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I am trying to understand asset price volatility.

Many of the news articles I read link how stock market volatility is linked to asset price volatility?

To give an example, in Mike Mackenzie's (Financial Times), February 4th article,

Volatility in the US equity market has retreated to its lowest level since early October as a pledge from the Federal Reserve to be patient with potential future interest rate rises and flexible with its balance sheet policy have soothed markets, writes Peter Wells.

Is there any economic intuition of why it is so important and what other factors are equally important for market volatility?

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    $\begingroup$ With low rates being a driver for economic growth and thus a positive for equities, impending rate hikes add to uncertainty about future equity prices, and drive up volatility. The recent dovish comments thus helped bring down volatility $\endgroup$ – ZRH Feb 5 '19 at 10:33
  • $\begingroup$ In theory volatility depends on the rate of information arrival. In practice it is hard to identify and measure the "information" and we are left to guess. Mr. Peter Wells' opinion is that investors were expecting big news about the economy (hence high volatility), now that the Fed has explained its stance they do not expect much further news for a while so vol is low. This is just one man's opinion and we have no way of proving that this is the reason for the vol change that we observed. $\endgroup$ – noob2 Mar 6 '20 at 13:19
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To be clear, journalistic assessments of the kind above refer to "IMPLIED volatility", ie the expected and priced level of future vol from options, that is effectively a measure of investor sentiment (as opposed to an observable economic reality).

This matters in so far as observations about the REALISED (as opposed to implied) volatility of stocks and how these might relate to other asset classes and the economy are based on a different (but obviously related) measure of the same concept...

So to answer the original question, there are two issues at work here.

The first and most obvious is the massive "left skew" in equities. They (long before options were liquidly traded) have tended to "grind up, and spike down". If you had to rationalise this behaviour economically, hark back to the Merton Capital model. Credit is the short put on the corporate's balance sheet; Equity is the long call. Anything that is "good" or "bad" for the corporate thus has non-linear "gamma" effects on stockholders and or versus bondholders. Given the capital cushion from the credit, the implicit "strike" on these options is out-of-the-money; you only start to see these effects once you start to stress-test the balance sheet.

The link in the FT oped to Fed policy is the other angle on this: the convexity of long-duration asset prices to changes in discount rates. Imagine a perpetual bond - it's the easiest thing in the world to price. Price = 1/Rate. The lower Rates go, the faster the change in Price per change in Rates will tend towards infinity. This is just a truism of asset valuation. That's the "convexity".

So the price of a perpetual bond is "Price = Coupon/K" (where K is the discount rate). Well, the original classic equity valuation is the so-called DDM (the dividend discount model) where "Price = Dividend/(K-G)" (where G is dividend growth). Assuming G>0, then stocks will be more converse, and thus more sensitive to discount rate changes, than perpetual bonds!

In the "good old days" (ie where textbooks live, in a world before 2008), it would be assumed that anything that lowered K thus would reflect slower growth that was also bad for G. So stock valuations would be (sort of, almost, mostly) invariant to interest rates. As it happens, I was an investment bank stockmarket strategist back then, and we used to have "what stocks win and lose when rates rise or fall" set up, almost as a zero-sum game back then.

The implicit but unspoken assertion in the FT oped, but it's "dogwhistle" if you know the code, is that K for bonds versus (K-G) for stocks (and even maybe the gold price) have all just become the same thing, courtesy of endless QE.

In which case, it would then be perfectly natural to assert that the volatility of the stockmarket was just as a leveraged expression of asset price volatility ('cos G>0), that was just a natural expression of interest rates ('cos of convexity 101).

I don't believe this narrative 100% myself; but it is (I think) the most internally consistent answer to the question you asked, as you asked it.

hope it helps,DEM

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Equity market volatility reflects the confidence/certainty about economic future. When it's a low volatility environment, it reflects the underlying psychology of participants (e.g. not a lot of tug of war between the bull and the bear, not much uncertainty of the direction of the economy.). It also reflects relatively stable trading conditions amongst the participants (no sharp move due to margin call or forced liquidation). In times of uncertainty, or when market participants are uneasy and have low convictions, any news could trigger reaction one way or another you would tend to see high volatility. These psychology and conditions are often time transferrable to other asset classes.

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To simply the discussion:

Realized volatility is observable simply as-> big price ranges fast.

Other metrics like VIX or market based maetrics will imply a view simply as -> what the market thinks volatility is.

The Risk free rate, or Fed Funds Rate / Tsy curve / SOFR or whatever metric you use as a proxy; is just that, a risk free rate.

If there is a shock in rate policy, you can expect volatility to spike, when prices move a lot based on whatever definition of volatility you use.

However anything that makes prices change a lot, or merely the perception of volatility change a lot, will cause articles to flow about the relationship.

Bottom line is that Volatility is prices moving or perception of prices moving; rates are just one component that can make that happen.

Hope that helps to bring things into perspective.

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