In part one of this series, we examined whether investing is a game. If you have not read that essay (https://cognitiveinvesting.com/2011/11/17/is-investing-a-game/#more-216), I suggest you read that first. Once we established that investing is a game, it is instructive to determine whether the game has more winners or more losers. Said another way, is investing a negative, zero, or positive-sum game?

A Friday night poker game with your pals is a zero-sum game. A bet on the outcome of next week’s football game with your best friend is also a zero-sum game. The total of all the winnings equals that of the losings.

A negative-sum game is a poker game in Las Vegas, when the casino takes a small portion of each pot or charges an entry fee to play the game. There might be some winners, but the sum total of money won is less than the money lost, after the casino’s take is figured in. (I am assuming the casino is external to the game, and not considered a participant.)

To visualize a positive-sum game, imagine an inverse situation to the Las Vegas poker game. In this fantasy world, the casino contributes a small amount to each pot, so that the total of all the winning amounts is greater than that of the losing amounts.

When I analyze the investing game, I conclude that it is both a positive- and negative-sum game, depending on how one invests.

Let’s examine the bond market first. In a very simple case, I buy a 10-year Treasury bond and hold it to maturity. I collect the interest and receive my original investment after the ten years. This is a positive-sum game, since I “win” all the interest payments and there are no losers. Now let’s say that the price of the bond went down after five years and I sell the bond at a loss. I received some interest payments, but I got less than my original investment back. However, the person who bought the bond from me holds the bond for the next five years to maturity and collects the original amount of the bond plus interest payments. He also gets some “extra” money since he bought the bond at a discount. His gain on the principal amount of the bond equals my loss.

So a bond investment can be broken down into several components: an interest rate stream, which is a positive-sum game; and a zero-sum game of trading bonds before they mature. But hold on a minute. There are trading costs whenever bonds are bought and sold in the aftermarket, so as in the Las Vegas poker case, that aspect of the game is a negative-sum game.

What happens when you mix a positive-sum game and a negative-sum game together? You could end up with any of three results, depending on how positive and how negative those particular parts are. Owners of bond funds are in this very situation. They receive interest payments, which is a positive-sum game. But bond funds buy and sell bonds, sometimes quite frequently. And this part of the game is a negative-sum game due to trading costs. Some bond funds turn over their portfolio quite frequently, sometimes more than 100% per year. For example, the Vanguard total bond market exchange-traded fund (BND) has an annual turnover of 75%, which is actually low for its category. A 100% turnover rate would mean that each bond is held for an average period of one year. Higher turnover rates imply even shorter holding periods. Short-term bond funds can have very high turnover ratios, since the bonds they hold are constantly maturing and need to be replaced.

Since this trading back and forth adds no aggregate value, but incurs costs, a cognitive investor should try to minimize this expense as much as reasonably possible. The easiest way to do this is to buy an individual bond and hold it to maturity. This way, you are playing the positive-sum game by collecting interest and entirely sidestepping the negative-sum game of bond trading.

Buying individual bonds might not make sense for all investors, and a discussion of all the other issues that should be considered before embarking on this path, such as size of portfolio, investors’ expertise, diversification, limiting credit risk, etc., requires a separate essay. However, if the goal is to maximize exposure to the positive-sum aspects of the game and reduce the exposure to the negative-sum aspects of the game, buying individual bonds and holding them to maturity is ideal.

If buying individual bonds does not make sense for you, then you should at least try to minimize the negative-sum aspects of the game by buying a bond fund with below-average turnover. Index funds are generally better at this than funds run by managers who need to justify their compensation by “adding value.” You might get lucky and own a bond fund from one of the winning fund managers, but the odds are not in your favor. More likely than not, you will end up on the losing side. Over long periods of time, in aggregate, fund managers underperform compared to passively-managed bond index funds.

Let’s now turn to the stock market. Is this a positive, zero, or negative-sum game? The answer to this question is dependent on the measurement period. If one measures over very short time periods like a day or a week, the chance of an advance vs. a decline is about equal. Thus, short term trading of stocks is a zero-sum game before transaction costs. Over longer periods of time, though, stocks (in the aggregate) have demonstrated a tendency to appreciate. Many also pay dividends, which can add to the investor’s return. The value of an equity investment increases as a result of the efforts and ingenuity of the company’s employees. As companies grow and prosper, some of that profitability usually returns to the shareholders (no guarantees, though).

Thus the game steadily becomes more of a positive-sum game as the holding period lengthens. There are still transaction costs, but since that cost is a constant amount no matter what the length of the holding period is, as time goes on, these costs are likely to be insignificant compared to the stock price appreciation.

Unlike in the case with a bond, a “final” value or date of a stock investment is never known. There is no promise that any single stock investment will maintain or return to any particular value in the future. If you hold a single stock for many years, it may provide a positive return, but the variability of returns of individual stocks is such that there is a sizable chance that you will lose money. This greater level of uncertainty and much higher variability of returns (vs. the bond situation) necessitates spreading this risk by owning many different stocks. Arguably, diversification in the stock arena provides more benefits than in the bond arena. By owning a large group of stocks, one can dramatically reduce the risk associated with owning a single stock that underperforms its peers.

So, similar to the bond case, the long-term holder of stocks should expect a positive return as long as he is diversified and waits for a sufficiently long enough period of time for the positive-sum game to materialize. Let’s now consider the shorter-term trading of stocks, which is what many investors follow on a day-to-day (or even shorter time frame) basis. This is similar to the bond market case. The owners of the stocks change hands, but no value is added from all of the trading activity. One person’s gain is another’s loss. When you aggregate all the gains and losses, it is essentially a zero-sum game, before transaction costs. Fortunately for stock market investors, transaction costs are less than they are for bonds, because the market is far more transparent, standardized, and competitive. But there are still some costs, so that short term trading is a negative-sum game.

Many people who play this game think they will be on the winning side (overconfidence reigns supreme), even though less than half of the money will end up on that side, due to the fact that it is a negative-sum game. But separating the shorter-term negative-sum games aspects from the longer-term positive-sum aspects is difficult, if not impossible. The fact that some players in the game are short-term-oriented and others are long-term-oriented at the same time muddies the waters as to determining exactly when the long-term positive effects of stock ownership outweigh the short-term costs of trading

So if one wants to avoid participating in negative-sum games and only participate in positive-sum games, the goal should be to buy and hold stock investments, and eschew short-term trading. Stock funds can provide good diversification, but they should keep trading to a minimum. Index funds fit this bill nicely.

Alternative asset classes such as commodities, futures, options, and currencies are all zero-sum games before transaction costs. When these costs are added, these games are negative-sum games. Willingly entering into a game with a negative expected return is another word for gambling, and thus these “investments” should be avoided by a cognitive investor.

An underlying assumption in this analysis is that participating in a positive-sum game is good, a zero-sum game is not nearly as good, and a negative-sum game should be avoided. But if you are one of the best players in the game, maybe this assumption should be revisited. The better players will still prosper in a negative-sum game as long as there are enough inferior players to take advantage of. So the next question is, “How much of this game is luck vs. skill?” That is the topic of the next essay. Stay tuned.