Modern backtesting with integrity

Machine learning offers powerful tools for backtesting trading strategies. However, its computational power and convenience can also be corrosive for financial investment due to its tendency to find temporary patterns while data samples for cross validation are limited. Machine learning produces valid backtests only when applied with sound principles. These should include [1] formulating a logical economic theory up front, [2] choosing sample data up front, [3] keeping the model simple and intuitive, [4] limiting try-outs when testing ideas, [5] accepting model decay overtime rather than ‘tweaking’ specifications, and [6] remaining realistic about reliability. The most important principle of all is integrity: aiming to produce good research rather than good backtests and to communicate statistical findings honestly rather than selling them.

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Commodity carry

Across assets, carry is defined as return for unchanged prices and is calculated based on the difference between spot and futures prices (view post here). Unlike other markets, commodity futures curves are segmented by obstacles to intertemporal arbitrage. The costlier the storage, the greater is the segmentation and the variability of carry. The segmented commodity curve is shaped prominently by four factors: [1] funding and storage costs, [2] expected supply-demand imbalances, [3] convenience yields and [4] hedging pressure. The latter two factors give rise to premia that can be received by financial investors. In order to focus on premia, one must strip out apparent supply-demand effects, such as seasonal fluctuations and storage costs. After adjustment both direction and size of commodity carry should be valid, if imprecise, indicators of risk premia. Data for 2000-2018 show clear a persistent positive correlation of the carry with future returns.

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Understanding the correlation of equity and bond returns

The correlation of equity and high grade sovereign bond returns is a powerful driver of portfolio construction and the term premia of interest rates. This correlation has turned from positive in the 1970s-1990s to negative in the 2000s-2010s, on the back of similar shifts in the correlation between inflation and economic growth and between inflation and real interest rates. The structural correlation flip has given rise to a risk parity investment boom and contributed to the compression in long-term yields. Both theoretical and empirical analysis suggests that negative equity-bond correlation is due largely to pro-cyclical inflation, i.e. higher inflation coinciding with better economic performance, as opposed counter-cyclical inflation or stagflation. Inflation is more likely to be pro-cyclical if it is low or in deflation (view post here) and driven by demand rather than supply shocks.

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CDS term premia and exchange rates

The term structure of sovereign credit default swaps (CDS) is indicative of country-specific financial shocks because rising country risk affects short-dated maturities more than longer-dated ones. This feature allows disentangling global and local risk factors in sovereign CDS markets. The latter align with the performance of other local asset markets. In particular, recent empirical research supports the predictive value of CDS term premia for exchange rate changes. The finding is plausible, because both local-currency assets and CDS term premia have common pricing factors, while CDS curves are cleaner representations of country financial risks.

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Realistic volatility risk premia

The volatility risk premium compensates investors for taking volatility risk. Conceptually it is based on the difference between options-implied and expected realized volatility. In equity markets this premium should be positive in the long run and fluctuate overtime depending on the market’s willingness to pay for protection against future changes in price volatility. In practice, measuring the premium overtime is challenging, particularly because expected realized volatility is not known. Using recent realized volatility as a proxy can be highly misleading. However, a realistic estimate can be constructed by considering the trade-off between timeliness and noise ratio of recent price changes and the long-term mean reversion of volatility. This “realistic” volatility risk premium has been positively correlated with subsequent daily volatility index future returns.

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Variance term premia

Variance term premia are surcharges on traded volatility that compensate for bearing volatility risk in respect to underlying asset prices over different forward horizons. The premia tend to increase in financial market distress and decrease in market expansions. Variance term premia have historically helped predicting returns on various equity volatility derivatives. The premia themselves can be estimated based on variance swap forward rates and their decomposition into expected underlying price variance and risk premia. In particular, the variance term premia are obtained as the difference between forward swap rates and realized volatility forecasts, whereby the latter are related to a “volatility state vector”.

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Multiple risk-free interest rates

Financial markets produce more than one risk-free interest rate. This is because there are several separate market segments where structured trades replicate such a rate. Differences in remuneration arise for two reasons. First, financial frictions can prevent arbitrage. Second, some risk-free assets pay additional convenient yields, typically by virtue of their liquidity and suitability as collateral. Put simply some “safe assets” have value beyond return. U.S. government bonds, in particular, seem to provide a sizable consistent convenience yield that tends to soar in crisis. This suggests that there are arbitrage opportunities for investors that are flexible, impervious to convenience yields and tolerant towards temporary mark-to-market losses.

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How lazy trading explains FX market puzzles

Not all market participants respond to changing conditions instantaneously, not even in the FX market. Private investors in particular can take a long while to adapt to changes in global interest rate conditions and even institutional investors may be constrained by rules and lengthy process. A theoretical paper shows that delayed trading goes a long way in explaining many empirical puzzles in foreign exchange markets, i.e. deviations from the rational market equilibrium, such as the delayed overshooting puzzle or the forward discount puzzle. Understanding these delays and their effects offers profit opportunities for flexible information-efficient traders.

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A brief history of quantitative equity strategies

Understanding quantitative equity investments means understanding a significant portion of market positions. Motivated by the apparent failure of the capital asset pricing model and the efficient market hypothesis, a large share of equity investors follows stylized “factors” that are expected to outperform the market portfolio in the long run. Yet, popularity and past performance of such factors can be self-defeating, while published research is prone to selection bias and overfitting. Big data has introduced greater information efficiency with respect to textual analysis, picking up short-term sentiment but without clear and documented benefits for long-term investment so far. In the future greater emphasis may be placed on dynamic factor models that – in principle – can apply plausible performance factors at the times that they matter.

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Predicting equity volatility with return dispersion

Equity return dispersion is measured as the standard deviation of returns across different stocks or portfolios. Unlike volatility it can be measured even for a single relevant period and, thus, can record changing market conditions fast. Academic literature has shown a clear positive relation between return dispersion, volatility and economic conditions. New empirical research suggests that return dispersion can predict both future equity return volatility and equity premia. The predictive relation has been non-linear, suggesting that it is the large changes in dispersion that matter.

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