The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

MEASURING A PORTFOLIO’S EXPECTED RETURN

We are now ready to define the actual and expected return of a risky asset and a portfolio of risky assets.

Measuring Single-Period Portfolio Return

The actual return on a portfolio of assets over some specific time period is straightforward to calculate using the formula:

(3.1)

where

Rp	=	rate of return on the portfolio over the period
Rg	=	rate of return on asset g over the period
wg	=	weight of asset g in the portfolio (i.e., market value of asset g as a proportion of the market value of the total portfolio) at the beginning of the period
G	=	number of assets in the portfolio

In shorthand notation, equation (3.1) can be expressed as follows:

(3.2)

Equation (3.2) states that the return on a portfolio (R_p) of G assets is equal to the sum over all individual assets’ weights in the portfolio times their respective return. The portfolio return R_p is sometimes called the holding period return or the ex post return.

For example, consider the following portfolio consisting of three assets:

Asset	Market Value at the Beginning of Holding Period	Rate of Return over Holding Period
1	$6 million	12%
2	$8 million	10%
3	$11 million	5%

 

The portfolio’s total market value at the beginning of the holding period is $25 million. Therefore,

w1

=

$6 million/$25 ...