Talk:Stock duration

Macaulay duration

Stocks do not have Macaulay duration - Macaulay duration applies when the cash flows are known and fixed. If we mention Macaulay duration here, we ought to confine the name to a footnote, and use other more generic terms in the text. We strive for accurate technical diction, so we downplay the association.

Specifically, most of the text space is hogged by an elaborate derivation of Macaulay duration that ought not to be in the article. The most plausible place would be in the article on Bond duration, but even there, the encyclopedia is a concise scholarly exposition, not a textbook on corporate fiance. So I'm moving the section to the talk page of the bond duration article for the editors there to mangle. Sbalfour (talk) 16:55, 14 March 2022 (UTC)

Duration section

The neat mathematical formula, which is the Macaulay duration formula by another name, is not applicable as it stands, because in order to make sense, the company and its dividends would have to have the characteristics of a bond.

The discount rate here has risk-free and volatility-associated risk components; where are they obtained? We don’t even show them. For most companies, the growth rate (growth rate of what?) isn’t constant, nor is it the growth rate in perpetuity. Analysts usually use a 2-stage or even 3-stage model to calculate the present value (and implied duration) of a stock.

Duration isn’t necessarily any simpler than calculating the present value of a stock (in fact, they’re intricately interrelated). There’s a lot of complexity that’s not at all apparent here. So much so that the formula for duration is unusable as it stands. A real-world example may run a few pages of analysis.

Yet, as a rule of thumb, duration 50% greater than a stock’s PE works out reasonably for most applications! Not all stocks have dividends, and among those that do, the yields may not be predictably related to cash flows, so dividend discount models are extremely limited in usefulness. We probably ought to use discounted free cash flow models, and call them by that name.Sbalfour (talk) 18:31, 14 March 2022 (UTC)

Duration section, redux

In some sense, the entire article comes down to this one section, and to the one formula that leads it. However, that formula is completely worthless - it doesn't include either the stock price or dividend amount!! It's utterly ridiculous. It wasn't sourced, and I can't find a source, so I'm deleting it and the text associated with it. I don't recognize the formula, so have no idea what it might represent or how to fix it. What I suspect happened was that someone with no knowledge of the subject matter copied the formula from a webpage and missed critical context. Failure to cite something like that means they shouldn't be editing at all, IMHO. Anyone without substantive knowledge of finance shouldn't be contributing to a highly technical article like this one.

The Price sensitivity section also omits the stock price and dividend amounts, and is badly botched and inapplicable, so it also needs to be deleted in its entirety until someone knowledgeable supplies appropriate text and formulas.

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The first approximation, in years, to the duration of a stock is the ratio of the two terms, stock price divided by the annual dividend amount. Since the present value of future dividends gets a bit less with each passing year (or even quarter or month), the duration is a bit longer than that approximation. But the duration of a stock, unlike that of a bond, isn't deterministic. The stock price and dividend are taken directly from the market, and they're tangible. Everything else is hypothecated into the future: interest rates, growth, volatility, ideosyncratic risks, and dividend amounts. For European stocks, dividends aren't fixed, but paid as a proportion of profits, so even the base amounts are hypothecated.

Historically, before the 1990s, the average dividend yield on U.S. stocks had been a little less than 4%, so the first approximation to duration has been a little more than 25 years. The hypothecated duration taking into account changes in the present value of future dividends, has been about 25% longer, which gives a duration in the low 30s (years), Traditionally, analysts have cited the duration of the U.S. market as 20-30 years. Since the last recession in 2008-09, multiples have become inflated and dividend yields have dropped, so the current implied duration of stocks according to the Dividend Discount Model (DDM) has risen to at least 80 years (Dec. 2021). However, the implied duration from other means isn't nearly that long. What's happened is that the DDM for implied duration has become inapplicable.

Sbalfour (talk)

References

The only reference, which originally appeared as an external reference, is essentially a blog entry by John Hussman, economist and principal of the Hussman hedge funds. In financial terms, he's a buy-side analyst, and the blog entry is a tongue-in-cheek infomercial for the Hussman funds. That said, it contains some useful basic info, and two glaring errors, which were dutifully copied into the article (I've since deleted them), so we need to be careful about what's borrowed. The article has been substantially rewritten since then, so it's unclear how much can now be attributed to the blog post.

I suggest we find a scholarly article to use in place of that webpage. I found this: "Implied Equity Duration: A New Measure of Equity Risk" at [1]. At least it's scholarly, though dense technical diction and mathematics. Citing specific pieces of the wiki article is going to take some work (we're going to at least need page numbers from the paper). Sbalfour (talk) 20:03, 16 March 2022 (UTC)