## Zero-Crossing Variant of Pairs Trading Strategy Friday, 14 October, 2016

**A related paper has been added to:**

#12 - Pairs Trading with Stocks

**Authors: **Donninger

**Title: **Is Daily Pairs Trading of ETF-Stocks Profitable?

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2816288

**Abstract:**

Pairs trading is a venerable trading strategy. There is agreement that it worked fine in the far past. But it is less clear if it still profitable today. In this working paper the universe of eligible pairs is defined by the holdings of a given ETF. It is shown that the stocks must be from ETFs which select high-quality, low-volatility stocks. The usual closeness measure presented in the literature performs poor. The paper presents a simple and clearly superior alternative based on zero-crossings. The strategy performs with the correct universe and the improved pairs selection rule before trading costs quite fine. It depends on the assumed trading costs if this is also in real-trading life the case.

**Notable quotations from the academic research paper:**

"The seminal paper on pairs trading is Gatev et. al. [1]. They authors did not invent the strategy. It was in common use since the 1980s. The pairs are formed from a universe of stocks. There is a one year formation period. Each stock is normalized to 1 at the beginning of this period. One selects for each stock the closest neighbor. The distance measure is the summed up squared daily difference of the normalized prices.

The initial results with the distance method were rather disappointing. Pairs trading is based on mean-reversion. The distance measures if the stocks stick together. But sticking together and mean-reversion are two different concepts. Vidyamurthy proposes zero-crossings as an alternative. One counts the number of times the spread moved above or below the mean-spread. But this measure is also not satisfactory. It is known from the theory of Brownian-motions that zero-crossings are much more likely in the first few steps of the motion. If one starts at zero a small up- followed by a larger down-move is a zero crossing. The path moves in the following away from zero and a crossing gets very unlikely. The situation is somewhat different for a mean-reverting process but the general behavior is still the same. A zero (or mean) crossing does also not create a profit. The interesting case is a crossing which started initially outside the two-sigma band. This is the main distance function. A larger number of crossings is of course better than a lower one. For two pairs with the same number of crossing the distance is used as a secondary measure. But a pair with 5 crossings is always closer than a pair with only 4. The strategy defines also a minimum number of crossings (usually 4). A pair with less crossings is never traded.

The strategy does not use overlapping formation periods. The set of tradeable pairs is determined each month (every 21 trading days). The formation window is like in most studies a year (252 trading days). But an open position is not automatically closed at the end of the trading period. An open position is – if mean reversion does not happen before – closed after 30 trading days. There are usually pairs from the previous formation period open. It makes no sense to close a position which was entered at day 20 of the trading period just because a new formation calculation is performed. The strategy does not reset the spread to zero at the end of the formation phase. It uses the mean and the standard deviation from the formation period also in the trading phase. A position is only opened, if the spread is between 2 and 4 standard deviations. It is unlikely that the spread is by chance larger than 4 deviations. A very large spread is a sign that the pair is in divorce. As an additional stop-loss an already open position is closed if the spread gets larger than 8 standard deviations. This stop-loss is only triggered a few times but it avoids some

really disastrous losses.

As already noted simulated trading is done from 2011-01-01 till 2016-07-26. The strategy has an overall profit of 144.4%, a monthly Sharpe ratio of 1.16 and a max. relative drawdown of 8.2%."

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## Cointegration and Pairs Trading in Stocks Friday, 7 October, 2016

**A related paper has been added to:**

#12 - Pairs Trading with Stocks

**Authors: **Do, Faff

**Title: **Cointegration and Relative Value Arbitrage

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2826190

**Abstract:**

We examine a new method for identifying close economic substitutes in the context of relative value arbitrage. We show that close economic substitutes correspond to a special case of cointegration whereby individual prices have approximately the same exposure to a common nonstationary factor. A metric of closeness constructed from the cointegrating relation strongly predicts both convergence probability and profitability in cointegration-based pairs trading. From 1962 to 2013, a strategy of trading cointegrated pairs of near-parity generates 58 bps per month after trading costs, experiences a 71% convergence probability and outperforms a strategy of pairs selected by minimized price distances.

**Notable quotations from the academic research paper:**

"In the pairs trading literature, the most common type of relative value arbitrage, substitutes for individual stocks are identified by minimizing the Euclidean distance in the daily price space over a historical period.5 Matching stocks over the price space instead of the return space is consistent with short-term relative value trading strategies, while removing the need to specify factors. Although the matching method is simple to perform, by design, it guarantees the existence of a counterpart for every stock, which is counterintuitive. More importantly, stocks that exhibit little variation in the price pattern over the formation period (possibly due to lack of news flow) would end up being labelled close substitutes, although they are not fundamentally related.

In this paper, we propose a simple method of identifying close economic substitutes using cointegration. When a pair of stock prices is cointegrated, one series co-moves with a scaled version of the other. We show that close economic substitutes can be represented by a system of cointegrated prices where the scaling factor, or the cointegration coefficient, is close to one.

We find that from 1962 to 2013, NonParity, a positive-valued metric of closeness that measures the distance of the cointegration coefficient from unity, strongly predicts both the probability that relative mispricing will subsequently be corrected as well as the profitability of the arbitrage trade. A one standard deviation increase in the variable reduces the convergence probability by seven percentage points and pairs trade payoffs by 2.78 percentage points. Further, predictability through NonParity also presents profitable trading opportunities. At the portfolio level, the pairs trading of cointegrated stocks is generally unprofitable. However, when trading is confined to pairs of stocks with NonParity close to zero, the strategy is profitable after reasonable estimates of brokerage, slippage, and short selling costs. Specifically, over the sample period, the average after-cost risk-adjusted return to trading a portfolio of cointegrated pairs with NonParity less than 0.5 (0.2) is 0.43% per month, with a t-statistic of 5.29 (0.58% per month, with a t-statistic of 4.77)."

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## Option Pricing Methods in the Late 19th Century Thursday, 29 September, 2016

**We at Quantpedia consider ourselves a history freaks as we love books and papers related to a history of finance. The work of Dotsis is a perfect example of an interesting paper about a history of option pricing and shows how people were remarkably skilled in assessing price of options even without current high performance IT tools. Academic paper could be related to #20 - Volatiity Risk Premium Effect ...**

**Authors: **Ghoddusi

**Title: **Option Pricing Methods in the Late 19th Century

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2831362

**Abstract:**

This paper examines option pricing methods used by investors in the late 19th century. Based on the book called “PUT-AND-CALL” written by Leonard R. Higgins in 1896 and published in 1906 it is shown that investors in that period used routinely the put-call parity for option conversion and static replication of option positions, and had developed no-arbitrage pricing formulas for determining the prices of at-the-money and slightly out-of-the-money and in-the-money short-term calls and puts. Option traders in the late 19th century understood that the expected return of the underlying does not affect the price of an option and viewed options mainly as instruments to trade volatility.

**Notable quotations from the academic research paper:**

"In this paper I show that option traders in the late 19th century not only had an intuitive grasp of the main determinants of option prices but they have also developed no-arbitrage pricing formulas for determining their prices. The option pricing formulas are described in a book called “PUT-AND-CALL” written by Leonard R. Higgins in 1896 and published in 1906.2 Higgins was an option trader in London and in his book he describes option pricing methods and option strategies used in the late 19th century in the City of London.

The pricing approach described in Higgins book could be summarized as follows: First, traders were pricing short-term ATMF straddles (30, 60 or 90 days to maturity. The prices of the ATMF straddles were set equal to the risk-adjusted expected absolute deviation (Higgins uses the term average fluctuation) of the underlying price from the strike price at expiration. The expectation of the absolute deviation was based on historical estimates plus a risk premium for future uncertainty as well as some other markups. Given the ATMF straddle prices as reference points Higgins is using a linear approximation formulae based on put-call parity to price slightly out-of-the-money (OTM) and slightly in-the-money (ITM) put and call options. I show that the approximation used by Higgins is analogous to a first order Taylor expansion around the ATMF straddle price.

Higgins’s book is an important reference in the history of option pricing because it provides a pricing framework based on empirical rules and approximation methods for determining option prices. Higgins’s method could be taught in introductory derivatives valuation courses before the Black and Scholes and the binomial model to help students appreciate the historical development of option pricing methods and the contribution of option market practitioners."

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## Does Interest Rate Exposure Explain the Low Volatility Anomaly? Saturday, 24 September, 2016

**Related to:
#6 - Volatility Effect in Stocks - Long-Short Version**

**Authors: **Driessen, Kuiper, Beilo

**Title: **Does Interest Rate Exposure Explain the Low Volatility Anomaly?

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2831157

**Abstract:**

We show that part of the outperformance of low volatility stocks can be explained by a premium for interest rate exposure. Low volatile portfolios have a positive exposure to interest rates, whereas the more volatile stocks have a negative exposure. Incorporating an interest rate premium explains part of the anomaly. Depending on the methodology chosen the reduction of unexplained excess return is between 20% and 80%. Our results provide evidence that interest rate risk is priced differently in the bond and equity market. Our results imply a strong implicit exposure of low volatility portfolios to bonds.

**Notable quotations from the academic research paper:**

"A relation between the low volatility anomaly and government bonds makes sense if volatility is thought of as an indicator of how far equity is removed from bonds in the capital structure. In this study our main finding is that the outperformance of low volatility stocks can be explained by differences in interest rate exposure. We find that low volatility portfolios have more exposure to this risk. Our results imply a strong implicit exposure to interest rate risk of low volatility portfolios. We estimate that the duration of the lowest volatility decile corresponds to a 30% weight to bonds. The duration of the highest decile corresponds to a short position of 100% short bonds.

Because of the differences in exposure, the risk premium that we estimate explains part of the excess return of a long short portfolio. We find a monthly compensation of interest rate risk in equities of 0.91%, with a standard error of 0.20%. The differences in interest rate exposure combined with the large estimated risk premium, results in a significantly reduced mispricing of low volatility stocks. We find these results to be robust for taking into account the time variance of the interest rate exposure.

For our study we use ten portfolios over the period from July 1963 to December 2014, defined by sorts on residual variance of individual US stocks using the Fama French 3 factor model. In section 3 we elaborate further on this. We define an interest rate factor as the return of an equal weight portfolio consisting of US government bonds with various maturities. In order to estimate the interest rate exposure we run time series regressions. Fama MacBeth regressions are employed to estimate the premium for the interest rate exposure. Combined these two enable us to evaluate the impact of this effect on the unexpected excess return of the long short portfolio. We use several different estimations of the premium in order to test the robustness of our findings."

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## Carry Trade Returns and Political Risks Tuesday, 13 September, 2016

**Related to #5 - FX Carry Trade**

**Author: **Kesse

**Title: **Exchange Rates, Carry Trade Returns and Political Risks

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2813028

**Abstract:**

This paper elucidates the channels through which sovereign risk, exchange rates and currency risk premia are related. I show that the channels are different depending on whether a country is classified as emerging or an advanced economy. Generally, for emerging market economies, local sovereign risk factors, namely country-specific political risk and macroeconomic risk do play a significant role in the depreciation of the local currency relative to the U.S. dollar. Whilst there is no convincing evidence that local determinants of sovereign risk cause a depreciation of currencies of advanced economies before the 2007 financial crisis, I do find that political risk does matter for advanced economies in the post-crisis era. For both sets of economies, global factors also play an important role in the relationship between sovereign risk and exchange rates. Secondly, double-sorting 34 currencies into different portfolios based on the level of macro risk and political risk, I provide evidence that local determinants of sovereign risk are priced in the FX markets, i.e. they can forecast currency carry trade excess returns in the cross-section. Local political risk in particular seems to have become an important carry trade risk factor in the post-2007 financial crisis era. This is the first research to explain carry trade excess returns with local sovereign risk factors as against sovereign risk as a whole.

**Notable quotations from the academic research paper:**

"The measure of country political risk is derived from the political risk rating of the International Country Risk Guide (ICRG). It is forward-looking and reflects political risk as opposed to an aggregate or broad measure of country risk which also incorporates macro-economic factors. While ICRG's rating is mostly subjective assessments of various country experts, there is ample evidence in the literature that it correctly reects the adverse effects of political risk on investment values across countries

The political risk rating is composed of 12 subcomponents namely: government stability, socioeconomic conditions, investment profile, internal conflict, external conflict, corruption, military in politics, religious tensions, ethnic tensions, law and order, democratic accountability and bureaucratic quality. This measure ranges from 0-100 with higher scores reflecting low level of political risk. Following (Bekaert et al., 2014), I construct country political risk as the difference of the log inverse of the ICRG rating for a country and the log inverse of the equivalent rating for the U.S.A, i.e. log(1/pr^f ) - log(1/pr^us).

I find that for emerging markets, an increasing level of political risk generally leads to a depreciation of the currency. A rising level of the other country-specific component of sovereign risk, i.e. macroeconomic risk also generally leads to a depreciation of the local currency. Of the two country-specific risks, political risk seems to have the stronger effect on currency depreciation in terms of magnitude. Whereas I find no such effect of country-specific political risk and macroeconomic risk on exchange rates for developed economies in the pre-2007 financial crisis period, I do find that political risk does matter for advanced economies post-2007 crisis. For both sets of economies, increasing global risk aversion generally leads to a depreciation of the currency under all sub-samples.

Secondly, I investigated whether our local determinants of sovereign risk have the ability to explain currency carry trade excess returns. I do find that they indeed do. Portfolios double-sorted on country-political risk and macroeconomic risk produce excess returns and slopes that increase from low political risk portfolios to high political risk portfolios under all macro risk groups in the post-2007 crisis sub-period. The argument for political risk being priced is less convincing under the pre-2007 crisis sub-sample. Instead, there is a stronger case for macro risk being priced pre-2007 financial crisis whereas the argument for macro risk is weaker post-2007 financial crisis."

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