Expected Return

State of Probability Return

Economy (P) Orl. Utility Orl. Tech

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%

For each firm, the expected return on the stock is just a weighted average:

Expected Return

State of Probability Return

Economy (P) Orl. Utility Orl. Tech

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%

For each firm, the expected return on the stock is just a weighted average:

k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn

Expected Return

State of Probability Return

Economy (P) Orl. Utility Orl. Tech

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%

k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn

k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%

Expected Return

State of Probability Return

Economy (P) Orl. Utility Orl. Tech

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%

k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn

k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%

Based only on your Based only on your expected return expected return

calculations, which calculations, which stock would you stock would you

prefer?prefer?

RISK?RISK?

Have you considered

What is Risk?What is Risk? Uncertainty in the distribution of

possible outcomes.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4 8 12

Company A

return

What is Risk?What is Risk? Uncertainty in the distribution of

possible outcomes.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-10 -5 0 5 10 15 20 25 30

Company B

return

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4 8 12

Company A

return

How do we Measure Risk?

A more scientific approach is to examine the stock’s STANDARD DEVIATION of returns.

Standard deviation is a measure of the dispersion of possible outcomes.

The greater the standard deviation, the greater the uncertainty, and therefore , the greater the RISK.

Standard DeviationStandard Deviation

n

i=1= (k= (kii - k) P(k - k) P(kii))

2

Orlando Utility, Inc. Orlando Utility, Inc. Orlando Utility, Inc. Orlando Utility, Inc.

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

n

i=1= (k= (kii - k) P(k - k) P(kii))2

n

i=1

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8

Variance = 12Variance = 12

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8

Variance = 12Variance = 12

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8

Variance = 12Variance = 12

Stand. dev. = 12 = Stand. dev. = 12 = 3.46%3.46%

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8

Variance = 12Variance = 12

Stand. dev. = 12 = Stand. dev. = 12 = 3.46%3.46%

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Technology, Inc. Orlando Technology, Inc.

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Technology, Inc. Orlando Technology, Inc.

(-10% - 14%)(-10% - 14%)22 (.2) = 115.2 (.2) = 115.2

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Technology, Inc. Orlando Technology, Inc.

(-10% - 14%)(-10% - 14%)22 (.2) = 115.2 (.2) = 115.2

(14% - 14%)(14% - 14%)22 (.5) = 0 (.5) = 0

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Technology, Inc. Orlando Technology, Inc.

(-10% - 14%)(-10% - 14%)22 (.2) = 115.2 (.2) = 115.2

(14% - 14%)(14% - 14%)22 (.5) = 0 (.5) = 0

(30% - 14%)(30% - 14%)22 (.3) (.3) = = 76.8 76.8

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Technology, Inc. Orlando Technology, Inc.

(-10% - 14%)(-10% - 14%)22 (.2) = 115.2 (.2) = 115.2

(14% - 14%)(14% - 14%)22 (.5) = 0 (.5) = 0

(30% - 14%)(30% - 14%)22 (.3) (.3) = = 76.8 76.8

Variance = 192Variance = 192

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Orlando Technology, Inc. Orlando Technology, Inc.

(-10% - 14%)(-10% - 14%)22 (.2) = 115.2 (.2) = 115.2

(14% - 14%)(14% - 14%)22 (.5) = 0 (.5) = 0

(30% - 14%)(30% - 14%)22 (.3) (.3) = = 76.8 76.8

Variance = 192Variance = 192

Stand. dev. = 192 = Stand. dev. = 192 = 13.86%13.86%

= (k= (kii - k) P(k - k) P(kii))2 n

i=1

Which stock would you Which stock would you prefer?prefer?

How would you decide?How would you decide?

Orlando Orlando

UtilityTechnology

Expected Return 10% 14%

Standard Deviation 3.46% 13.86%

Orlando Orlando

UtilityTechnology

Expected Return 10% 14%

Standard Deviation 3.46% 13.86%

SummarySummarySummarySummary

It depends on your tolerance for risk! It depends on your tolerance for risk!

Remember there’s a tradeoff between risk and return.Remember there’s a tradeoff between risk and return.

Return

Risk