risk and rates of return

5-1

Risk and Rates of Return

Stand-alone risk Portfolio risk Risk & return: CAPM / SML

5-2

What are Investment Returns Investment returns measure the

financial results of an investment. Returns may be historical or

prospective (anticipated). Returns can be expressed in: Taka Percentage Terms

5-3

Investment returnsThe rate of return on an investment can be calculated as follows:

(Amount received – Amount invested)

Return = ________________________

Amount invested

For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is:

($1,100 - $1,000) / $1,000 = 10%.

5-4

ReturnIncome received Income received on an investment plus

any change in market pricechange in market price, usually expressed as a percent of the beginning market price beginning market price of the

investment.

DDtt + (PPtt - P - Pt-1t-1 )PPt-1t-1

R =

5-5

Return ExampleThe stock price for Stock A was $10$10

per share 1 year ago. The stock is currently trading at $9.50$9.50 per share, and shareholders just

received a $1 dividend$1 dividend. What return was earned over the past

year?

5-6

Return ExampleThe stock price for Stock A was $10$10 per share 1

year ago. The stock is currently trading at $9.50$9.50 per share, and shareholders just

received a $1 dividend$1 dividend. What return was earned over the past year?

$1.00 $1.00 + ($9.50$9.50 - $10.00$10.00 )$10.00$10.00RR = = 5%5%

5-7

What is investment risk? Two types of investment risk

Stand-alone risk Portfolio risk

Investment returns are not known with certainty.

Investment risk is related to the probability of earning a low or negative actual return.

The greater the chance of lower than expected or negative returns, the riskier the investment.

5-8

Investment alternatives

Economy Prob.

A B C D E

Recession

0.1 8.0% -22.0%

28.0% 10.0% -13.0%

Below avg

0.2 8.0% -2.0% 14.7% -10.0%

1.0%

Average 0.4 8.0% 20.0% 0.0% 7.0% 15.0%Above avg

0.2 8.0% 35.0% -10.0%

45.0% 29.0%

Boom 0.1 8.0% 50.0% -20.0%

30.0% 43.0%

5-9

Return: Calculating the expected return for each alternative

17.4% (0.1) (50%) (0.2) (35%) (0.4) (20%)

(0.2) (-2%) (0.1) (-22.%) k

P k k

return of rate expected k

HT^

n

1iii

^

^

5-10

Summary of expected returns for all alternatives

Exp returnB 17.4%E 15.0%D 13.8%A 8.0%C 1.7%

B has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

5-11

How to Determine the Expected Return and Standard Deviation

Ki Pi (Ki)(Pi)

-.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 .090.090

The expected return, R, for Stock is .09 or 9%

5-12

Risk: Calculating the standard deviation for each alternative

deviation Standard

2Variance

i2

n

1ii P)k̂k(

5-13

Standard deviation calculation

15.3% 18.8% 20.0%

13.4% 0.0%

(0.1)8.0) - (8.0

(0.2)8.0) - (8.0 (0.4)8.0) - (8.0

(0.2)8.0) - (8.0 (0.1)8.0) - (8.0

P )k (k

E

DB

CA

21

2

22

22

A

n

1ii

2^

i

5-14

How to Determine the Expected Return and Standard Deviation Ki Pi (Ki)(Pi) (Ki -

K)2(Pi) -.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .09 .40 .036 .00000 .21 .20 .042

.00288 .33 .10 .033 .00576 Sum 1.00 .090.090 .01728.01728

5-15

Determining Standard Deviation (Risk Measure)

= ( Ki - K )2( Pi )

= .01728

= .1315.1315 or 13.15%13.15%

5-16

Comments on standard deviation as a measure of risk Standard deviation (σi) measures

total, or stand-alone, risk. The larger σi is, the lower the

probability that actual returns will be closer to expected returns.

Difficult to compare standard deviations, because return has not been accounted for.

5-17

Determining Expected Return (Continuous Dist.)

K = ( Ki ) / ( n )K is the expected return for the asset,

Ki is the return for the ith observation,

n is the total number of observations.

5-18

Determining Standard Deviation (Risk Measure)

= ( Ki - K )2

( n )

5-19

9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, 10.5%

Calculate the Expected Return and Standard Deviation

5-20

Comparing risk and returnSecurity Expected

returnRisk, σ

A 8.0% 0.0%B 17.4% 20.0%C 1.7% 13.4%D 13.8% 18.8%E 15.0% 15.3%

5-21

Coefficient of Variation (CV)A standardized measure of dispersion about the expected value, that shows the risk per unit of return.

^k

Meandev Std CV

5-22

Risk rankings, by coefficient of variation

CV A 0.000

B 1.149C 7.882D 1.362E 1.020

C has the highest degree of risk per unit of return.

B, despite having the highest standard deviation of returns, has a relatively average CV.

5-23

Investor attitude towards risk Risk aversion – assumes investors

dislike risk and require higher rates of return to encourage them to hold riskier securities.

Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.

5-24

Portfolio construction:Risk and return

Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections.

Expected return of a portfolio is a weighted average of each of the component assets of the portfolio.

Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised.

5-25

Calculating portfolio expected return

9.6% (1.7%) 0.5 (17.4%) 0.5 k

kw k

:average weighted a is k

p^

n

1ii

^ip

^

p^

5-26

An alternative method for determining portfolio expected return

Economy Prob.

B C Port.Port.

Recession

0.1 -22.0%

28.0% 3.0%3.0%

Below avg

0.2 -2.0% 14.7% 6.4%6.4%

Average 0.4 20.0% 0.0% 10.0%10.0%Above avg

0.2 35.0% -10.0%

12.5%12.5%

Boom 0.1 50.0% -20.0%

15.0%15.0%9.6% (15.0%) 0.10 (12.5%) 0.20 (10.0%) 0.40 (6.4%) 0.20 (3.0%) 0.10 kp

^

5-27

Calculating portfolio standard deviation and CV

0.34 9.6%3.3% CV

3.3%

9.6) - (15.0 0.10 9.6) - (12.5 0.20 9.6) - (10.0 0.40

9.6) - (6.4 0.20 9.6) - (3.0 0.10

p

21

2

2

2

2

2

p

5-28

Comments on portfolio risk measures σp = 3.3% is much lower than the σi

of either stock (σB = 20.0%; σC. = 13.4%).

σp = 3.3% is lower than the weighted average of B and C’s σ (16.7%).

Portfolio provides average return of component stocks, but lower than average risk.