# Outperformance: Find the right Stocks to beat the Index

Whenever you try to beat an index you will have to be invested in an asset which outperforms your benchmark. This article is about how to calculate outperformance and how to make use of it.

## Outperformance

In its most simple definition outperformance just means that one asset is performing better than an other asset. But this simple definition is not enough for investors. You will not be happy if your investment outperformed at the end of the year but caused huge losses within the year. We will have to find a smarter definition of outperformance, one we can use for building an out performing portfolio.

## Alpha

Alpha is the term used in finance to define outperformance. If the market runs 10% and your profit is 11%, your alpha is 1%. Of course, your goal as a fund manager would be to achieve this alpha with lower volatility than the overall market. Otherwise, with rising markets, you just could use a leveraged position. So, to define a useful measure for outperformance, we will have to combine alpha and volatility.

## Outperformance: Alpha and Volatility

In the article about Sharpe Ratio you have seen the idea of a volatility normalized return. Sharpe Ratio does not describe how much percent our asset rose last year, it tells us how many times we have earned the overall volatility of the instrument.

Instead of telling us that our stock rose by 20% over the last year, it tells us that our stock had a Sharpe ratio of 4, if it made 20% last year and only had an in between monthly volatility of 5%. (if risk free yield is 0%)

Using this idea, we just have to subtract the overall markets Sharpe Ratio from our stocks Sharpe Ratio to come up with a volatility normalized measure of outperformance.

## Outperformance Indicator

The chart above shows the volatility normalized outperformance of Boeing against the Dow Jones. Positive indicator levels indicate, that an investment in Boeing would have yielded a higher multiple of volatility than an investment in Dow Jones would have done. Using a VAR, value at risk, position sizing, this higher volatility normalized return will directly lead to a higher absolute return.

## Scanning Stocks to find Outperformance

To find stocks which currently outperform their index on a volatility normalized basis you can use a simple market scan. The table above shows the current results for the Dow Jones industrial stocks. Stocks with a reading above zero outperformed over the last year, stocks with a reading below zero would not have been the perfect investment to beat the index.

## Proof of concept Back-Test

To see if it is really useful to be invested in assets with an outperformance versus their index have a look at the results of a simple proof of concept back-test.

On the left side of the chat you see a buy and hold strategy of a basket of 30 stocks. It will be used as benchmark for the other two outperformance-based strategies on the right side of the chart.

The benchmark is based on a VAR portfolio consisting of the stocks currently contained in Dow Jones. It equally risks the same amount of money in each stock, using a weekly adjustment of position size. The rolling yearly standard deviation was used to define risk.

## Positive – Negative Outperformance Portfolio

The chart in the middle uses the same stocks and position-sizing algorithm as the benchmark portfolio, but only invests in stocks with a positive volatility-normalized outperformance. The portfolio on the right only invests in stocks underperforming the benchmark. The out- and under-performance, like the standard deviation, was calculated on a rolling-yearly basis.

This test for the outperformance indicator clearly shows the advantages of being invested in assets out-performing the market on a volatility-normalized basis. The back-test of the outperformer portfolio shows the same profits as the benchmark portfolio but has been achieved with lower overall volatility. The portfolio based on under-performing stocks shows a way higher volatility than the benchmark. Investing in quality pays off.

## Outperformance Indicator Code

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