I do agree with that the relationship between data liqudity and price volatility is complex, although would actually argue that the efficient market hypothesis does not make a direct claim on the relationship - it states that market prices reflect all available information (assuming strong form). If information itself can is being generated continuously, and can be expected to change the price of a stock, even if EMH holds, the volatility of stock price can increase as opposed to decrease.

It is useful to look at the actual claim a bit more formally, as it reaches a similar conclusion - data availability can increase, decrease or not change the price of a stock, depending on relevant conditions - although EMH may or may not hold in any of those scenarios.

**Scenario 1- Volatility and data liquidity are positively correlated**

- Volatility = sudden deviations in price of an asset (typically compared to its average, as with standard deviation)
- Price of an asset (theoretically) is given by present value of its future cash flows (note this is not, in itself, imposed by EMH)
- Future cash flows cannot be observed, so prices of publicly traded assets are given by investors beliefs on prospective cash flows, based on available information (assuming strong form EMH holds), and if investors have rational expectation (assuming rational expectation hypothesis - REH -holds).
**Assuming above theories hold, any sudden deviation in price (i.e., volatility), therefore, can be only driven by data liquidity only if it releases new information about the stock’s prospective cash flows, and if investors act rationally on the information**

**Scenario 2 - Volatility and data liquidity are not correlated**

Conversely, data liquidity may not translate to any volatility if:

- The data does not impact the stock’s cash flows (EMH can still hold)
- Investors are not, or were not acting rationally all along (failure of REH), so that prices were never given by available data (failure of EMH)
- There were limitations which restrict investors from acting on new information (e.g., regulatory limitations on short selling, which will render EMH as false, but not REH)

**Scenario 3 - Volatility and data liquidity are inversely correlated**

Finally, lack of data liquidity could also translate into more volatility if the investors were basing decisions on incomplete information, which can encourage them change their opinion more sporadically (EMH can still hold if this is true, although this is not a necessary condition, as the volatility can be driven by a range of other factors, such as investor sentiment).

Empirically, Robert Shiller’s work (https://www.nber.org/papers/w0456) has shown that for publicly traded equity stocks (given by prices of S&P composite index), the volatility cannot be explained by information on prospective cash flows that were publicly available (i.e., historical dividend distributions). One could argue that volatility was driven by insider information, but actual dividend distributions (ex-post) also does not explain the volatility, which begs the question - what were investors basing their investment decisions on?

History is also littered with examples where data availability cannot explain asset price volatility (https://www.amazon.co.uk/Manias-Panics-Crashes-Financial-Investment/dp/0471467146), as investors do not always base investment decisions on rational assumptions. I personally think crypto-related financial products can only go as far as increasing data availability - their use has to be tightly controlled if the data has to be used to form rational expectations.