What is an arbitrage-free valuation?
Arbitrage-free valuation is the value of an asset or financial instrument based solely on actual performance or the cash flows it generates. When the market price of an asset deviates from its arbitrage-free value, there is an opportunity to arbitrage by trading the asset against another asset or portfolio of assets that replicate its underlying performance or cash flows, or by trading the assets bought and sold in different markets where the price differs.
The central theses
- Taking advantage of price differences in different markets is known as arbitrage – it is a hallmark of business and stock trading.
- Arbitrage-free valuation is the valuation of an asset without considering derivative or alternative market prices.
- Exchanges and trading platforms often do not allow for risk-free arbitrage trades, and information technology has eliminated many arbitrage profits.
- Arbitrage can be applied to derivatives, stocks, commodities, utilities, and many other types of liquid assets.
Understand arbitrage-free valuation
The arbitrage-free valuation of an asset is based solely on the value of the underlying asset, without considering derivative or alternative market prices. It can be calculated for different types of assets using financial formulas that take into account all cash flows generated by an asset.
Arbitrage is when you buy and sell the same security, commodity, currency or other asset in different markets or through derivatives in order to take advantage of the price differential of those assets. For example, buying a stock on the NYSE and selling it at a higher price on the LSE in the UK is arbitrage.
Arbitrage can only occur when there is some price differential between market prices for an asset, or between a market price and the underlying value of the asset. For a stock, the company does the same work and has the same underlying capital structure, asset mix, cash flow, and all other metrics, regardless of what exchange it’s listed on or the stock’s derivatives prices. An arbitrage-free valuation is when price variances are eliminated, allowing for a more accurate picture of the company’s valuation based on actual performance metrics.
When such differences exist, they offer traders an opportunity to profit from the price range by engaging in arbitrage trading. However, each arbitrage action (each arbitrage trade) tends to bring the market price closer to the non-arbitrage valuation, eventually eliminating the opportunity for arbitrage profits.
Applications of Arbitrage-Free Valuation
Arbitrage-free valuation is used in a number of ways. First, it can be the theoretical future price of a security or commodity based on the relationship between spot prices, interest rates, holding costs, exchange rates, transportation costs, convenience yields, and so on. Holding cost is simply the cost of holding inventory.
It can also be the theoretical spot price of a security or commodity based on the futures price, interest rates, storage costs, convenience yields, exchange rates, transportation costs, etc. Liquid assets. An example would be holding onto a barrel of oil versus holding onto an oil futures contract. If the actual futures price does not match the theoretical futures price, arbitrage profits can be made.
Arbitrage is more useful for traders than investors.
While Warren Buffett-style long-term investors may not be interested in companies that are heavily arbitraged, traders can use arbitrage as a way to make money. If you think about it, it’s one of the oldest tricks in the book; buy cheap and sell dear.
Cash and carry trades, reverse cash and carry trades, and dollar roll trades are all examples of trades made by arbitrage traders when theoretical and actual prices are out of whack. A cash and carry trade takes advantage of the price difference between an underlying asset and its derivative. Of course, setting up and executing such trades is complex.
For trading to be truly risk-free, variables must be known with certainty and transaction costs must be considered. Most markets are too efficient to allow risk free arbitrage trades as prices adjust to quickly eliminate any spread between market price and arbitrage free valuation.
Arbitrage-free valuation example
Suppose oranges that cost $1 a piece off the tree in Florida are sold on the street in New York City for $5 because they can only be grown in Florida (and other places where the weather permits). If the transportation, storage, marketing, and other associated costs to bring each orange to market from Florida to New York is $4, then the respective market price ($1 in Florida or $5 in New York ) in both places of arbitrage – free valuation of the orange ($1 for growing the orange in Florida vs. $1 for growing the orange + $4 in associated costs to get it to market in New York).
Now suppose that transportation costs decrease due to technological improvements or lower fuel prices and, as a result, the cost of bringing a Florida orange to market in New York decreases from $4 to $3. Now the arbitrage-free value of the orange in New York is $4 (it costs $1 to grow the orange in Florida and $3 to put it on the market in New York).
Smart businessmen would take advantage of this and use the resulting arbitrage to make money by buying truck oranges from Florida at the lower price of $4 and reselling them for $5. In doing so, however, they must compete against new orange retailers who are lured into the market by the arbitrage profit opportunity by offering lower prices. This competition will eventually drive the market price closer to its arbitrage-free value of $4.
In this sense, traders of financial assets can do the same. You can take advantage of exchange rates, futures, and various other forms of investment where the market price does not take into account all of the income and expenses associated with a particular asset. However, this depends on staying alert and spotting opportunities to profit from spreads between non-arbitrage implied prices and market prices, which can be very short-lived as all traders compete to take advantage of the same opportunities.