Analyzing divestment

Suppose that I’m considering investing $1 in EvilCo (ticker EVL), but decide I don’t like the company’s activities so I refrain. Or maybe I decide to short EVL. Is this effective in reducing EvilCo’s activities?

In this post I’ll argue:

  1. Divestment can be reasonably effective, despite replaceability. My best guess: I can often sacrifice <$1 to reduce EvilCo’s output by >$5. This contrasts with the received wisdom amongst people I know, that divestment is only symbolic.
  2. The first dollar of divestment is extremely effective, probably more than an order of magnitude better, such that it’s likely that many people should divest a little bit.
  3. Optimized long/short divestment funds could make divestment much easier and more effective.

I’m not very confident in these conclusions—this is a complicated analysis with lots of room for conceptual or empirical errors—but it’s my best guess. I’d love to get feedback about how this picture is wrong.

Universities Superannuation Scheme Divest from Fossil Fuels

I also don’t engage very much with the existing literature. Consider this an independent attempt to figure out what’s going on with divestment.

I. The effects of divestment

Suppose that I’m $1 short EVL. What does that mean, and what happens?

In the purest case, EvilCo was going to sell a share of EVL to Alice for $1. Then I swoop in and sell a share of EVL to Alice for $1 instead (which I’ve borrowed from some other current shareholder Bob).

If EvilCo want to sell that share of EVL they’ll have to find a new buyer. In general the new buyer will be willing to pay less—Alice was the person willing to pay the most money for EVL, and so they need to go to the next person down the line.

(If you’re skeptical about equity, you can consider the roughly-equivalent case of debt—Alice was about to lend $1 to EvilCo, in return for a constant stream of interest payments. Instead I stepped in, and said “Alice, I’ll take your $1, and if EvilCo successfully pays off its other investors then I’ll pay you as much as they would have.” Then EvilCo will need to find another lender, who will demand a marginally higher rate of return.)

At the reduced price / raised interest, EvilCo is less excited about selling shares / borrowing money. So EvilCo will do less Evil™. At the same time, the new price makes other investors more willing to invest. The sum of these two effects—other investors investing more, and EvilCo doing less—will add up to exactly $1, offsetting the $1 that Alice would have invested but didn’t.

I’m going to do this analysis in the fictional efficient-market-land. I think this is more reasonable than it looks because criticisms of divestment usually come from an analysis based on market efficiency. In reality I suspect the story will be if anything a bit more favorable to divestment, but that’s also something to think about. One relevant fact about efficient market-land: if EvilCo’s activity had no risk, then the returns would converge to the risk-free rate, investors would make no premium, and divestment woud a zero effect and zero cost. In efficient market land, all of the action comes from uncertainty about EvilCo’s returns.

IA. Elasticity of Evil

A key question is how much less Evil™ EvilCo will in fact do. This is a complicated empirical question, but here’s a simple way to get an intuition:

  • Suppose the price of EVL (or cost of EvilCo bonds) goes down by 1%. That raises EVL’s capital costs by 1% per unit of Evil™. (They’ll substitute to less capital-intensive processes, but to first order that doesn’t change the calculation.)
  • Capital costs were just one component of EvilCo’s cost. I think a typical value is 20% of costs (say 10% profit and 10% interest payments).
  • If costs go up by 1%, then EvilCo will do less stuff. I think a plausible response is 1:1—after a 1% cost increase a company can spend the same amount of money to do 1% less stuff. Note that EvilCo is likely to pass these costs onto consumers (especially in a competitive market) and so changes in quantity largerly reflect decisions by consumers, not EvilCo itself.
  • If capital is 20% of costs and elasticity is 1:1, then a 1% decrease in the price of EVL leads to 1% * 20% * 1 = 0.2% reduction in EvilCo’s activity.

Throughout the rest of the post I’ll call this number K: a 1% decrease in the price of EVL leads to a K% reduction in EvilCo’s output. I think that 0.2 is a plausible value for K but you could certainly make a better estimate with some empirical research.

Note that this is an ongoing reduction in activity, as long as the change in capital costs persists.

IB. Elasticity of investor demand

As EVL becomes cheaper, other investors will buy more of it. This will soften the effect of divestment, but how much?

Utility-maximizing investors will generally hold just enough EVL that they are indifferent between holding more and holding less—the extra risk from holding more EVL exactly offsets the extra returns. (Otherwise they would increase or decrease their holdings until equality is attained.)

I’ll informally define the “excess returns” of EVL as the returns a risk-free asset would need to receive, in order to be as attractive as EVL on the margin for a portfolio that doesn’t yet contain any EVL. Write r̃ for these returns. Roughly speaking, this is the return to EVL, minus the risk-free rate, minus the cost of the correlation between EVL and the rest of the portfolio.

Put another way, r̃ measures how much a rational investor would be willing to pay to be able to include the first $1 of EVL in their portfolio. For example, if EVL has no risk, r̃ is the difference between its returns and the risk-free rate. If EVL’s return is a sum of a term that behaves just like the rest of the market and another uncorrelated term, then r̃ is the expected return of the uncorrelated part.

So what is the effect of lowering the price of EVL by 1%?

  • If we increase r̃ by 1%, then a utility-maximizing investor will increase their holding of EVL until the risk from marginal holdings also increases by 1%. That requires increasing holdings by exactly 1%. (They’ll also change their other holdings and how much they want to invest, but to first order that doesn’t change this calculation.)
    I think this is a key claim, and it’s kind of counter-intuitive, so I’ll go through an example in the appendix.
  • A 1% decrease in EVL leads to a 1% increase in the returns r (not a 1 percentage point increase), which corresponds to more than a 1% increase in excess returns, by a factor of r / .
    For example, if EVL cost $1 and returned $0.05 per year, it has a return of 5%/year. If the risk-free rate is 3%/year and EVL is uncorrelated with the market, then the excess return is 2%. If the price of EVL falls to $0.99, the earnings of $0.05 are now 5.05%/year, i.e. the return has gone up 1%. But the excess return is now 5.05%-3% = 2.05%/year, so the excess returns have gone up by 2.5%; the ratio 2.5%/1% is precisely r / r̃.

The factor r/r̃ measures what fraction of EVL’s returns are excess returns. You can probably estimate this quantity from public financial information. I’ll use 10 as a representative value, but I think it will vary a lot from industry to industry, whether EVL represents a single company or a whole sector, levels of idiosyncratic risk, etc.

Note that this is also an ongoing change in other investor’s positions, as long as the price change persists.

IC. The net effect

So suppose I divest, selling $1 of EVL. This will increase the return by some unknown proportion x. That will in turn decrease EvilCo’s outstanding equity+debt by Kx * (current level), and increase other investment by (r/)x * (current level).

Those two terms will add up to $1. Moreover, current levels of equity+debt = current levels of investment, so that the net effect is to decrease EvilCo’s outstanding equity+debt by K / (K + r/).

That tells us how much outstanding debt changes, but what about output? Write O for the ratio of output/(debt+equity). If we shrink debt+equity while holding fixed capital-intensity, then a $1 change in debt+equity leads to an $O change in output.

O is roughly the inverse of (Enterprise Value / Sales), a ratio sometimes analyzed in finance. A typical value of O in the US is about 0.3-2/year, with a median of 0.75 (Table 20.1, note that the average is very different from the median). I expect companies with higher values of O to (all else equal) have lower values of K.

On the margin, my divestment decreases EvilCo’s output by:

K / (K + r/) * O

So, if K = 0.2, r/ = 10, O = 0.75/year, then me divesting $1 will decrease EvilCo’s output by $1 * 0.2 / 10.2 * 0.75/year = $0.015/year.

II. The cost of divestment

This may not sound good, but note that the cost of divesting $1 is (much) less than $1/year. How costly is it?

If I divest completely, my last unit of divestment costs me r̃—by definition, r̃ is precisely the excess returns from including the first unit of EVL in a portfolio. So the actual cost of complete divestment is typically quite low. r itself is probably more like 5%/year, and if r/ = 10 then r̃ ~ 0.5%, and so me forgoing one dollar of investment returns actually decreases EvilCo’s activities by several dollars.

But before I’ve divested at all, when I’m holding an optimal portfolio, the first unit of divestment actually has a cost of zero: I’m holding enough EVL that the costs from holding more (in terms of increased risk) exactly offset the benefits (of better returns than the risk free rate), so I’m exactly indifferent between investing in EVL or investing in government debt (or anything else for that matter).

So the first unit of divestment is free, and the last unit costs r̃. In between the cost scales up linearly until I reach full divestment (and then goes on increasing linearly as I take out increasingly large short positions). The average cost for complete divestment is r̃/2.

If divesting costs me r̃, and decreases output OK/(K+r/), then the cost-effectiveness depends on which of K and r/r̃ is larger:

  • In the typical case where (r/) >> K, then the impact is OKr̃/r, and the cost is roughly r̃. So $1 of cost to me decreases EvilCo output by about OK/r.
    For example, if K = 0.2, O=0.75/year, and r = 5%/year (the S&P 500 P/E ratio is 20), then divesting $1 decreases EvilCo’s output by about $3.
  • K could be larger than (r/) if almost all of the returns are excess returns (e.g. if EvilCo is basically uncorrelated with the market) and K > 1 (e.g. if EvilCo behavior is very sensitive to costs).
    In this case, my bang for my buck is O/r̃. For example, if O=0.75 and =0.1, then $1 of cost to me decreases EvilCo output by about $7.50.
    (This could also happen if r is actually much smaller than , which can happen if EVL’s returns are significantly anticorrelated with the market. That’s a bad situation for a divestor.)
  • If K and r/are comparable, then these two estimates are equal, and my actual cost-effectiveness is about half of that.

These numbers are the cost-effectiveness of the final unit of divestment, where I completely remove EVL from my portfolio. The average effectiveness of totally divesting is twice this high. If I divest a fraction of my portfolio, then my marginal bang-for-my-buck is 1/x larger than this (and the average bang-for-my-buck is 2/x larger).

To know how much I should rationally divest, I need to know both this bang-for-my-buck and how much I care about reducing EvilCo’s spending.

For example, if my bang-for-my-buck is 3, and I’d be willing to pay $0.10 to reduce EvilCo spending by $1, then I should divest 30% of the way—since then the marginal bang for my buck is $3/30% = 10, and the average bang-for-my-buck is 20. If my bang-for-my-buck is 10 and I’m willing to pay $1 to reduce EvilCo spending by $1, then I should divest 1000% of the way, i.e. if I’d previously held 10 shares of EVL, I should now be short 90 shares.

III. Many divestors

The previous analysis considered a single divestor, whose effect is marginal. How does the picture change if many people divest?

My overall summary is that divestment probably becomes slightly less impactful when there are many divestors, but that divestors would need to be having a very large impact on stock prices (think cutting the price 2x) before this effect becomes significant.

The most obvious (but mild) effect is that as the number of divestors grows, the excess returns r̃ for the first unit of EVL increase—it becomes an increasingly cheap stock, and divestors are making a larger and larger sacrifice. This has a surprisingly mild effect on the impact of divestment:

  • As long as the elasticity of investment to interest rates K is smaller than 1, divestment increases both r̃ and r, and so (r/r̃) remains much larger than K and the term K/(K+r/r̃) will be approximately equal to Kr̃/r.
  • In this regime the divestors’ bang-for-their-buck is K/r. So the efficacy of investment decreases linearly as the interest rate for EvilCo increases.
  • If you had enough divestment to double the interest rate, it would only decrease the cost-effectiveness of divestment by a factor of 2. I think that’s a much higher level of divestment than is likely in any industry in the short term, so I think the presence of other divestors won’t decrease the impact of divesting by very much through this channel.

A less obvious effect is that as people divest from EVL, the optimal portfolio involves larger and larger investments in EVL. This offsetting effect is factored into the cost benefit analysis—that’s why we had to divide by (K+r/r̃).

This introduces a divergence between the market portfolio—what you get if you index—and the optimal portfolio—what you’d do to optimize profit. In other words, once some people are divesting, anyone using a broad market index to invest is effectively divesting by the “average” amount. (The index also reflects all of the overweight investments in targeted industries, but that doesn’t change this picture—that’s already taken into account with the analysis above.)

This has two effects:

  • Divestment is amplified by roughly 1/(1 – indexing fraction). E.g. if a third of investors index (my best guess), then divestment is 50% more effective. Indexes make the average level of divestment a strong default; and more broadly people who want to avoid divesting need to actively decide to overweight EVL. I think for some investors there is a relevant act-omission distinction that makes them feel bad about this even if they wouldn’t have divested themselves (I’m a consequentialist, but don’t consider this unreasonable—I think it’s relevantly uncooperative to reap profit by deliberately offsetting soeone else’s divestment). Overall I expect the impact of divestment to be amplified by 1.5-2x based on this kind of factor.
  • As someone who is considering divestment, I need to be aware that I may already be doing the “average” level of divestment simply by not overweighting EVL. So if there are many EvilCo divestors, then I’m no longer in the regime where the first unit of divestment is “free.” (But the first unit of dievestment still has higher bang-for-my-buck, with the multiple equal to the “average” divestment fraction. E.g. if 10% of people totally divest from EVL and everyone else is profit-maximizing, then my first unit of divestment is still going to have 10x the bang-for-my-buck.)

A still more subtle effect is that the quantities K and O will change as divestment continues. In general, divestment will increase debt service as a fraction of total costs, increasing K. At the same time, EvilCo will substitute to less capital-intensive processes, decreasing K and increasing O. I think the net effect of these changes will be small, unless divestment is very significant.

IV. Facilitating divestment

Divestment is hard for at least two reasons:

  • It’s hard to implement. Many people either invest in a broad index, or invest in managed funds, and avoiding an industry involves using a totally different fund; given that different people want to divest from different things, and have different investment goals, this is a huge pain. In practice people who care “a little bit” don’t usually divest. It would be easiest to implement this via shorting the industries an investor wants to divest from, but many people can’t or aren’t comfortable shorting stocks.
  • Deciding how to divest is quite challenging. The superficial problem is identifying and weighting companies based on their impacts, to build a diversified portfolio to short, which is already challenging. But there is a much harder problem, because EVL can be correlated with the rest of the market. If I neglect these correlations, profit-oriented investors will substitute from EVL to correlated assets, and most of my divestment-impact will be on the broader industry rather than EvilCo.  I can have the same impact on EvilCo, with much less risk to myself, if I hedge out all of the parts of the risk that are not distinctive to EvilCo.

By running a long/short fund (or issuing an ETF) that optimizes divestment impact, I can address both of these issues:

  • The fund can be short the target industries, so that an investor can easily add it to a normal portfolio (and doesn’t need to have a margin account to short anything). If it’s an ETF this is as easy as buying a publicly-listed asset. The fund can be constructed to have roughly zero expected return, and to maximize divestment impact per unit risk. The fund can be leveraged so that a small investment can offset a much larger long position.
  • We can have a range of funds for different values—a divestment fund for carbon emissions, a fund for animal welfare, and so on. Investors can make their divestment decisions separately from their other decisions.
  • The fund can do analysis to decide how to maximize divestment impact per unit risk. You can imagine a spectrum of possibilities, from simple heuristics to “GiveWell for divestment.” I’m not sure what the optimal policy looks like—I don’t know whether you get the best bang for your buck by divesting broadly, or with pairs of closely matched stocks that differ as narrowly as possible in their carbon emissions (or animal welfare standards, or whatever).

These funds would only be appealing to an unusual audience—one interested in divestment for consequentialists reasons, not-too-focused on the act-omission distinction or concerned with the superficial symbolism, interested in quantitative analysis, and open to slightly unusual financial engineering.

I think right now that audience is pretty small, and that more quantitatively-minded investors typically aren’t very interested in divestment. If consensus amongst quantitative folks shifted in the direction that divestment could be reasonably cost-effective, I could imagine enough interest to justify a fund.

An easier way to facilitate divestment might be a careful analysis of what an investor should add to a market portfolio, if they want to have the maximum divestment effect per unit risk. Then investors with margin accounts could easily add that to their portfolio, or ask their advisors to do so.

Making divestment easy seems particularly attractive because the costs of divestment grow quadratically and “divesting a little” is so cost-effective. It makes sense for large donors to handle most of the hard choices in philanthropy, but in the case of divestment the work does need to be distributed broadly across investors.

V. Intuition behind shorting

Shorting stocks feels very weird to most people, and lacks the intuitive appeal of “not investing.” From a consequentialist perspective though they have basically the same effects. I think it’s worth having a clearer intuitive picture of shorting, to understand why it’s a reasonable way to minimize the harm from the industry rather than a piece of speculative financial engineering.

When an investor buys a share of EVL, they are trading $1 for a small percentage of the revenue from all of EvilCo’s future Evil™ exploits.

When I short EVL, I’m approaching one of those investors and offering the following deal:

I know you wanted to invest in EvilCo, to get a share of their evil revenues. But how about you give that money to me instead. Then in the future we’ll see how much money EvilCo actually paid out to its investors, and I’ll give you that much. From your perspective this is all the same. From my perspective, I’m taking a small financial hit. But I think it’s worth it, because I think the cost to the world from EvilCo’s activities is larger than the financial return they are generating.

This isn’t an antagonistic relationship with anyone except EvilCo, who should be upset because I am now their competitor—they are offering people a financial return that is correlated with the success of their Evil endeavors, and now I am also in the business of offering the same financial return.

From the perspective of someone who doesn’t like Evil, I think it’s a natural thing to be doing. People want the returns that come from Evil activities. Short of taxing or prohibiting Evil, one of the most natural ways to get less Evil is to fill that demand so that people don’t actually have to do the Evil stuff to realize those returns.

Appendix: investor response to change in returns

For simplicity, suppose that EVL is perfectly uncorrelated with the market, and the risk-free rate is zero. Then the excess return of EVL is exactly its expected return.

A utility-maximizing investor wants to maximize something like E[R + H * R²], where R is their financial return and H is a constant representing risk aversion. (For larger changes R we may need to consider higher-order terms in the approximation to their utility function, but if asset prices change continuously then over sufficiently short time periods we can neglect them.)

If they hold X shares of EVL, their utility is then their return is X*A – X²*H*B, where A is the expected return of EVL and B is its variance. Then the optimal investment X is A/HB.

Critically, this scales linearly with the excess returns A. So if we double the excess returns, we expect to double how much investors invest.


7 thoughts on “Analyzing divestment

  1. It seems that the crux of the claim is that divestments permanently change a company’s capital costs. (“Note that this is an ongoing reduction in activity, as long as the change in capital costs persists.”) I think it’s quite intuitive that if divestments permanently lowered a company’s stock price it would hamper the company’s activities. But is this actually the case?

    In the efficient market hypothesis framework prices reflect all available information, so uninformed trading has no impact on price. We would expect other investors to take into account the divestment decision and fully negate it.

    However, in the real world traders are limited in their ability to take on risk. In the Almgren-Chriss framework trades have linear permanent market impact, permanently lowering the stock price linearly to the trade size.

    So in the real world divestments can work by denying a company access to a potential pool of capital. The remaining pool of capital (non-divesters) will have limited ability to absorb risk and “take up the slack”.

  2. Either you’ve disproved the strong efficient market hypothesis or something is wrong here. The strong EMH says that a stock’s value is determined by its long term expected profitability (and implicitly that determines it’s interest rate on debt as well). Now either you’ve given an elementary proof that this isn’t true or something is wrong in your analysis. I’m pretty sure it’s the latter and I have some ideas about where.

    1) Your writing is kinda hard to follow but it looks like you compute how much divesting $1 from EvlCo’s raises it’s cost of capital and thus reduces it’s efficiency and only THEN ask how much other investors buy. That’s not how this works. EvlCo’s cost of capital is set by it’s expectation of what it’s cost of capital will be at equilibrium not in the instant you sell before the next guy snaps it up.

    In other words if I owned a billion dollars of IBM and sold it all the new investors wouldn’t evaluate their investment as if IBM’s cost of capital had permanently decreased and thus assume IBM is going to produce less products this year. They will figure out what IBM’s cost to capital will be once things return to equilibrium and use that to guide their investment.

    2) For profitable large healthy companies changing the price of their shares doesn’t affect their cost of capital at all since that only makes a difference when they sell shares and unless they run out of money or need some giant one time expansion they don’t do that . You could frame an analysis about blocking new projects but that would be a different computation.

    3) I don’t think you properly account for the effect of investing your money elsewhere in the market. If your analysis was correct then there would be more money in the market excluding EvlCo. Yet that money needs to go somewhere so the net effect will be to lower interest rates until things balance out. Now EvlCo can replace it’s decrease in stock price by borrowing more at lower rates (or the same thing happens to reduce returns elsewhere pushing investors back to EvlCo).

    I think I’ll leave it there until I hear your response in case I’m totally misunderstanding you. I also think there is something funny about your use or r tilde over r but let’s see what you have to say.

    More practically I doubt that most publicly traded companies are actually capital limited in their main business. They are opportunity limited. Intel is going to build the same number of fabs regardless of small fluctuations in interest rates. A mine owner is going to run one mine not 1.1 or .9. Rather than change the amount of EvlCo activity they do you probably just change how many other companies they invest in or similar places to stash their profits. This is true even if they are perfectly rational and if we imagine an actual company I bet it gets worse.

    1. When I say “efficient-market-land” I mean “all the investors behave rationally, incorporating all information.”

      Other investors face higher expected value after I invest, but as they increase their holdings they increase their risk. They can’t drive prices (and hence returns) back down to the old level, since they’d have higher risk and that would no longer be an attractive investment. This effect is generally very small, but of the same order as my personal cost from divestment.

      I think this post ended up being very unclear. I’m planning to write a clearer example at some point. Hopefully that will be easier to engage with to see where you disagree.

      1. I found the apparent contradiction with the EMH initially puzzling as well; I believe the key assumption behind the post is that only a finite number of arbitrageurs exist. Based on the paper “The Noise Approach to Finance”, the EMH does not hold under this assumption given the presence of traders who do not rationally act to maximize profits (noise traders in the paper or divestors in this post).

  3. Shit, yah here’s the problem in a short version. You just assume outright at the start that divesting from EvlCo increases their cost of capital without even waiting to see if you selling your $1 actually drops the value of the stock at all.

    What actually happens is that your $1 divestment is placed elsewhere. That $1 either reduces the rate of return on the company you invested into (or it get’s pushed forward and lowers interest rates …same thing) and that incentivizes other investors more to invest into EvlCo. If you balanced all your equations you’d find out that EvlCo’s stock price remains the same in equilibrium (assuming market very large). As such not decrease in output.

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