4.2Portfolio Returns

There are two equivalent methods to compute portfolio returns. The ratio method

divides the dollar value of the portfolio at the end of the period (plus distributed cash,

such as dividends) by the portfolio value at the beginning of the period and then sub-

tracts 1 from the ratio. The portfolio-weighted average methodweights the returns of

the investments in the portfolio by their respective portfolio weights and then sums the

weighted returns.

Example 4.4 illustrates both methods.

Example 4.4:Computing Portfolio Returns fora Two-Stock Portfolio

A $4,000,000 portfolio consists of $1,000,000 of IBM stock and $3,000,000 of AT&T stock.

If IBM stock has a return of 10 percent and AT&T stock has a return of 5 percent, deter-

mine the portfolio return using both (1) the ratio method and (2) the portfolio-weighted aver-

age method.

Answer:(1) For $1,000,000 of IBM stock to have a 10 percent return, the end-of-period

value plus dividends for the stock must amount to $1,100,000.Similarly the end-of-period

value of the AT&T stock plus dividends must amount to $3,150,000 to yield a 5% return.

Hence, the portfolio’s end-of-period value is $4,250,000, the sum of $1,100,000 and

$3,150,000, implying that the return of the portfolio is

$4,250,000

1 .0625 or 6.25%

$4,000,000

(2) The portfolio weight is .25 for IBM and .75 for AT&T.Thus, the portfolio-weighted aver-

age return is .25(.1) .75(.05) .0625.

For Nstocks, indexed 1 through N, the portfolio return formula becomes

˜		xr˜xr˜		.	.	.		xr˜
R
p		112 2						NN	(4.1)
		N
		xr˜.
		i i
		i 1

Grinblatt224Titman: Financial	II. Valuing Financial Assets	4. Portfolio Tools	© The McGraw224Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

Chapter 4

Portfolio Tools

103