17. Applications in Finance
A portfolio is a linear combination of assets. Each asset contributes
with a weight
to the portfolio. The performance of such a portfolio
is a function of the various returns of the assets and of the weights
.
In this chapter we investigate the ``optimal choice'' of the
portfolio weights
. 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).