Risk and Rates of ReturnRisk and Rates of Return

ReturnReturn

RiskRisk

RequiredRequired

rate of rate of

returnreturn==

Risk-freeRisk-freerate ofrate ofreturnreturn

For a Treasury security, what is the required rate of return?

For a Treasury security, what is the required rate of return?

Since Treasury’s are essentially free of default risk, the rate of return on a Treasury security is considered the

“risk-free” rate of return.

RequiredRequired

rate of rate of

returnreturn==

Risk-freeRisk-freerate ofrate ofreturnreturn

++RiskRisk

PremiumPremium

For a For a corporate stock or bondcorporate stock or bond, what , what is the required rate of return?is the required rate of return?

How large of a risk premium should we require to buy a corporate security?

ReturnsReturns

Expected Return - the return that an investor expects to earn on an asset, given its

price, growth potential, etc.

Required Return - the return that an investor requires on an

asset given its risk.

Expected ReturnExpected Return

State of Probability ReturnEconomy (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 ReturnExpected Return

State of Probability ReturnEconomy (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 ReturnExpected Return

State of Probability ReturnEconomy (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)*knk (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%

Expected ReturnExpected Return

State of Probability ReturnEconomy (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%

What is Risk?What is Risk?

The possibility that an actual return will differ from our

expected return.

Uncertainty in the distribution of possible outcomes.

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?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= (ki - k) P(ki)

2

Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2(10% - 10%)2 (.5) = 0

(14% - 10%)2 (.3) = 4.8Variance = 12Stand. dev. = 12 =

3.46%

Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2(10% - 10%)2 (.5) = 0

(14% - 10%)2 (.3) = 4.8Variance = 12Stand. dev. = 12 =

3.46%

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

n

i=1

Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2(14% - 14%)2 (.5) = 0

(30% - 14%)2 (.3) = 76.8Variance = 192

Stand. dev. = 192 = 13.86%

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

n

i=1

Orlando

Orlando Utility Technology

Expected Return 10% 14%

Standard Deviation 3.46% 13.86%

Orlando

Orlando Utility Technology

Expected Return 10% 14%

Standard Deviation 3.46% 13.86%

SummarySummary