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Investments with Positive Convexity

Convexity is one of the most important concepts when it comes to analyzing investments, though it is often ignored by investors. In this post, we analyze what positive convexity is, how to identify it, and some investments with convexity.



In geometric terms, the convexity of a curve can be used to describe its curvature. Applied to financial markets and economics, convexity is used to describe how two variables are related to each other. For example, we could build a chart that shows how the profits of a company change when sales increase:

Using that example, a convex chart would be one in which, as sales increase, profits increase at a faster rate. Investments with positive convexity are very attractive to investors. Let us discuss how to use the concept of positive convexity for investment decisions.

Once you understand how it works, you will realize that it is one of the most powerful concepts when taking investment decisions. In fact, convexity can be considered as important as diversification.

If an investor dominates convexity, diversification and discipline, they will be in a very good positive generate very good long-term returns.

Origin of Positive Convexity in Financial Markets

The origin of convexity in financial markets comes from fixed income assets. Convexity is used to describe the relationship between the price of a bond and its interest rate. Price and interest rate move in opposite ways.

When the price of a bond goes up, it becomes more expensive, and its interest rate goes down. Conversely, when bond prices drop, they become cheaper, and their interest rate increases.

If we were to illustrate graphically how bonds prices and interest rates move, we would not get a straight line. We would get a curve. That curve would probably be convex. It would indicate that a bond price rises more when interest rates go down than it drops when interest rates go up.

To give you an example, let us imagine that a bond has a price of 100 and interest rate of 4%. If the interest rate drops to 3%, its price increases to 105. However, if the interest rate goes up to 5%, its price only drops to 96. As you can see, the price moves more on the upside than the downside for an equivalent interest rate drop. Convexity is a very desirable feature in bonds.

Positive Convexity in Investments

When analyzing investments outside of the fixed income market, convexity can be used to describe the relationship between potential gains and potential losses.

If we buy a stock for $50, we know what our maximum potential loss is: $50. That would happen if the company went bankrupt. However, if things go well, the potential for gains is unlimited.

Obviously, investing is not just about picking assets with the greatest upside potential if things go well. The probability of the best-case scenario is rarely 50%. Therefore, convexity has to be assessed together with probabilities.

The analysis of individual assets can be combined within the concept of diversification. The goal is to own different assets whose future returns are not highly correlated. Those assets will have different potential returns and potential losses. The important thing is that, once all these assets are part of a portfolio, the portfolio has positive convexity.

Assets with Positive Convexity

There are many types of potential investments with positive convexity. Convexity depends on the price at which an asset is traded, its long-term potential and the market environment. Therefore, there are certain assets that are more prone to offer positive convexity to investors:


Stocks are one of the assets with positive convexity and widely owned by the investing public. Stocks tend to give us positive returns when the economy grows and prices increase moderately.

Because the economy tends to grow in the long run and prices generally rise, we are interested in owning stocks.

As a result, stocks have unlimited upside potential, at least theoretically. In the long term and in a diversified way, the probability of achieving positive returns by investing in the equity market is extremely high.

Real Estate

Another of our favorite assets is real estate. Real estate benefits when there is economic growth and inflation. In fact, if inflation is very high, real estate reacts more positively than stocks.

Thanks for economic growth and inflation dynamics, real estate investments have positive convexity.

As with everything, gains are not guaranteed. Certain real estate markets have been flat or are even down after a few decades, including Japan.

This is the risk of investing in real estate if there is bubble. From a convexity perspective, when prices get so high that they enter bubble territory, convexity starts to go down until it is eventually negative. Negative convexity indicates that the potential for losses is greater than the potential for gains.


Gold is a very interesting asset. It does not yield anything as it is just a metal. But gold has been money for more than 5,000 years and is a safe haven asset. In fact, gold is the best asset to own in times of currency crisis.

The 2020s global economy is dominated by highly indebted countries, massive public deficits, aging population in the West and geopolitical tensions. Any and all of them can be highly inflationary and lead to monetary problems. This can make the price of gold skyrocket.

Conversely, in the unlikely event that governments manage to introduce strong enough budget reforms, lower public debt and stabilize public finances, the price of gold is likely to go down.

Because the potential for gains in the first scenario is much greater than the potential for losses in the second scenario, gold is an asset with positive convexity. And the probabilities would be on our side too.


Finally, we have to highlight Bitcoin as one of the investments with the most positive convexity. Bitcoin is a digital cryptocurrency without a central bank. Its proponents emphasize it combines the best convenience features of most fiat currencies with the inflation hedge features of gold.

Introduced about a decade ago, the price of Bitcoin has been steadily and staggeringly going up over time. It has also suffered various crashes of more than 80%. Consequently, it is a highly speculative asset that should be traded and owned with caution.

Nonetheless, there is no doubt that the potential for gains is much greater that the potential for losses. While Bitcoin may theoretically go down to 0 and cause 100%, its price can also continue to skyrocket as it has done for about 15 years.

The positive convexity we see in Bitcoin also applies to other cryptocurrencies such as Ethereum.

Positive Convexity in our Life

Finally, I would also like to talk about positive convexity in our lives. We have seen how assets can be analyzed in terms of comparing potential gains with potential losses. Similarly, life decisions and projects can also be assessed by weighing potential gains with potential losses.

Not only is the outcome of such decisions and projects important, but also the risks involved, the investment we have to make in terms of time, energy and money, and even the potential for future opportunities with positive convexity.

If you are considering studying something, changing jobs, starting a business or a project, moving to a different country, etc. think about convexity. Analyze what you stand to gain and lose, and you will realize if there is positive convexity in those things.

This is something that Nassim Taleb always talks about in his brilliant books.

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And if you are interested in an asset that seems to have plenty of convexity, check out the following post:
Investing in Uranium – The Energy Source of the Future

Published in Learn How To Invest

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