Solvency Cone

A solvency cone is a mathematical model that considers the estimated impact of transaction costs when trading financial assets.

A solvency cone represents a range of portfolios that can be traded at a specific time frame after taking bid and ask prices into account.

The spread between the bid and ask prices essentially measures the the difference between the highest price that a buyer is willing to pay for an asset and the lowest price that a seller is willing to accept. This spread represents an important part of overall transaction costs.

Of note, the spread tends to be wider during periods of market volatility. Moreover, it tends to widen among assets and asset classes that trade less frequently.

Financial transaction costs tend to come down over time. Perhaps you’ve noticed that online brokerage accounts tend to out-duel each other on fees every few years. As a result, the less than $10 a trade these brokerages offered more than a decade ago is now typically less than $5 a trade.

However, transaction costs still must be accounted for, especially in particular aspects of trading. Short-term and high-frequency trading strategies that swap positions on an intraday or intraweek basis sometimes incur transaction costs that overwhelm the profit potential. Even longer-term, or so-called position trading strategies incur significant costs that can’t be ignored.

The solvency cone helps to estimate these costs.

Part of the problem with classic financial models is that many don’t take transaction costs into account. This makes these models difficult to replicate in the real world, since costs are such a meaningful factor when making trading decisions.

The solvency fixes this problem. It lets mathematicians apply an estimate of real-world transaction costs when utilizing mathematical and financial theory. For this reason, the solvency cone has applications in the foreign exchange, currency and options markets, in addition to just bonds and stocks.

Another area where the solvency cone comes into play is so-called portfolio replication, or trying to match the trading style, or specific market moves, of an expert trader.

It seems worthwhile to try and match what proven experts do in the markets. However, even with perfect information in near-real time, it’s almost impossible to match their precise performance. The reason is trading costs; the initial trades put on by the expert likely were made at more favorable bid-ask spreads. So even trading them in near-real-time won’t result in the same performance.

The solvency cone helps to make better performance assumptions for these replicated portfolios.