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What is no free lunch with vanishing risk (NFLVR)?

No free lunch with vanishing risk

It is a mathematical concept based on arbitrage used in asset pricing and investment modelling. Arbitrage is the practice of taking advantage of price differentials between two or more markets.

Where have you heard about no free lunch with vanishing risk?

Unless you have been mathematically modelling asset pricing or studied investment strategies academically, it is very unlikely you'll have come across the term.

What you need to know about no free lunch with vanishing risk.

It is difficult to capture NFLVR simply but a free lunch with vanishing risk is when a sequence of self-financing portfolios (where the purchase of an asset is financed by the sale of other assets and money is not added or removed) which converge to an arbitrage strategy and allows the approximation of a self-financing portfolio (the free lunch and with no risk). NFLVR is the no-arbitrage argument against that possibility.

If you're keen on seeing the maths, part of the calculation looks like this!

If  is a semimartingale with values in  then S does not allow for a free lunch with vanishing risk if and only if there exists an equivalent martingale measure  such that S is a sigma-martingale under.

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