Nobel laureates Markowitz, Miller and Sharpe greatly contributed toquantitative economics. They established core principles ofquantitative finance. Markowitz and his colleagues transformedfinance completely. We cannot imagine what finance was like beforethe portfolio theory.

For Markowitz, risk and return are two fundamental concepts thathave remained pillars of finance. A possible risk in finance means apossible expected return. He recognized that investors are faced byappropriate risks termed as portfolio risks and how much their entireportfolio of risky assets were likely to fluctuate. According to him,a risk averse investor does not like taking risks and given anopportunity to choose he would choose and investment that is lessrisky. The opposite is a risk loving investor who would choose aninvestment that is more risky instead of the less risky one. Hedeveloped the theory of portfolio optimization, the risk measure ofstandard deviation which became very popular as an explanation ofoptimization method for risk averse investors. This led him to winthe 1990, Nobel prize. The portfolio selection was an applied toquadratic programming problem which is today used in many papers. Thebasic thought of mean variance analysis is the squared standarddeviation through finding a suitable mean combination of the(expected return) and variance (risk) for an investor as explainedbelow. Fractions of wealth invested in each available risk assets isthe choice variable. The quadratic objectives function of thevariance of return on the resulting portfolio. The linear constraintis the expected return of the portfolio to achieve target value. Hisformulation of portfolio optimization leads to the fundamental pointof stock riskiness not being measured just by variance but bycovariance. Markowitz developed practical ways of determining thecritical line from linear programming’s infancy. Through hisapproach, every efficient portfolio containing risky assets and ariskless asset would be achieved through combining two portfolios,risk-free asset and risk-return combination.

The next great contribution to the portfolio theory was a simplifiedway to perform the computation by William Sharpe. He was a doctoralstudent at UCLA and amongst the first to take economics and financecombination courses. Sharpe was advised to talk to Markowitzregarding his thesis who later became his unofficial thesis advisor.This was useful for Sharpe and Markowitz as he put his computationalaspects of portfolio theory to work. Sharpe’s two majorcontributions to finance were the single factor model and CAPM. Thesetwo theories are confused easily. However, single factor model is asupply side model while CAPM is a demand side model. Supply sidemodel explains how returns are generated while CAPM explains therelationship between risk and expected return. It is a simplemanipulation of first order conditions yielding to this model. CAPMwas truly a revolutionary innovation for finance, its shows how thetheory of individual behavior is taken and aggregated to determineequilibrium pricing relationships. For Sharpe, CAPM was a result ofsimple manipulations of the first order conditions (mean varianceefficient- lies on the frontier of the efficient set and thereforesatisfies the first order conditions of efficacy).

Capital Asset Pricing Model is more of a general equilibrium theoryas compared to the portfolio optimization problem. It reigns as afundamental achievement in financial economics and is taught in everyfinance textbook to date.

Merton Miller was in the 90’s a distinguished personalityrecognized for many contributions including finance. He worked on theasset principals and to some extent contradicted Markowitz on theportfolio diversification. According to him, assets should be worthmore combined in a portfolio with other assets rather than whenstanding alone due to diversification benefits. The point is thatasset values in well functioning securities market reflect theachievable value by portfolio optimization already. This is CAPM’schief insight whereby equilibrium value of an asset depends on how itco varies with other assets. The principal of the value additivity ismore fundamental than CAPM. The equilibrium relationship of the valueas a whole has to be the sum of the value parts. Following thisobservation, Millers theory defines the sum of values of its debt andits equity. If the firm can increase its value by changing the cashflow paid to bondholders and stockholders, any investor can constructa free lunch. An investor can buy a fraction of the outstanding stockand the same fraction of the outstanding bond to get the total cashflow. This home-made leverage argument proves MM’s theory.