ポートフォリオ理論と資本資産価格モデル

最近マートン教授の説明を読んでいます。不明なところが少なくない。
The chapter discusses the implications of portfolio theory for the operation of capital markets. Basically, it seems to combine the notions of efficient portfolios, market equilibrium, and the Capital Asset Pricing Model. My fundamental questions are:
1. what is meant by portfolio theory?
2. what is meant by the CAPM?
3. what exactly is the "efficient frontier"?
4. what do these concepts enable us to deduce about portfolio selection?

Assumptions for the CAPM to hold include perfect competitive markets, perfect information distribution, unlimited lending and borrowing at the risk-free rate, and rational investors who are price-takers. It basically seems to be a single formula:
E(Ri) = Rf + beta*(E(Rm)-Rf)
The expected return on an investment is equal to the risk free rate plus a multiple(beta) of the expected value of the market return minus the risk-free rate. Rf is the risk-free rate, and Rm the market rate. Beta is the ratio Cov(Zi,Zm)/Var(Zm). When at equilibrium and expectations are homogeneous Correlation(Zm,Zi) = 1, so beta = stdDev(Zi)/stdDev(Zm). In this case, the equation is known as the Capital Market Line.
The efficient frontier apparently is the curve denoting the best return that can be obtained for a given volatility. Why exactly this corresponds to the Capital Market Line discussed above is unclear. It seems that the optimal portfolio in equilibrium must consist of a weighted combination of the optimal market portfolio and the risk free rate.
This dovetails into portfolio theory, which seems to endeavor to determine the optimal weights for securities in a portfolio so as to achieve a given return and variance. In this case, the expected return for a variance minimizing portfolio is equal to the right side of the above capital market line. The weights are based on the ratio of the market value of a given security to the value of all risky securities in the market.
wi = N*Pi/Sum(NPi)
This (the supply weight) time M (amount of wealth in market) must equal the demand (in money) for the security.
wi*M = Di