Why Expected Stock Returns Do Not Create Forward Arbitrage
Summary
The discussion asks whether a stock forward priced using the risk-free rate creates an expected profit for a long investor when the stock’s physical-measure expected growth rate is higher. The responses distinguish expected return from arbitrage: holding the stock with borrowed funds can also have a positive expected payoff, but that payoff carries risk and is not a guaranteed profit.
Forward pricing under no-arbitrage and market-completeness assumptions is a pricing relation, not a forecast of the stock’s realized performance. The physical expected return does not determine the arbitrage-free forward price in the way the question suggests. The answers are conceptual and brief; they do not develop a formal derivation or specify frictions such as dividends and financing details.
Key ideas
- A positive expected payoff on a long forward does not by itself imply arbitrage.
- Borrowing to buy the stock can expose an investor to similar risky expected returns.
- No-arbitrage forward pricing is distinct from forecasting the stock’s physical expected return.
- The explanation relies on simplified pricing assumptions and does not address market frictions in detail.
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# Stock forward price argument # Stock forward price argument Hi I am strangling to understand where is the mistake with the following strategy. Can anyone help me with the following argument? Assuming a stock price follows geometric Brownian motion then the expected value, under the physical measure, is $S\exp(μt)$. If the forward price is $S\exp(rt)$ then if I always long the forward I will be profitable in the long run ( i understand there is a risk envolve and that this difference it can be explain by the market price of risk. I also understand that if the price of the forward is $S\exp(μt)$ there will be arbitrage by borrowing money buying the stock and selling it at the forward price.) But still under those assumptions if the price of forward is $S\exp(rt)$ by entering long I will be profitable in the long run. Can anyone point out where my mistake is? ## Answer by dm63 (score 2) https://quant.stackexchange.com/a/43010 You ask where the mistake is, but there isn't one. If you buy stocks using money borrowed at the risk free rate you will expect to make money, but there is risk. There's no contradiction. ## Answer by MaPy (score 0) https://quant.stackexchange.com/a/40756 With the same argument you can just long the stock (no need to long the forward). The whole idea is to find a price for the forward under the assumptions of no arbitrage, market completeness. In that case the performance of the stock disappears for the pricing problem.
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