Applications in Finance

A portfolio is a linear combination of assets. Each asset contributes with a weight \(c_j\) to the portfolio. The performance of such a portfolio is a function of the various returns of the assets and of the weights \(c = (c_1,\ldots ,c_p)^{\top }\) . In this chapter we investigate the “optimal choice” of the portfolio weights c. The optimality criterion is the mean-variance efficiency of the portfolio. Usually investors are risk-averse, therefore, we can define a mean-variance efficient portfolio to be a portfolio that has a minimal variance for a given desired mean return. Equivalently, we could try to optimize the weights for the portfolios with maximal mean return for a given variance (risk structure). We develop this methodology in the situations of (non)existence of riskless assets and discuss relations with the capital assets pricing model (CAPM).