Portfolio Optimization

Chapter 2

The Efficient Frontier

2.1 The Efficient Frontier

A portfolio consists of various amounts held in different assets. The

number of possible assets can be quite large. Standard and Poor’s lists

500 assets (S&P 500) and in Canada, the Toronto Stock Exchange lists

300 assets (TSX 300). The basic portfolio optimization problem is t o

decide how much of an investor’s wealth should be optimally invested

in each asset.

Consider a universe of n assets. Let µ

i

denote the expected return

1

on a sset i, i = 1, 2, . . . , n and σ

ij

denote the covariance between the

returns of assets i and j, 1 ≤ i, j ≤ n. Let

µ = (µ

1

, µ

2

, . . . , µ

n

)

′

and Σ = [σ

ij

].

Σ is called the ...