Arbitrage Explained: Value Additivity vs. Dominance
Arbitrage is one of the foundational ideas in finance, especially relevant for those preparing for the FRM (Financial Risk Manager) exam. In this video, we dive into two types of arbitrage: Value Additivity and Dominance.
What is Value Additivity?
Value Additivity is the principle that the value of a combined package of financial instruments should equal the sum of the individual values of the instruments. For example:
- Product A pays \$1 one year from today. At a 10% discount rate, its fair price is \$0.91.
- Product B pays \$110 one year from today. It can be seen as 110 units of A, hence its fair value should be $110 \times 0.91 = 100$.
- If B is priced at \$96, an arbitrage opportunity arises: buy B and sell 110 units of A, locking in a \$4 profit today.
What is Dominance?
Dominance occurs when two products carry the same risk, but one offers a higher return. For instance:
- Product C offers a payout of \$105 one year from today and is priced at \$100. Product D offers a payout of \$220 one year from today and is priced at \$200. Both products are from the same, hence same carry the same (issuer related) risk.
- On a per-dollar basis, D offers higher returns than C — so D dominates C.
- Arbitrage opportunity: buy D and short 2 units of C. Net cash flow today is zero, but you earn \$10 after one year.
These principles highlight how inconsistencies in pricing create risk-free profit opportunities — a core idea in understanding financial markets.
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