Assume an arbitrage-free market. Let's say that the current price of an asset is $100$, its forward price in 1 month is $110$

Is it possible that the true expected value of the asset is not $110$? Sheldon Natenburg in Option Volatility and Pricing says that

If we assume that the underlying market is arbitrage-free, the expected value for the underlying contract must be equal to the forward price.

Why would this be so?


Arbitrage no, profitable yes. Remember arbitrage implies riskless, and given only the underlying and a bond you can't create a riskless profit. However, in this case just buying the forward and waiting for expiry would give you an expected positive return.

The forward price almost never matches the markets expected value of any given asset. It is one of the reasons people speculate with forwards. For example, in FX currencies with large interest rate differentials (like EM vs USD) tend to have very high forward prices. So selling forward as a carry trade is a very popular strategy as the spot price at maturity is generally lower than the forward price sold.


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