The banking sector has been one of the most discussed among regulators, journalists and practitioners across the globe in the last 10 years. This article aims to analyse a dual simple systematic trading strategies for both USA and EU (EMU area) banking sector. We select the following 10 banks for the European market: Unicredit, Intesa Sanpaolo, Ubi Banca (Italy); Deutsche Bank, Commerzbank (Germany); BNP Paribas, Credit Agricole, Societé Generale (France); Banco Santander, BBVA (Spain). As far as the more heterogeneous banking sector in the USA concerns, we select the following 10 firms: Morgan Stanley, Goldman Sachs, JPMorgan, Wells Fargo, Bank of America, Toronto Dominion Capital, Capital One, Bancorp, BNY Mellon, and Citigroup.

Investing in an equally weighted portfolio (Let us suppose our portfolio is composed by 10 securities, it will be 10% of our wealth invested in each of them every week) performed poorly, giving a -56.6% for the European Banking sector and +31.6% for the USA Banking Sector in 10 years. Even if the performance of the US looks like good, it turns to be not positive as it appears when we take into account some measure of risks like yearly volatility of 38.6%, maximum drawdown of 76% and kurtosis of the returns distribution of 27.

For whom of you not familiar with these measures of risk the volatility is the square root of the variance statistical measure, it is the most common measure of risk used by Wall Street. The max drawdown is the maximum loss a portfolio suffers for after a peak has been reached. The kurtosis is a measure of the fatness of the tails of a probability distribution function, therefore the higher the kurtosis the more likely to observe abnormal returns.

The strategies we would like to discuss are two of the most famous in the asset management world: Mean reversion and Momentum. They are both dollar neutral strategies, in fact we pick with an opposite criteria 5 long and 5 short position among the 10 firms we selected each week.

## THE MEAN REVERTING STRATEGY

The mean reverting strategy suggest that prices and returns eventually move back towards the mean. We supposed the ten stocks within our portfolio to be highly correlated to each other. This idea is straightforward: being part of the same sector, these stocks have to be affected by the same systematic factors and their idiosyncratic factors are likely to be somehow correlated. The mean reverting strategy implies that markets keep moving erratically, therefore if the week t ISP performs +2% and UCG performs +0.5% the strategy for the week t+1 will be long UCG (buy) and short ISP (sell).

## THE MOMENTUM STRATEGY

The momentum strategy is by definition a trend following strategy. It aims to capitalize on the continuance of existing trends in the market. Momentum investor believes that large increase in the price of a security will be followed by additional gains and vice versa. The idea is that markets are efficient and a positive return is because of positive signal in the market arise. Therefore, if the week t ISP performs +2% and UCG performs +0.5% the strategy for the week t+1 will be long ISP (buy) and short UCG (sell).

## HOW DO WE DEVELOP THE STRATEGIES?

We develop the strategies as if they were a mirror in accordance to the following rule. We observe the week t return for each stock in our portfolio. We rank it from 1 to 10 from the best to the worst performer. As far as the mean reverting strategy concern, we buy the stocks that have been ranked from 6 to 10 and we sell the best 5 performers. We did the opposite for the momentum strategy. The weights used for these strategies are [0.3 0.25 0.2 0.15 0.1] for the long side and the opposite sign for the short side. The goal is to overweight stocks, which gave us the best signal according to the selected strategy.

## RESULTS

On the right, you can see the results of these two strategies for the all sample: EW stands for the equally weighted portfolio, MR for the Mean reverting strategy and MOM for the momentum strategy. The green highlights the best results. As you can see the Banking sector tends to have a mean reverting property on a weekly basis. MR performs very well with an average Sharpe Ratio (risk adjusted return) of 1.13 and 0.66 respectively for European and US market. It is impressive how the MR controls the risk of the portfolio very well reducing MaxDD (maximum drawdown) and Kurtosis systematically. It is important to remember that it is a core feature of a long-short portfolio.

Next, you can see the results of the 3 strategies for each year within the sample both for EU and US banking sector. For the European Market the MR strategy gets a better return than the momentum strategy 8 years out of 11, while it happens 7 out of 11 for the US market. It is possible to spot that while the Equally Weighted portfolio sometimes gives a better return; the volatility is always lower for the Mean Reverting and the Momentum strategy as it was expected.

Year by year it is interesting to see the performance of

every strategy. It is quite impressive that the 2008 and 2009 have been Mean reverting year for the baking sector. It suggests that every week during the financial crises the market was changing his mind on the relative valuation between different banks. It is possible to spot the same effect for the European debt crises of 2011 when the Mean reverting strategy in Europe clearly outperforms the momentum, while the opposite happens in the US market that dropped 26.64% but just because of consequences of the European crises.

## A LITTLE BIT OF ECONOMETRICS IN ORDER TO UNDERSTAND WHAT IS GOING ON

From the results above it seems that the banking sector is mean reverting on a weekly basis, but the most important question to address is: when does it happen?

In order to provide a feedback on it, we regressed the Mean Reverting returns on the Equally weighted portfolio returns as if it was the “sector market” for both European and USA banking sectors with the following descriptive regression:

Looking at the regression statistics it seems that for both European and USA banking sector the Mean reverting portfolio tends to have a positive performance when the market (EW used as a proxy for the market) is positive as well on a weekly basis. This evidence is weak for the EW with an R-squared of 5.18%, while it is stronger for the US sector. The coefficients for the EW returns are positive and significant (p-vale close to 0) for both the sectors. It is important to highlight that this evidence appeared to be reversed with respect to the statistics above on a yearly basis. This suggests some form of threshold or non-linearity, which cannot be captured by a linear OLS regression.

## A LITTLE BIT MORE OF ECONOMETRICS IN ORDER TO FORECAST WHAT WILL HAPPEN

The utility of the above regression is limited to its descriptive power on average. As investors or traders, we would like to understand what to do tomorrow conditioned on the set of information we can observe right now. In order to do this we use a simple one lag predictive regression where just known information have been used. Now we can easily calculate the expected value conditioned to the time t-1, therefore with all the information that a trader could observe at the end of the week.

As we can observe from the table above there is no predictability in the European market where the R-squared is close to 0 and all the estimated parameters are not significant. On the other side the USA banking sector shows a certain amount of predictability, with R-squared close to 4% and a negative but significant coefficient for the Equally weighted portfolio in the USA. The negative coefficient means that when the equally weighted portfolio shows a negative return in this week we will make profit using the mean reversion strategy the next week that on average will return positive.

## FORECASTING INSTABILITY

The predictive regression above could result unstable over time. Instability means that the coefficient is on average negative but could somewhere turns to be positive. In a very simply way we divide the sample in two subsample the first one from 2006 to the end of 2009 (end of the financial crises) and the other form 2010 to date. Performing the predictive regression just for the US market where we could spot a certain amount of predictability we get the following results.

The regression on the left takes into account the first period, while the one on the right takes into account the rest of the sample. Looking at the predictive coefficient on USEW(-1) we observe a shift in the predictive relation, and an increase in both the R-squared. Although the different sign, both term are significant so that there is opposite predictability in the two samples. We built a mixed strategy of Mean reversion and Momentum that takes into account this predictability therefore the so called MIXED strategy will investing according to the following rules:

à Before 2010. If in the week t the equally weighted portfolio shows positive return the week t+1 we will employ the Momentum strategy (negative expected return for the Mean reverting strategy) and vice versa if the equally weighted portfolio shows negative return the week t.

à After 2010. If in the week t the equally weighted portfolio shows positive return the week t+1 we will employ the Mean reverting strategy (positive expected return) and vice versa if the equally weighted portfolio shows negative return the week t.

Here the results of the MIXED portfolio versus the Mean Reversion within the USA banking sector. We can notice that the average Sharpe Ratio goes from 0.66 for the mean reverting strategy to 1.76 for the mixed one.

Looking at the results it is important to consider that we are not taking into account transaction costs and jump in the opening. The black line in the chart indicates the moment where we perform the switching in the predictive regression.

The problem for an investor is to understand which regimes he is going to observe. In order to do this and to develop future and more profitable trading strategy an investor could directly model the instability in the predictive regression through for example a more complex econometric tool like the Switching Model.

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