Fundamentals of Financial Management (Concise 6th Edition)

Chapter 8 Risk and Rates of Return 241

8-3a Expected Portfolio Returns, rˆp

The expected return on a portfolio, rˆp, is the weighted average of the expected
returns of the individual assets in the portfolio, with the weights being the per-
centage of the total portfolio invested in each asset:

rˆp " w 1 rˆ 1 + w 2 rˆ 2 $... $ wN rˆN

" ∑

i=1

N

wirˆi 8-4

Here rˆi is the expected return on the ith stock; the wi’s are the stocks’ weights, or
the percentage of the total value of the portfolio invested in each stock; and N is
the number of stocks in the portfolio.
Table 8-4 can be used to implement the equation. Here we assume that an ana-
lyst estimated returns on the four stocks shown in Column 1 for the coming year, as
shown in Column 2. Suppose further that you had $100,000 and you planned to in-
vest $25,000, or 25% of the total, in each stock. You could multiply each stock’s per-
centage weight as shown in Column 4 by its expected return; get the product terms
in Column 5; and then sum Column 5 to get the expected portfolio return, 10.75%.
If you added a " fth stock with a higher expected return, the portfolio’s ex-
pected return would increase, and vice versa if you added a stock with a lower
expected return. The key point to remember is that the expected return on a portfolio is a
weighted average of expected returns on the stocks in the portfolio.
Several additional points should be made:

1. The expected returns in Column 2 would be based on a study of some type,
   but they would still be essentially subjective and judgmental because different
   analysts could look at the same data and reach different conclusions. There-
   fore, this type of analysis must be viewed with a critical eye. Nevertheless, it is
   useful, indeed necessary, if one is to make intelligent investment decisions.


2. If we added companies such as Delta Airlines and Ford, which are generally
   considered to be relatively risky, their expected returns as estimated by the
   marginal investor would be relatively high; otherwise, investors would sell
   them, drive down their prices, and force the expected returns above the returns
   on safer stocks.


3. After the fact and a year later, the actual realized rates of return, r-i, on the
   individual stocks—the r-i, or “r-bar,” values—would almost certainly be differ-
   ent from the initial expected values. That would cause the portfolio’s actual
   return, r-p, to differ from the expected return, rˆp $ 10.75%. For example, Micro-
   soft’s price might double and thus provide a return of "100%, whereas IBM
   might have a terrible year, fall sharply, and have a return of !75%. Note,
   though, that those two events would be offsetting; so the portfolio’s return still
   might be close to its expected return even though the returns on the individual
   stocks were far from their expected values.

Expected Return on a

Portfolio, rˆp

The weighted average of

the expected returns on

the assets held in the

portfolio.

Expected Return on a

Portfolio, rˆp

The weighted average of

the expected returns on

the assets held in the

portfolio.

Realized Rate of

Return, r-

The return that was

actually earned during

some past period. The

actual return (r-) usually

turns out to be different

from the expected return

(rˆ) except for riskless

assets.

Realized Rate of

Return, r-

The return that was

actually earned during

some past period. The

actual return (r-) usually

turns out to be different

from the expected return

(rˆ) except for riskless

assets.

Tabl e 8 - 4 Expected Return On a Portfolio, rˆp

A B C D E F

52

53

54

55

56

57

58

59

60

61

62

Product:

(2)!(4)

(5)

Stock

(1)

10.75% $100,000 100.0%

Microsoft

IBM

GE

Exxon

Expected

Return

(2)

12.00%

11.50

10.00

9.50

Dollars

Invested

(3)

$25,000

25,000

25,000

25,000

Percent of

Total (wi)

(4)

25.0%

25.0

25.0

25.0

3.000%

2.875

2.500

2.375

10.750% = Expected rp