"I revel in the dream of numbers" is the first line of my novel, a novel which I suspect I shall never finish. I suspect if I end up writing a second book, it will most likely be on numbers and markets, a follow up to my first, Trading Thalesians! For whatever reason, I just enjoy mathematics, no matter how abstract it can somehow seem. For the most part, I suspect most people do not share such a deep love of numbers. Despite this, mathematics and its closely related fields are becoming more crucial to modern life. Mathematics builds the bridge, on which humans are increasingly progressing.

It is also true of real bridges, which have been an important factor in facilitating the expansion of economic activity. Perhaps one of the most famous bridges in the United States, is the Golden Gate bridge in San Francisco, which spans the Golden Gate strait and is 1.7 miles long, its distinctive red colour visible from a distance. If you ever get an opportunity, I would recommend walking the entire length of the bridge. The sound of the traffic is not perhaps, the most appealing aspect of the walk. The view, however, is spectacular. On one side lies the expanse of the Pacific Ocean and on the other the San Francisco Bay. Taking the time to walk along the entire duration of its length gives you a true appreciation of how much of an achievement building the bridge was in the 1930s. Of course, in order to walk along the bridge, you do not need to have any understanding of precisely how the bridge was engineered. Mathematics was used as a tool by engineers seeking to build the bridge, so that today we can cross it.

The markets are no different. Mathematics can help to explain a lot about markets, although it is very often in the background. Indeed, a similar point was made very well by Vyas from CPPIB at a talk which I heard recently at Global Derivatives USA. He stressed that he viewed quant as a tool, when it comes to investing. We can illustrate this point using a few examples.

When it comes to discretionary traders, I so often hear the comment, "No, we're just discretionary traders, we don't use any quant stuff". When we distil precisely what a trader does, it is inescapable that all traders will end up using some quant techniques to some extent.

Let us take the example of volatility traders examining volatility surfaces. They might be trying to understanding the relative value of certain options. They wants to understand which parts of the volatility surface are cheap and which are expensive. They might also look at various tenors to try to understand anomalies in time space. Let us consider how much data is needed to do this effectively. Each tenor has 5 quotes and you might have at least 10 tenors (often more). That's 50 points for every trading day. If you have 5 years of data that is 12,500 points. Across 10 currency pairs that is 125,000 points. How else are you supposed to crunch that data, without doing some heavy duty coding and mathematics to summarise it into a digestible form to make a trading decision? At the end of the process, a discretionary trader would still have a final say on the whether to buy or sell based on the output from the analysis. This contrasts with a systematic trader, who would go with whatever the trading model suggested. However, much of the thought processes of these two traders are very similar.

Whilst we have illustrated this point with options, we could easily have the same issue with many other areas of the market, notably with stocks. If a trader has a mandate to trade any of the stocks in the S&P500, how can he or she possibility know all the fundamental details of all 500 companies? Quant tools can help flag trading opportunities, which a discretionary trader can dig into in more detail, before deciding to trade. Alternatively, we can create the final output to be a buy or sell signal for a systematic trader.

So is mathematics a pancea for markets? Not really. Like any tool, it can be misused. As I discuss in my book, Trading Thalesians, mathematics should be used as a tool to explain how markets work. It should not be used to proof something which you do not know is true!

If you're a discretionary trader, don't always dismiss what quant analysis can do to help you in your decision making. As an example, it can help summarise very large datasets, so they are easier to interpret from a discretionary perspective. Very often, you might well be walking on the bridge mathematics built, but perhaps you might not realise it. Drop me a message and I might be able to tell you more! Equally, if you're a quant trader, don't dismiss what discretionary trading can teach you.. that will be a theme for a future article.

It is also true of real bridges, which have been an important factor in facilitating the expansion of economic activity. Perhaps one of the most famous bridges in the United States, is the Golden Gate bridge in San Francisco, which spans the Golden Gate strait and is 1.7 miles long, its distinctive red colour visible from a distance. If you ever get an opportunity, I would recommend walking the entire length of the bridge. The sound of the traffic is not perhaps, the most appealing aspect of the walk. The view, however, is spectacular. On one side lies the expanse of the Pacific Ocean and on the other the San Francisco Bay. Taking the time to walk along the entire duration of its length gives you a true appreciation of how much of an achievement building the bridge was in the 1930s. Of course, in order to walk along the bridge, you do not need to have any understanding of precisely how the bridge was engineered. Mathematics was used as a tool by engineers seeking to build the bridge, so that today we can cross it.

The markets are no different. Mathematics can help to explain a lot about markets, although it is very often in the background. Indeed, a similar point was made very well by Vyas from CPPIB at a talk which I heard recently at Global Derivatives USA. He stressed that he viewed quant as a tool, when it comes to investing. We can illustrate this point using a few examples.

When it comes to discretionary traders, I so often hear the comment, "No, we're just discretionary traders, we don't use any quant stuff". When we distil precisely what a trader does, it is inescapable that all traders will end up using some quant techniques to some extent.

Let us take the example of volatility traders examining volatility surfaces. They might be trying to understanding the relative value of certain options. They wants to understand which parts of the volatility surface are cheap and which are expensive. They might also look at various tenors to try to understand anomalies in time space. Let us consider how much data is needed to do this effectively. Each tenor has 5 quotes and you might have at least 10 tenors (often more). That's 50 points for every trading day. If you have 5 years of data that is 12,500 points. Across 10 currency pairs that is 125,000 points. How else are you supposed to crunch that data, without doing some heavy duty coding and mathematics to summarise it into a digestible form to make a trading decision? At the end of the process, a discretionary trader would still have a final say on the whether to buy or sell based on the output from the analysis. This contrasts with a systematic trader, who would go with whatever the trading model suggested. However, much of the thought processes of these two traders are very similar.

Whilst we have illustrated this point with options, we could easily have the same issue with many other areas of the market, notably with stocks. If a trader has a mandate to trade any of the stocks in the S&P500, how can he or she possibility know all the fundamental details of all 500 companies? Quant tools can help flag trading opportunities, which a discretionary trader can dig into in more detail, before deciding to trade. Alternatively, we can create the final output to be a buy or sell signal for a systematic trader.

So is mathematics a pancea for markets? Not really. Like any tool, it can be misused. As I discuss in my book, Trading Thalesians, mathematics should be used as a tool to explain how markets work. It should not be used to proof something which you do not know is true!

If you're a discretionary trader, don't always dismiss what quant analysis can do to help you in your decision making. As an example, it can help summarise very large datasets, so they are easier to interpret from a discretionary perspective. Very often, you might well be walking on the bridge mathematics built, but perhaps you might not realise it. Drop me a message and I might be able to tell you more! Equally, if you're a quant trader, don't dismiss what discretionary trading can teach you.. that will be a theme for a future article.

**Like my writing? Have a look at my book Trading Thalesians - What the ancient world can teach us about trading today is on Palgrave Macmillan. You can order the book on Amazon. Drop me a message if you're interesting in me writing something for you or creating a systematic trading strategy for you! Please also come to our regular finance talks in London, New York and Budapest - join our Meetup.com group for more details here.**

**Our next London Thalesians talk is on Wednesday 25th March by Matthew Dixon on speeding up high level languages, tickets here.**

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