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The Market The Importance The aggregate of the global markets is called the Market. The Market’s dynamics and risk/reward profile are determined by the actions and inactions of shareholders and potential shareholders around the globe. The Market represents the aggregate portfolio of every potential shareholder in the world. The fiduciary duty of publicly-traded corporations is to maximize True Shareholder Value, which is the value the Market would place on the corporation if the Market had the same information as the corporation’s insiders (see True Shareholder Value). An accurate model will contain many possible states of the future world. The discount rates from one state to the next can only be accurately calculated by using relationships between the model’s uncertainties and the Market. As our intuition would suggest, the better the Market tends to do in changing states, the higher the discount rate. The exact discount rate will reflect the world’s attitude toward risk and reward. Accordingly, when there is no active relationship with the Market, a state change is discounted at the risk-free rate. One of the major benefits to modeling with the goal of maximizing True Shareholder Value is that all arbitrage opportunities are automatically removed. With almost any other goal, we’d either have to ignore or explicitly model market trading opportunities. For example, if we used a constant discount rate, we could always borrow money and invest in a risky market opportunity that would give us an expected return that exceeds the constant discount rate. Explicitly modeling every trading opportunity would be extremely burdensome and make even the simplest models suddenly complex and impractical. Maximization of True Shareholder Value avoids this issue and allows us to focus on modeling the essential business problem. The Definitions We want to find a precise definition for the Market that is as close as possible to the global markets. In practice, we should look for a definition that is easy to relate to because it is simple and well-known, that covers or is highly correlated with all major industries, and that has a long historical data record. Most often, an historical data summary will represent our best expectations about the Market going forward. The S&P500 Composite Index is perhaps the only choice that meets these requirements. For example, Ibbotson’s “Stocks, Bonds, Bills, and Inflation 2006 Yearbook” was the premier data source for US Capital market returns in 2007. This yearbook contains market data over the relatively long time period of 1926-2005 and found that the S&P500 has a geometric mean of 10.4% and a standard deviation of 20.2% over that period. Historically, there has been a sizable positive correlation between the return of stocks and bonds. Therefore, our estimate of the S&P500’s future growth rate should consider the current risk-free rate. To define the risk-free rate in practice, we should look for a definition that has zero or very low correlation with the S&P500, is easy to track, is forward-looking, and has a long historical data record. The 30-day US Treasury Bill is perhaps the best choice toward meeting these requirements, although it has historically had a low positive correlation with the S&P500. Shareholders demand to be rewarded for holding risk. An important indicator of how shareholders perceive reward and risk is the expected Market Price of Risk1. Historically, the S&P’s Price of Risk against the 30-day US T-Bill has been relatively stable compared to the S&P500’s growth rate. Therefore, it is generally preferable to calculate the expected growth rate of the Market moving forward from the prevailing risk-free rate and a constant Price of Risk and volatility from historical data. Where appropriate, the risk-free rate may be matched to the prevailing U.S. Treasury yield curve (and perhaps its derivatives) and modeled as a known or unknown variable. As an example, from Ibbotson’s 2006 yearbook, we calculated the historical growth rate of the S&P500 as 9.89%, the volatility as 17.86%, the growth rate of the 30-day US T-Bill as 3.63%, and the S&P500’s Price of Risk with the US TBill as .4398. The numbers we’ve calculated here are historical and arguments can be made to suggest that our expectations should be changed2. Although the S&P500 will usually be the best proxy for the Market and the 30-day US T-Bill growth rate will usually be the best proxy for the riskfree rate, there may be special cases when other definitions will be better. For most corporate decision-making models, small changes in our expectations or changes to the definitions would likely result in second-order effects. 1 A reward-to-risk ratio called “Price of Risk” is defined as a stock’s growth rate plus one-half of the stock’s volatility squared minus the risk-free rate with the total divided by the stock’s volatility. 2 See Pablo Fernández’s “Equity Premium: Historical, Expected, Required and Implied” at http://www.fma.org/Barcelona/Papers/EquityPremiumHERI.pdf.
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