The Nature of Market Growth, Risk, and Return

In the model of asset appreciation advanced here, the market economy and the market of asset claims on the economy are modeled as organic (or exponential growth) processes, similar to those commonly seen in nature and the biological sciences. In “Dempsey's organic growth model of appreciation” (DOGMA), investors have a log-wealth utility function. Within the framework, the market risk premium is derived as the premium that balances supply and demand among risky and risk-free assets. The model indicates that the premium is less than is indicated by ex post returns observed on U.S. stock markets. The model is consistent, however, with empirical observations that idiosyncratic risk and small company size are rewarded by the markets. In terms of the model, investors choose to allocate their portfolios long in both the risky market and the risk-free asset. Furthermore, their portfolios are independent of the investment time horizon. I consider the nature of the market, risk, and the manner in which returns are generated consistent with risk. For the practitioner, the article offers a number of valuable insights. In particular, I draw attention to the nature of financial investing in which investment offers, on the upside, unbounded returns with, on the downside, the possibility of losing substantially. A novel offering of the article is the consideration that the potential reward may be inherent in the risk. So, for example, if half of one's investment doubles in value ($1 becomes $2) while the other half loses half its value ($1 becomes 50 cents), the investment grows by (2.5 − 2)/2 × 100 percent = 25 percent. Such reward might by itself be sufficient to compensate the investor for bearing the implied risk.In developing the model, I model the market economy—and the market of asset claims on the economy—as an organic or exponential growth process, in which investors have a log-wealth utility function. Such a growth process is representative of growth processes in nature and is consistent with observations of stock market growth performance. A log-wealth utility function implies that investors tend to balance the possibility of, say, doubling their initial investment wealth with an equal possibility of halving their investment wealth, for which psychological propensity empirical support exists.The implications of the organic model with continuous growth differ from those of the discrete one-period model. In particular, whereas the traditional one-period model assumes that periodic growth rates of +x percent and −x percent on uncorrelated investments are equally likely and hence effectively cancel each other, the organic growth model implies that it is exponential growth rates +x percent and −x percent that are equally likely. Because the exponent of +x is unbounded but the exponent of −x is limited to zero, such exponential growth rates, in combination, generate a growth factor that is always greater than unity. This outcome is consistent with the realization that the investment outcome on the upside is unbounded but cannot be less than zero on the downside. Thus, the organic model of capital appreciation predicts that given two well-diversified portfolios with similar betas, the one whose assets have the higher idiosyncratic volatility will have the higher return. The prediction is borne out by empirical findings for the returns of U.S. stocks for the 1963–90 period. Empirical evidence also indicates that the volatility of stocks is correlated closely with the inverse of company size. My model findings thus support a satisfying theoretical explanation for the research findings that returns on stocks are correlated with the inverse of company size.Within the model's framework, the market risk premium is that which balances supply and demand among risky and risk-free assets. It turns out that the clearing price for the risk premium as it equates supply and demand depends on stock market volatility. Thus, the model predicts that an annualized stock market volatility of 15 percent, as was measured for the 1980–94 period, is consistent with a risk premium of as little as 2 percent whereas a volatility of 30 percent (it was closer to 33.6 percent in the 1926–39 Depression period) is consistent with a risk premium closer to 7 percent. When the individual or idiosyncratic volatility of individual stock returns is allowed for, an additional annualized return of as much as 4 percent may be generated in terms of the model.The model predicts further that the portfolio choices of investors will likely remain long in both the risky market and the risk-free asset and that such portfolio choices will remain effectively indifferent to the investor's time horizon.