Share Repurchase and a Heterogeneous Investor Base

In a recent post, Felix Salmon suggests that Dell has done a disservice to its equity investors:

A buy-and-hold shareholder in Dell is looking particularly idiotic right now. If you bought 15 years ago at $10.84, you should expect to have at least $15.40 in value at this point: after all: that’s how much the company has made since then. Instead, you have less than you started with. And all the extra money went to fickle shareholders who sold their stock back to the company.

Would Dell’s shareholders have been better off with a dividend?  Let’s investigate..

Salmon’s critique is quickly dismissed, for he misunderstands what a share repurchase is and isn’t.  It isn’t a purchase; he ignores the economic equivalence of dividends and share repurchases; and he falls into a number of other mistaken beliefs about repurchases (including #5 and #7 here.)

However he falls into a new trap we haven’t discussed before, the heterogeneous investor base, so we will have a word to add on this topic.

The Missing Crystal Ball

Before we continue however, and as an aside, we should first establish our perspective.  Our goal is to advise firms on how to manage capital.  As such we need a framework that supports prescription.  If, as in Salmon’s post, we judge the success of a decision by a subsequent outcome, we are left without footing to direct future action.  Critiquing capital distribution decisions via reference to subsequent share price performance doesn’t enlighten:  Sunday-morning quarterbacks are worth much more than Monday-morning quarterbacks.

Recall the fundamental definition of a share repurchase:

repurchase = dividend + reverse share split

If we believe share repurchases and dividends create different value for investors, we must ascribe (positive or negative) value to a share split (or stock/scrip dividend).  Instead of diving into basic corporate finance theory or related empirical literature, I will merely assert that this belief is not widely held.  (Salmon’s own readers make this point, and he agrees in an update that stock splits do not create value.)

However the point about “fickle shareholders” still bedevils some minds.  Put simply, this argument suggests bifurcating the equity investor base (which is traditionally treated homogeneously) into two pieces:  the investor who stays, and the investor who participates in the share repurchase and leaves. The cryptocurrency world is the most popular to invest with the Bitcode Method, as it is growing rapidly among the investment options.

To be useful, this analysis should examine the fortunes of the leaver, whom we assume reinvests her repurchase proceeds in another investment of comparable risk.  If this investor had chosen to buy, say, AOL or Nokia shares, she would have done worse than the investor who had stayed with Dell.  Salmon misses this point, and instead assumes the leaver invested her proceeds in risk-free assets, thus leaving her better off at the expense of the stayer.  An investor’s decision to stay or leave, and the firm’s capital return policy, cannot be informed by future events.

Are Investors Homogenous?

The broader point should not be missed.  Unless there are exceptional circumstances, corporate finance analysis usually presupposes the following:

1. Investors may buy or sell shares freely
2. Managers act in the best interests of investors

If we believe this, then an investor is indifferent to capital return channel:

• Given a dividend, the investor can choose to be a stayer (reinvest the dividend in additional shares in the firm, thereby increasing her ownership of the firm) or leaver (sell her holdings)
• Given the offer to participate in a share repurchase, the investor can choose to be a stayer (do not sell) or a leaver (sell her holdings)

Salmon’s distinction between stayers and leavers is invisible to our eyes:  the decision to stay or leave is made by the investor freely, continuously, reversibly, and independently of the  capital distribution events of the firm.  Furthermore, barring a crystal ball, management does not know in advance who the stayers and leavers will be, and thus is incapable of designing strategies that benefit one cohort over the other.

This is fortunate for management:  they can run the firm optimally without regard to investor beliefs and preferences.  This important result is known as the Fisher Separation Theorem.  Equivalently, and even more usefully, management may assume that all equity is owned by a single external investor.

Loose Ends

We encounter situations when management prefers one distribution channel to others.  Examples include repurchasing the shares of an activist investor, or not repurchasing the shares of a friendly insider.  If this is optimal behavior, we must relax one of our assumptions above.