Markowitz while reading the book The Theory of Investment Value written by John Burr Williams noted that the author proposed that the value of a stock should be the present value of its dividends. Markowitz argued that the problem with this novel theory was that the future dividends were not known for certain because they were random variables.
He decided to work on extending Williams’ theory. For an investor to maximize the expected value of the portfolio of stock he owns he should buy one stock with the highest expected return. Markowitz believed that investors should be concerned about the expected return of their wealth and the risk. The fact that investors should care about the risk and the return on investments is so commonplace today it is hard to believe this view was not appreciated back in 1952.
He was guided to study the problem of finding the portfolio with the maximum expected return for a given level of risk. Markowitz wanted to minimize the variance of a portfolio with the limitation of an expected return. The key insight that arises is that the marginal increase in variance depends on both the variance of a given asset’s return plus the covariance of the asset return with all the other asset returns on the portfolio.
Using mathematics he failed to pick a single optimal portfolio but identified a set of efficient portfolios with the lowest possible risk for each possible expected return. Secondly, he identified the appropriate risk facing an investor was portfolio risk which measures how much an entire portfolio of risky assets would fluctuate. Markowitz’s formulation of portfolio optimization shows the important point that the riskiness of a stock should be measured by both the variance and the covariance of the stock.
If a portfolio is highly diversified such that the amount invested in any given asset is small and the returns on the stocks are highly correlated then most of the marginal risk from increasing the fraction of a given asset in a portfolio is due to the covariance effect.
Markowitz succeeded in developing practical methods describing mean-variance efficient portfolios. This initial work was described in two papers which he published between 1952 and 1956. The writings led to the publishing of his classic book in 1959.
Sharpe was one of the first students to take courses in both economics and finance as a doctoral student at UCLA. His lecturer suggested that he should talk to Markowitz concerning his thesis. Sharpe studied Markowitz’s portfolio theory or model portfolio selection which focused only on the choice of risky assets. Someone needed to find out which proportions of stock comprised the magic portfolio which was a difficult and costly computation. The next contribution to this theory was a simplified way to perform this computation.
Sharpe explored the market or single-factor model approach which assumes the return on each security is linear related to a single index. His drive in formulating this model was empirically based on the knowledge that most stocks moved together most of the time. Sharpe’s approach reduced the dimensionality of the portfolio problem dramatically and made it much simpler to compute efficient portfolios. This work led to Sharpe publishing his theory in 1963 and a Ph.D. thesis.
Sharpe concentrated on equilibrium theory that states that the total amount of wealth invested in a company is divided by the total wealth of the stock market. This observation showed that the market variance is mean-variance efficient as it lies on the frontier of the efficient set, therefore, satisfying the first-order conditions for efficiency. The portfolio of risky assets that was optimal for each individual would just be the portfolio of risky assets held by the market. Some simple manipulations of the first-order conditions led to the Capital Asset Pricing Model (CAPM) which is truly a revolutionary discovery for financial economics. The model is an example of how to take the theory of individual optimizing behavior and aggregate it to determine the equilibrium pricing relationships.
The demand of an asset, therefore, depends on the prices of all assets due to the nature of the portfolio optimization problem. It is inherently a general equilibrium theory.
Sharpe’s two major contributions are the single factor model which is a supply-side model based on how returns are generated and CAPM which is a demand-side model. These two models can hold dependently or separately and are both used in finance practice. Subsequent research has relaxed many of the conditions of the original CAPM like unlimited short sales and provided some qualifications about the empirical observables of the model. Sharpe provides a brief review of these points in his published work in 1991. CAPM reigns as one of the fundamental achievements of financial economics as it is taught in every finance textbook and intermediate microeconomics text.
Miller’s most recognized paper on corporate finance was on portfolio theory and the CAPM focus on the behavior of demanders of securities who are the individual investors. Corporate finance focuses on the suppliers of the securities who are the corporations that issue stock and bonds.
The major issue in corporate finance then and now is how to raise capital in the best way. Broadly speaking a company can issue new equity and new debt to raise money. Each has its advantages and disadvantages. Issuing debts increases the fixed costs of the firm while equity dilutes the shares of the existing shareholders. There were a lot of rules of thumb about when to do one and when to do the other.
Miller while teaching corporate finance at Carnegie College in 1952 started to look at data to see if he could determine how corporate financial structure affected firms’ value. He found no particular relationship between the financial structure and firm value. Some firms had a lot of debt while some had a lot of equity but there did not appear to be a pattern in terms of how the debt-equity ratio affected the market value.
Miller joined Franco Modigliani who taught in the same college while working on the same issues that he was working on. The world of corporate finance has never been the same. They considered a simple world without taxes or transaction costs and found that in such a world the value of a firm would be independent of its capital structure.
The MM theory is a consequence of value additivity that states that the value of the portfolio must be the sum of the values of the assets that make it up.
At first, this principle seemed to contradict the insights of Markowitz about portfolio diversifications where an asset should be worth more combined in a portfolio with other assets than standing alone due to the benefits of diversification.
Asset values in a well-functioning securities market already reflect the value achievable by portfolio optimization. The principle of value additivity is more fundamental than the CAPM since it rests solely on arbitrage considerations. The theory of the MM proposition is solidly established. The controversies arise from the assumptions of a frictionless world such as nil taxes and bankruptcy costs and lack of asymmetric information.