Go with the flows, part two
Rigid mandates and buybacks revisited
Robert Armstrong
Welcome back.
There were loads of responses to the ESG piece on Tuesday, mostly positive, but I will pull the criticisms together and respond to them in Thursday’s letter.
In the meantime, back to the slippery notion of supply and demand, and how it applies to stocks.
More on flows, stock prices, and buybacks (now with maths and charts)
I keep thinking about the academic paper I wrote about on Monday, by Xavier Gabaix and Ralph Koijen, describing how new money flowing into the stock market affects prices.
Before I read it, I usually defaulted to the most common way of thinking about stock prices: that they are determined by rational expectations about future cash flows, or they are wrong, reflecting how dumb people are.
Now I’m trying to think about stock prices as reflecting supply and demand, which feels simple and liberating.
To recap.
G&K reconcile two contradictory propositions, both of which most people who think about markets believe:
One: Flows of money into stocks affects the price.
It matters for prices when a lot of people take cash from outside the market and invest it.
Two: Every time someone buys a stock, someone else sells it.
There are no flows “into” stocks.
Someone always has the stocks, someone always has the money.
As I said on Monday, G&K solve this riddle by defining an inflow as an investment into an investment fund that must be put to work in the stock market, and which was not funded by a stock sale.
And their key insight is about that “must”.
The great majority of stock market investment takes place though funds that have rigid mandates governing their mix of stocks and other assets.
The result is that when they put money to work in stocks, the funds are price insensitive.
Oddly, this means that $1 of flows can drive up the capitalisation of the stock market by a lot more than $1.
Why?
Here is a very, very simplified model for how this works (thanks to Ralph Koijen for walking me through this):
1. Suppose that there are only two funds that own stocks, and they own all the stocks there are (don’t you love economics?).
2. One is Pure Stock Fund, with a mandate that requires it to own only stocks; the other is Mixed Fund, which must have 50 per cent of its value stocks and 50 per cent in bonds.
3. There are 150 shares in the stock market, and they cost $1 apiece at the outset, making the capitalisation of the market $150.
PSF owns 100 shares, and MF owns 50, plus 50 bonds, also at $1 apiece.
There is also Pure Bond Fund; the size of its holdings is not relevant.
4. Someone out in the world invests $1 in PSF.
That dollar did not itself come from a stock sale.
5. PSF must put that money to work in the stock market.
The only place to buy stocks from is MF, so they buy 1 share from MF.
6. MF, new cash in hand, buys a bond from PBF.
7. PSF now owns 101 shares of stock.
MF owns 49 shares of stock and 51 bonds.
8. (Here is the part you have to pay attention to) What is the constraint on the situation that determines the price at which MF will have sold that share?
There is just one constraint available: MF’s 50/50 value mandate.
In order for MF to sell and for the market to clear, the price must be one that makes the value of MF’s shares and its bonds the same.
The bonds are still worth $51.
So MF’s 49 shares must be worth $51, or $1.04 apiece.
9. There are still 150 shares outstanding.
The market is now worth $156, $6 more than it was, because of that $1 flow.
Weird!
There are not only two funds in the world, and not all investors have rigid mandates.
This is just a toy model.
But G&K’s point is the world is a heck of a lot more like this model than people think.
In particular, they show empirically that most investment is through rigid funds, and potential arbitrageurs are too thin on the ground to provide much liquidity or elasticity, and usher prices back towards their fundamental value.
So the mandates of blended funds turn out to be important to determining the multiplier of a given flow by which the market rises in value.
Maybe it’s 3, maybe it’s 8, but it ain’t 0, which is what the classic model says.
On the classic model, prices are based on expectations of future cash flows, which are unaffected by flows.
The G&K theory is a reasonably good match with historical data about flows and returns. Here are normalised log returns on the US stock market charted against flows (in G&K’s meaning of that term):
On Monday I said that the G&K model should make us reassess the importance of stock buybacks to the market.
I included a chart showing that buybacks are a far bigger source of flows than mutual funds, ETFs and the like — with tech company buybacks leading the way.
Several readers pointed out, rightly, that this was a rather dumb thing to say.
What matters is net buybacks, that is, buybacks less share issuance.
And tech companies in particular issue a lot of shares!
If there is clean data on net buybacks in the US market, I have not yet been able to find it (if you have it, send it!).
So let’s start with some imperfect data.
Here is the total share count of the S&P, as provided by Howard Silverblatt at S&P Dow Jones Indices:
The S&P’s share count hasn’t fallen much since about 2005, despite zillions in buybacks over that time.
It’s only about 5 per cent lower than it was then.
Now, this chart has been adjusted for Apple’s big 4-1 split last year, which would have made it look like the number of shares had gone up a lot.
But it’s not adjusted for other splits, or for changes in the index’s constituents over time.
Dozens of S&P companies did splits every year before the great financial crisis, accounting for much of the steep part of the blue line.
In the past 10 years, though, its been about eight companies a year.
I don’t know the size of those companies, but it’s reasonable to guesstimate that adjusting for splits, net buybacks are bringing the index’s share count down by a per cent or two a year.
Under the G&K theory, that volume of inflows — if they are not matched by outflows from elsewhere — could account for very significant market appreciation.
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