Goosing Equity Returns via Dividend Re-investment?

The Old Barkeep is not impressed with various book peddlers and optimists advertising the possibility of high "total" returns in excess of GDP growth.

Here is the algorithm:

1. Start with a notional account. E.g. $1 in the DJIA index, invested in 1900
2. Over each time period, if the index changes by X%, assume that your equity does, too.
3. Over each time period, if a dividend payout of D% is given, add back that amount to the equity value, via a "dividend re-investment model".
4. Watch your holdings increase at a compound annual growth rate in excess of the growth rate of the index.
5. Peddle books, or drive a pension fund into the ground.

Do you see the flaw?

First, some background.

The market cap of a firm reflects investors' beliefs about the present value of all future earnings of that firm. Some of those earnings are retained -- re-invested by the management --  and the remainder are classified as "surplus profits" and are distributed as dividends.

The decision to make a distribution amounts to a belief by the firm that it cannot re-invest those profits while maintaining the expected growth rate -- so it distributes those dividends to investors.

On the ex-dividend date, the equity value falls by the distribution amount -- since the "value" of the company is now less (it has one less future earning!), and on the distribution date, the owners receive a cash payment.

The total value of the owners' stake has not changed, they just have some of that value in the form of cash that they control as opposed to having that cash locked up in their equity accounts. For this reason, you do need to include cash-holdings in any calculation of total return. A total return calculation should  include all holdings.

In the real world, some of those dividends are re-invested in equities, and to the degree that they are, this drives up the equity value of target investments as investors compete to bid up the share price of the target firms. So the net effect is to lower the cost of capital for some firms while raising it for others as investors continually engage in a process of valuation.

This process supposedly results in no company being without sufficient capital to give investors the return they demand. So for the market as a whole, the dividends flowing out of the entire market are surplus profits for all the firms in the market. In other words, over time, investors believe that no company can increase its capital base while maintaining the expected yield;  otherwise they would bid up the share price and drive down yield.

Therefore when looking at a historical time series of prices, whatever equity re-investments actually occurred, they are already recorded in the time series.  It is double-counting to include the observed market cap increases of those firms that are the targets of investment, and to not count the market cap declines of firms that made distributions. Moreover, any dividends thrown out by the entire index should be assumed to be surplus capital for the index as a whole. This means, if those dividends were re-invested, they would come at the expense of a fall in yield.

Equity prices are everywhere and always subject to a process of valuation, and this means that you should not always re-invest. You cannot always throw surplus capital back into the hands of management and maintain the same rate of return. You cannot always bid the price of equity up and expect profits to rise. At some point, additional investment results in stock price bubbles followed by crashes, because the earnings growth rate is constrained by GDP growth rates, and you cannot goose GDP sustainably by bidding up the price of equity.

At some point, you are better off buying a bond or even holding the dividend in a cash-equivalent, rather than overpaying for low yield.

Now, the specific flaw in the algorithm: the mistake is in Step 3.

The book-peddler is inserting a fake transaction into the historical time series, by assuming that you will be able to increase your holdings of the company without bidding up the price. All these backwards looking "what-if" scenarios suffer from the same flaw, which is that they are minority strategies. If enough people followed these strategies, the price would shoot up, the dividend yield would collapse, and the strategy would underperform the historical time series. Any time you see someone peddling a "total return" strategy that is greater than long-run GDP growth (which was 6%, in nominal terms, over the last 100 years), then you are being sold snake oil.

How much does the fake transaction that allows for purchases of shares without bidding up the share price distort the historical time series? One way to measure this is that if the "average" investor's equity holding could grow, by any series of transactions at the rate of the dividend payout + the observed rate of equity growth, then the total equity value of the whole market would also grow faster than the observed rate (by the same amount). Moreover, the synthetic model assumes that the dividend yield on this larger equity value would be the historical yield. This means that there would be a divergence between the observed profits and the profits as predicted in the model:

Given that aggregate earnings grow at the rate of GDP growth, a strategy that claims to outperform GDP growth by 3%, will after 100 years predict

• dividend payments 19 times the observed payments
• market caps 19 times greater than the observed market caps 
• "total returns" 19 times greater than the total returns of the average investor.

Long run indeed!

But, what about our investor, who suffered an equity loss of $1 and has $1 in his cash account? Can't we add $1 to his total returns? Absolutely! If by "total returns" you mean a real-time mark-to-market of all the holdings of a particular investor, then this is valid (and necessary) to gauge performance. And you should add total dividends paid to the cash account of any historical time-series. The only flaw is when you insert fake transactions into the historical time series, by assuming re-investment without assuming that this will change the historical prices  --  i.e. assume it is possible to buy or sell shares without altering the historical prices. That is fundamentally a minority strategy, and will not succeed if engaged by the public at large, or even by a sizeable minority of the public. Certainly it will fail if large players such as pension funds use the strategy.

So, then, what are the expected "total returns" of the market?

• A first order long run estimate is the long run GDP growth estimate. This has been the observed returns over 50 year time periods, at least for equities.

• John Hussman authored an analysis that takes the "gap" between current stock values and the long run GDP growth rate, taken to be 6%, with the assumption that mean-reversion will occur in the longer run. There is evidence for this over 10 year time periods

Note that, in general, there is nothing wrong with specifying an asset allocation strategy in an attempt to outperform. Most try to outperform! Just be aware that any strategy promising returns in excess of GDP growth will be a minority strategy, that if followed by enough people, will fail to outperform.