What Is a Solvency Cone?

A solvency cone is a mathematical model that considers the estimated impact of transaction costs when trading financial assets. The solvency cone, in particular, represents a range of possible trades or portfolios that can be traded at a specific time frame after taking the bid-ask spread into account.

Key Takeaways

  • A solvency cone is a tool used in financial mathematics to understand the realm of possible trades that could be made given transaction costs in a market.
  • The solvency cone uses the spread between the bid and ask price, in addition to direct transaction costs like commissions, to narrow the universe of possible investments.
  • Traders who buy and sell frequently must take into account both direct and indirect transaction costs as these can reduce profits and may even generate net losses over time.
  • Solvency cones are also used when trying to replicate the holdings and after-cost performance of a professionally-managed portfolio.

Understanding Solvency Cones

The spread between the bid and ask prices essentially measures 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. When spreads are wide, the costs of entering and exiting a trade, or making a round trip transaction, are higher.

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 (HFT) 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 cannot be ignored. The solvency cone helps to estimate these costs.

Other Uses For the Solvency Cone

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.