Arbitrage-Free Valuation

What Is Arbitrage-Free Valuation?

Arbitrage-free valuation is the value of an asset or financial instrument based solely on the real performance or cash flows that it generates. When an asset’s market price differs from its arbitrage-free value, then an opportunity for arbitrage exists by trading the asset for another asset or portfolio of assets that replicate its underlying performance or cash flows or by buying and selling the assets in different markets where the price differs.

Understanding Arbitrage-Free Valuation

Arbitrage-free valuation of an asset is based solely on the value of the underlying asset without taking into consideration derivative or alternative market pricing. It can be calculated for various types of assets using financial formulas that account of all of the cash flows generated by an asset.

Arbitrage is when you buy and sell the same security, commodity, currency, or any other asset in different markets or via derivatives to take advantage of the price difference of those assets. For example, purchasing a stock on the NYSE and selling it on the LSE in the U.K. for a higher price is arbitrage.

Arbitrage can only occur when some price difference exists between market prices for an asset or between a market price and the underlying value of the asset. For a stock, the firm is doing the same work and has the same underlying capital structure, asset mix, cash flow, and every other metric regardless of what exchange it is listed on or derivative pricing of the stock. Arbitrage-free valuation is when price discrepancies are removed, allowing for a more accurate picture of the firm’s valuation based on actual performance metrics. 

When such differences exist they present an opportunity for traders to profit from the price spread by engaging in an arbitrage trade. However, every act of arbitrage (every arbitrage trade) will tend to move the market price closer toward the arbitrage-free valuation, eventually eliminating the opportunity for arbitrage profits. 

Applications of Arbitrage-Free Valuation

Arbitrage-free valuation is used in a couple of different ways. First, it can be the theoretical future price of a security or commodity based on the relationship between spot prices, interest rates carrying costs, exchange rates, transportation costs, convenience yields, etc. Carrying costs are 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, carrying costs, convenience yields, exchange rates, transportation costs, etc. Convenience yield is when you hold on to the actual physical good versus the liquid asset. An example would be holding on to a barrel of oil versus holding on to an oil futures contract. When the actual futures price does not equal the theoretical futures price, arbitrage profits may be made.

Arbitrage is more useful for traders rather than investors.

Special Considerations 

While long-term Warren Buffett style investors may not be interested in companies that are heavily arbitraged, traders can utilize arbitrage as a way to make money. If you think about it, it’s one of the oldest tricks in the book; buying low and selling high.

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 get out of line. A cash-and-carry trade exploits the price difference between an underlying asset and its derivative. Of course, setting up and executing such trades is complex. 

For the trade to be truly risk-free, variables must be known with certainty and transaction costs must be accounted for. Most markets are too efficient to allow risk-free arbitrage trades, because prices adjust to quickly eliminate any spread between market price and arbitrage-free valuation.

Arbitrage-Free Valuation Example

Suppose that oranges that cost $1 a piece off the tree in Florida sell for $5 on the street in New York City because they can only be grown in Florida (and additional places where weather permits it). If the transportation, storage, marketing, and other related costs to bring each orange to market from Florida to New York come to $4, then in both places the respective market price ($1 in Florida or $5 in New York) is equal to the arbitrage-free valuation of the orange ($1 to grow the orange in Florida vs. $1 to grow the orange + $4 in associated costs to bring it to market in New York).

Now suppose that transportation costs fall due to technological improvement or lower fuel prices, and as a result, the cost of bringing a Florida orange to market in New York falls from $4 to $3. Now the arbitrage-free valuation of the orange in New York is $4 ($1 cost to grow the orange in Florida and $3 to bring it to market in New York).   

Savvy businesspeople would take advantage of this and utilize the resulting arbitrage to make money by buying oranges off the truck from Florida at the lower price of $4 and re-selling them at $5. However as they do so, they will have to compete against and against new orange resellers will be attracted 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 valuation of $4.

In that same spirit, financial asset traders can do the same thing. You can take advantage of exchange rates, futures, and various other forms of investments where the market price does not account for all the revenues and expenses linked to a given asset. But doing so depends on staying alert and discovering opportunities to profit from spreads between arbitrage-free implied prices and market prices, which may be very short lived as all traders compete to exploit these same opportunities.