Introduction to Stochastic Finance pp 33-73 | Cite as

# Portfolio Selection Theory in Discrete-Time

## Abstract

When a broker (economic agent) invests in a stock market, he must select an appropriate portfolio. As a saying goes: do not put all your eggs in one basket. A core issue of portfolio selection is the trade-off between profit and risk. To tackle this issue, Harry M. Markowitz (1952) developed a mean-variance analysis, which was the first quantitative treatment of portfolio selection under uncertainty. This approach was further developed by James Tobin (1958). In the mid-1960s, based on Markowitz’s mean-variance analysis and Tobin’s two-fund separation theorem, William F. Sharpe (1964), John Lintner (v), and Jan Mossin (1966) independently observed that there exists a linear relation among expected rates of return on portfolios; in a competitive equilibrium market, the coefficients of the linear relation are related to the so-called betas of rates of return on portfolios with respect to the rate of return on the market portfolio. This relation is the so-called *capital asset pricing model* (CAPM). CAPM implicitly assumes that the returns on risky assets depend on a single market factor. Ross (1976) proposed a multifactor model for the behavior of asset prices in capital markets, which is called the *arbitrage pricing theory* (APT).

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