Modern portfolio theory (MPT)
1. Risk and return ......................................................................................................................  1
Mean and variance ............................................................................................................  2
Mathematically  ..........................................................................................................  3
Diversification  ................................................................................................................... 4
Capital allocation line .......................................................................................................  5
The efficient frontier .........................................................................................................  5
2. The risk-free asset .................................................................................................................  6
Mathematically  ..................................................................................................................  6
Portfolio leverage ..............................................................................................................  7
The market portfolio ......................................................................................................... 7
Capital market line ............................................................................................................  8
3. Asset pricing  ..........................................................................................................................  8
Systematic risk and specific risk .......................................................................................  9
Security characteristic line ................................................................................................  9
Capital asset pricing model .............................................................................................  10
Securities market line ...................................................................................................... 10
4. Applications to project portfolios and other "non-financial" assets .................................... 11
5. Comparison with arbitrage pricing theory ..........................................................................  12
6. References ...........................................................................................................................  12
Modern portfolio theory (MPT) proposes how rational investors will use
diversification to optimize their portfolios, and how a risky asset should
be priced. The basic concepts of the theory are Markowitz diversification,
the efficient frontier, capital asset pricing model, the alpha and beta
coefficients, the Capital Market Line and the Securities Market Line.
MPT models an asset' s return as a random variable, and models a portfolio
as a weighted combination of assets so that the return of a portfolio is
the weighted combination of the assets' returns. Moreover, a portfolio' s
return is a random variable, and consequently has an expected value and
a variance. Risk, in this model, is the standard deviation of return.
1. Risk and return
The model assumes that investors are risk averse, meaning that given two
assets that offer the same expected return, investors will prefer the less