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What return should you expect when you take on a given amount of risk? Howshould that return depend upon other people's behavior? What principles can youuse to answer these questions? In this paper, we approach these topics byexploring the consequences of two simple hypotheses about risk.  The first is a common-sense invariance principle: assets with the sameperceived risk must have the same expected return. The second hypothesisconcerns the perception of time. We conjecture that in times of speculativeexcitement, short-term investors may instinctively imagine stock prices to beevolving in a time measure different from that of calendar time. They mayinstead perceive and experience the risk and return of a stock in intrinsictime, a dimensionless time scale that counts the number of tradingopportunities that occur.  The most noteworthy result is that, in the short-term, a stock's tradingfrequency affects its expected return. We show that short-term stockspeculators will expect returns proportional to the temperature of a stock,where temperature is defined as the product of the stock's traditionalvolatility and the square root of its trading frequency. We hope that thismodel will have some relevance to the behavior of investors expectinginordinate returns in highly speculative markets.

The Perception of Time, Risk and Return During Periods of Speculation