Principles of Managerial Finance

CHAPTER 5 Risk and Return 227

TABLE 5.7 Expected Return, Expected Value, and Standard

Deviation of Returns for Portfolio XY

A. Expected portfolio returns

Forecasted return

Expected portfolio

Asset X Asset Y Portfolio return calculationa return, kp

Year (1) (2) (3) (4)

2004 8% 16% (.508%)(.5016%) 12%

2005 10 14 (.5010%)(.5014%) 12

2006 12 12 (.5012%)(.5012%) 12

2007 14 10 (.5014%)(.5010%) 12

2008 16 8 (.5016%)(.508%) 12

B. Expected value of portfolio returns, 2004–2008b

kp 1



2



%

C. Standard deviation of expected portfolio returnsc

kp



% 0



%

aUsing Equation 5.5.

bUsing Equation 5.2a found in footnote 9.

cUsing Equation 5.3a found in footnote 10.

^0

4

0%0%0%0%0%

4

(12%12%)^2 (12%12%)^2 (12%12%)^2 (12%12%)^2 (12%12%)^2

5  1

60%

5

12%12%12%12%12%

5

13. The general long-term trendsof two series could be the same (both increasing or both decreasing) or different
    (one increasing, the other decreasing), and the correlation of their short-term (point-to-point) movementsin both
    situations could be either positive or negative. In other words, the pattern of movement around the trends could be
    correlated independent of the actual relationship between the trends. Further clarification of this seemingly inconsis-
    tent behavior can be found in most basic statistics texts.

positively correlated
Describes two series that move
in the same direction.

negatively correlated
Describes two series that move
in opposite directions.

correlation
A statistical measure of the
relationship between any two
series of numbers representing
data of any kind.

Correlation

Correlationis a statistical measure of the relationship between any two series of

numbers. The numbers may represent data of any kind, from returns to test

scores. If two series move in the same direction, they are positively correlated.If

the series move in opposite directions, they are negatively correlated.^13