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# Second chances with momentum

### Javier Cárdenas

#### 10/02/2021

A couple of days ago we were seeing in the news the story about GameStop, and how small investors made some hedge funds abandon their short-selling positions after some big losses.

After reading the article I couldn’t resist thinking about short-selling strategies and their performance in the stock market. In today’s post, and hoping to find an answer, we will try to evaluate the impact of short selling with the momentum strategy.

## Introduction to momentum

When it comes to investing, there are some strategies more complex than others. Today we are going to talk about one of the simplest ones, the momentum strategy.

This strategy is well known for being simple and highly effective in different periods and assets. However, it presents in turn high-risk levels, concatenating long periods of negative profitability [1].

## How does it work?

The formula for a given stock can be expressed as a relative return:

$$Momentum_i = \frac{Price_{i, t} – Price_{i, t-n}}{Price_{i, t-n}}$$

Where $$n$$ is the window from which we want to calculate the returns.

There are mainly two types of momentum strategies:

• Relative momentum:  Where the performance of several assets is compared,  buying/selling the winners/losers. In general, the performance of an asset is usually measured with a 3 to 12-month window, see [2]. We will be using this strategy in the post.
• Absolute momentum: In this case, the momentum is defined by the return of a specific asset, buying/selling that asset when its return is positive/negative.

## Evaluation

To evaluate our strategy we have used the universe of the S&P 500 from 2015 until today.

The evaluation was made by following the steps below:

• First, we have calculated the relative returns with period $$n$$ for all the companies listed in the index, for all the days in the period.
• Second, we have bought/sell the top 5 companies with the highest/lowest returns, everyday for all the days in the period.
• Third, we have calculated the average return of the next day obtained by buying/selling the top 5 companies, again for all the days in the period.
• Finally, we have repeated these three previous steps with different windows $$n$$ and evaluate the results.

As you can see, the momentum strategy has somewhat different results depending on the window $$n$$ used, but always with poorer performance than the index.

On the other hand, if we focus only on selling the top 5 companies with the poorest performance, as can be seen in the following graph, the results are even worse. By the beginning of 2021, almost all the combinations tested with the strategy have lost the initial capital.

So the next question to be made is:

## What if we buy the losers?

In this case, we would need to buy the stocks with the poorest performance expecting that they will improve in the future (or at least the following day).

The image below shows the result given by buying the losers. Surprisingly, if we had bought the worst-performing companies on the S&P on a daily basis from 2015 until today, we would have obtained a positive return for all the windows studied.

Nevertheless, if we take a closer look at the beginning of 2020 the strategy suffers from a big drawdown. Although it later recovers, we could say that the strategy is still very volatile.

Note that in this simulation we are not taking into account commissions and other expenses.

## Conclusions

We have evaluated the performance of a short-selling strategy using momentum in the S&P 500 stocks for the last 6 years.

With the data observed, at least since 2015, the strategy of selling the losers (the 5 biggest losers) does not seem to be a very profitable strategy.

On the contrary, it seems to be a better strategy to give them a second chance and buy the losers.

## References

[1] Daniel, K., & Moskowitz, T. J. (2016). Momentum crashes. Journal of Financial Economics122(2), 221-247.
[2] Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance48(1), 65-91.