There are several notions of the idea of optimizing a portfolio of securities,
options, bonds, cash, etc. In this chapter we will explore optimality in the
sense of maximizing the rate of return, minimizing the variance in the rate
of return, and minimizing risk to the investor. We will also introduce the
Capital Assets Pricing Model which attempts to relate the rate of return of a
specific investment to the rate of return for the entire market of investments.
We will see in this chapter that the difference in the expected rates of return
for a specific security and the risk-free interest rate is proportional to the
difference in the expected rates of return for the market and the risk-free
interest rate. In order to explain this proportionality relationship we will
introduce two additional statistical measures, covariance and correlation.
We will also make use of these concepts in developing additional hedging
strategies.