For standing issuance quotes exposed until a later governance action, a fixed voting delay is not a fixed risk budget: loss exposure also depends on the intervening relative-price path and on whether withdrawal can execute.

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The multifractal model also has many implications for practical finance. As indicated, portfolio theory needs rethinking; options need revaluing; trading strategies need review. A small example: “stop-loss” orders are imperfect, to put it mildly. Many investors or traders leave instructions to close a position when a price hits a particular target. But as many have learned to their grief, when prices are really flying, they typically whiz past the target so fast that even the most attentive broker cannot execute the “sell” orders fast enough. Result: Greater losses, or smaller profit, than the investor intended. Another example: the mathematics of this model offers some potentially new yardsticks to measure volatility and risk. Instead of the standard deviations and “betas” of conventional finance, one can imagine new scales based on two new variables to be described later in this book: the $H$ exponent of price dependence, and the $\alpha$ parameter characterizing volatility. A few fund managers have experimented with these concepts. They often call it chaos theory—though strictly speaking, that is marketing language riding on the coattails of a popular scientific trend. In reality, the mathematics is still young, the research barely begun, and reliable applications still distant.

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A small example. Stop-loss orders are imperfect, to put it mildly. Many investors or traders leave instructions to close a position when a price hits a particular target. But as many have learned to their grief, when prices are really flying, they typically whiz past the target so fast that even the most attentive broker cannot execute the sell orders fast enough. Result? Greater losses or smaller profit than the investor intended. Another example. The mathematics of this model offer some potentially new yardsticks to measure volatility and risk. Instead of the standard deviations and betas of conventional finance, one can imagine new scales based on two new variables to be described later in this book, the h-exponent of price dependence and the a-parameter characterizing volatility. A few fund managers have experimented with these concepts. They often call it chaos theory, though strictly speaking, that is marketing language writing on the coattails of a popular scientific trend.