance for shedding risk early in distress, rules for following market trends, and an adaptation of risk management to liquidity conditions.

The below post is an updated summary on the management of systemic risk on this site.

The importance of managing systemic risk

A critical and neglected factor of investment performance

Systemic risk in finance refers to the probability of the financial system failing at its essential functions, such as providing credit, making markets, or safeguarding securities and deposits. Typically, systemic risks build gradually over many years but materialize abruptly. They are hence a cause of extreme endogenous or setback risk (view summary of setback risk here) with rare incidences. Since years or decades pass between systemic crises, with many bonuses being awarded and vesting in the meantime, systemic risks are easily neglected in the day-to-day dispositions of investment managers.

However, how a manager prepares for and deals with systemic risk often makes or breaks long-term performance. Most investment strategies rely on some combination of directional or alternative risk premia and estimations of absolute and relative value. The basic principles of these are common across institutions. A systemic crisis typically derails all of these at the same time. This is because, in contrast to normal market drawdowns, systemic pressures trigger funding, accounting, or legal constraints that force position liquidation with little freedom of choice for portfolio managers. When a systemic crisis escalates the priority of institutions shifts from seeking returns to short-term capital preservation. As a result, the principles of efficient positioning or flows are often not only suspended but reversed. The best positions become the worst. With forced liquidations in thin liquidity, the trades that offered the most convincing value positions (by conventional standards) suddenly incur the greatest mark-to-market drawdowns. This happens because the expected return in the asset management industry is correlated with positions in normal times; good opportunities are rarely secret for long.

Moreover, standard risk management techniques fail in systemic crises. As volatility is soaring and correlations “all go to one”, positions that were calibrated according to value-at-risk give rise to unsustainable mark-to-market profit-and-loss volatility. Hedges may reduce average directional risk but give rise to large “basis risk” (profit and loss swings due to disparities in the returns of the main positions and the hedges). Also, as hedges typically raise the leverage of positions they make trades even more susceptible to forced deleveraging. Finally, diversification is of little help because the scope of inefficient flows is wide. Empirical research shows that a single global financial cycle floats or sinks most markets at the same time. (view post here).

A critical and neglected factor of financial system stability

Consideration of systemic risk in asset management also reduces the risk and consequences of crises themselves.

  • Investment managers’ attention to specific systemic risks makes it more likely that markets will charge a price for such vulnerabilities. Most crises follow from excesses and economic imbalances. For example, an excess of leverage reduces the capacity of institutions to absorb price drawdowns. The recognition of this risk means that borrowing costs and equity premia rise upon excesses, slowing or reducing them. Another relevant example is the unsustainable use of the environment and climate change (view post here). However, markets can only serve sustainability if managers think beyond annual performance fees. That is because “shorts” and protection strategies are typically negative carry trades with unknown duration.
  • The impact of shocks on the financial system and the economy is less severe if asset managers are prepared for systemic crises. It is often the very lack of protocol for difficult situations that leads to poor decisions and crisis escalation (view post here). Decision-makers rationally pay attention to rare potential crises only if expected losses from unpreparedness are more than proportionate to their rarity. There is ample evidence of regular boom and bust investment cycles, herding, trend-chasing (view post here), inefficient expectation formation, and speculative bubbles. Also, it has been shown that standard cognitive behavior is often inconsistent with efficient markets (view post here).

The standard policy response to private investment managers’ negligence of systemic risk is regulation. Yet, regulatory rules respond slowly to the evolution of the financial system and invite their own inefficiencies. A complementary policy is to increase the transparency of financial-economic information and reduce costs for allowing such information to be used in the investment process, for example through “quantamental systems” (view post here).

Approaches to managing systemic risk

Calibrating tail risk

Standard risk management relies on past volatility of price changes, historical correlation, and assumptions regarding outliers of price changes beyond normal ranges. On this basis, the majority of portfolios of liquid financial instruments is managed based on some form of Value-at-Risk (VaR) model, a statistical estimate of a loss threshold that will only be exceeded with a low probability.

Unfortunately, past volatility is not always a helpful gauge for financial markets risk. Volatility is merely the magnitude of historic price fluctuations, while risk is the probability and scope of future permanent losses (view post here). The two concepts are not only different but may even become opposites.  In particular, reliance on historic volatility can create an illusion of predictability that gives rise to excessive risk-taking. Indeed, low volatility itself is often a cause of high leverage and crowded positioning and hence conducive to subsequent outsized market movements.

Therefore, it is helpful to go beyond conventional risk metrics when assessing and calibrating the risk of large outlier events (“tail risk”):

  • Risk estimation should incorporate expert assessment. Historic data are not the only source of valuable judgment. For example, the risks and consequences of political upheavals, policy regime breaks, or first-time sovereign defaults are not easily quantifiable through price history. However, judgment and experience can be put into numbers, even if they take the form of wide confidence intervals. Logic, a broad perspective, and common sense prevent risk management from being trapped in the close confines of standard models.
  • Portfolio risk estimates can explicitly consider extreme market regimes. Thus, the basic idea behind extreme value theory is to fit an appropriate limiting distribution over returns that exceed a specific threshold. In particular, extreme value mixture models simultaneously estimate the threshold for extreme distributions and the extreme distribution itself (view post here). An alternative statistical approach is Bayesian risk forecasting, which accounts for the considerable distributional parameter uncertainty of Value-at-Risk and Expected shortfall estimates (view post here).
  • There are also quantitative warning signs of increased “tail risk” other than volatility. The simplest are valuation metrics for detecting bubbles (view post here), i.e. asset prices that are unusually high relative to the present value of estimated future cash flows. Academic papers have argued that equity markets with low dividend yields relative to local government bond yields are prone to large corrections (view post here). Similarly, countries with overvalued exchange rates and high short-term interest rates are prone to currency crises (view post here).
  • Standard volatility-based risk management metrics can be adapted for “tail events” and “gap risk”.Historically, diversification and downside risk analyses have assumed normal (“Gaussian”) probability distributions. Those are convenient for calculation but give little weight to large outliers. By now this “normality assumption” has been widely refuted and better gauges of tail risk are available (view post here), such as conditional Value-at-Risk. The distribution assumption is crucial for setting risk management parameters realistically and for assessing the potential upside of long-volatility and short-risk strategies.

Preparing crisis strategies

Having a plan of action in a systemic crisis can greatly diminish its impact on performance. An effective contingency plan can be based on (i) continuous research of systemic vulnerabilities that gives familiarity with pressure points, (ii) a rational protocol for shedding risk early in market distress, (iii) rules for following market trends, and (iv) adaptation of risk management to liquidity conditions.

  • Know the systemic weaknesses: It is very hard to predict the timing and dynamics of systemic crises. However, it is not so hard to understand the nature of vulnerability in specific economies and markets. Systemic risk indicators have been created for larger markets and have proven their value and relevance in the past (view post here). Their pace of change may be sluggish and their lead times ahead of crises long. Yet, through awareness of (i) systemic vulnerability and (ii) the degree of preparedness of the financial sector, asset managers can judge whether a specific shock is likely to be transitory or escalating after it has occurred. The two key criteria for escalation risk are (i) vulnerability of the system and (ii) rarity of the type of shock that hit it.
    • Vulnerability here measures the reliance of parts of the financial system on favorable conditions. Typically, protracted periods of low market volatility lead to build-ups of leverage and risk until the financial system reaches a tipping point (Minsky hypothesis, view post here). Long-term empirical analysis suggests that asset price booms are most dangerous when they are associated with rising financial leverage. Combinations of housing price bubbles and credit expansions have been the most detrimental of them all. (view post here). Also, economies that have grown accustomed to low real interest rates for long periods of time are typically susceptible to stress when rates or credit spreads are rising. Whether this stress is likely to escalate depends on whether the government or central bank have the means and the mandate to intervene. (view post here).
    • Rarity here measures the inverse of the a-priori probability of a specific type of shock. Rarity of shock means that it was not on the radar screen of either investors or policymakers. Theory suggests that senior decision-makers rationally do not prepare for rare events as they can only process a limited quantity of information. Technically speaking, rare events derail markets by raising “ambiguity premia”, whereby ambiguity means uncertainty about the probability distributions of an asset’s returns. Experimental research suggests that ambiguity premia are typically far more powerful drivers of price changes than traditional risk premia (view post here). Therefore, expected losses from unpreparedness are inversely proportionate to an event’s rarity(view post here). Indeed, expected losses from unpreparedness are even higher if managers bear only limited liability because they have particularly low incentives to prepare for low events.
  • Be early in shedding risk: There are two valid bases for adjusting positions quickly as systemic risk is rising: information advantage and market stress.
    • Information advantage depends on understanding and tracking the main mechanisms of systemic crises, contagion, and self-fulfilling dynamics (view post here). A particularly useful metric is the ‘financial stability interest rate’, a threshold above which the real interest rate in an economy triggers financial constraints and systemic instability (view post here). The relationship between the financial stability interest rate and the natural interest rate may be one of the most important predictors of medium-term market direction and future crisis risk.
    • Tracking market stress is simpler and, hence, far more common. A wide range of systemic risk indicators has been developed that rely on market prices, correlations, and volatility (view post here).
      In particular, volatility targeting is a valid default rule for containing mark-to-market risk if one is uncertain as to the severity of systemic pressure. This is because recent volatility is a good predictor of future volatility but not generally for future returns (view post here). Judging from U.S. equity data, volatility targeting strategies have over longer periods of time produced significant increases in return per unit of tail risk (view post here).
      Effective volatility targeting and dynamic hedging can make use of option-implied volatilities. Implied volatility only helps to predict future actual volatilities and future asset price correlations (view post here). High implied volatilities translate into high correlation whenever a single global factor is dominating price moves across all global markets.
  • Running with the herd: Following market trends is often rational and macro research can help to figure out when this is the case. For example, research may tell us that markets face a critical threat (e.g. a major bank may be at risk of default) but may not tell whether or not the risk will manifest (e.g. there may be a government bailout). In “make-or-break” situations it is rational for non-insiders to herd, i.e. to trade in the direction of prices, as private information disseminates in the market through prices (view post here). In this case, inaction would be an irrational and dangerous choice, even if we had no information advantage on the evolution of the crisis.
    Historically, simple trend-following strategies have reduced maximum drawdowns in equity portfolios and provided some hedging against losses in FX carry trades (view post here). Trend following removes psychological and institutional obstacles to exiting positions early in escalating crises. Trend following is a market directional strategy that promises “convex beta” and “good diversification” for outright long and carry portfolios as it normally performs well in protracted good and bad times alike (view post here). Drawdown control strategies, such as volatility targeting and “MinMax” (view post here), use elements of trend-following for risk management.
  • Controlling liquidation: Market liquidity can evaporate in systemic crises. This can give rise to outsized price movements and, at the same time, make position adjustments prohibitively expensive. To the extent that liquidity rather than fundamental change triggers market moves, position liquidations destroy investor value. Indeed, structural and regulatory changes in recent years seem to have made liquidity more precarious than in the past (view post here, here, and here). Hence, calibrating or structuring positions such as to withstand liquidity events can be a major cost saver and performance factor. This typically requires some flexibility in respect to risk management and mark-to-market-based drawdown limits. Researching the nature and potential of systemic risk is critical, both for preparation and for forming judgment whether it is really in the investor’s interest to liquidate positions.

With the right preparations, investment managers can even benefit directly from systemic events, particularly if they have sufficient flexibility and risk limits to exploit price distortions and high-risk premia paid. For systemic value based on price distortions see the related summary here. And for detecting and receiving high-risk premia see the section on “implicit subsidies” here.

Exchanging market risk information

No single investor or institution has all pieces of the puzzle that is systemic risk. Investors typically specialize in markets or geographic regions. However, every financial market depends on all other financial markets to some extent. At times particular market segments, such as asset-backed securities or technology stocks, can have a dominant global influence. Even small and remote markets, such as Iceland or Greece have in the past triggered sizeable global market moves. Links between seemingly separate markets often reflect their communal dependence on global liquidity, which is the ease of financing transmitted by a small number of financial centers (view post here).

Therefore, investment managers must engage in active risk information exchange, trading their insights for the insights of colleagues. Indeed, theoretical and experimental research suggests that portfolio managers will generally share ideas and research if mutual feedback is valuable (view post here). This creates investor value at all times but particularly when systemic risk is rising because investment managers that are part of an information network are better positioned to act early, as they know more and know better what others know. From a social welfare angle, this process of information exchange is essential to disseminate concerns over systemic crises. The dissemination turn may serve to warn market participants, policymakers, and the broader public, smoothing market volatility.

How to estimate credit spread curves

Credit spread curves are essential for analyzing lower-grade bond markets and for the construction of trading strategies that are based on carry and relative value. However, simple spread proxies can be misleading because they assume that default may occur more than once in the given time interval and that losses are in proportion to market value just before default, rather than par value. A more accurate method is to estimate the present value of survival-contingent payments – coupons and principals – as the product of a risk-free discount factor and survival probability. To this, one must add a discounted expected recovery of the par value in case of default. This model allows parametrically defining a grid of curves that depends on rating and maturity. The estimated ‘fair’ spread for a particular rating and tenor would be a sort of weighted average of bonds of nearby rating and tenor.

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Statistical learning and macro trading: the basics

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

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

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

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

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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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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Fundamental value strategies

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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