Why is randomness the signature of an efficient market, and why can a perfectly calm market be the least efficient of all?
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Three desirable properties of a market
List random and unpredictable prices, quick and correct reaction to news, and no easy abnormal risk-adjusted returns, and tie the third property to a highly competitive market.
Trading on a pattern destroys it
Reproduce the sine-wave market argument from buying troughs and selling peaks to the vanishing pattern, give the election volatility trade as the example, and describe a random walk with drift.
Low volatility is not efficiency
Describe the calm but inefficient two-stock, buy-only exchange, name predictability per unit of volatility as the relevant measure, and record that the volatile markets of 2008 were not therefore inefficient.