Lecture # 3

Risk and Return
Lecture # 3 (CH 6)
Topics in Chapter
 Basic return concepts
 Basic risk concepts
 Stand-alone risk
 Portfolio (market) risk
 Risk and return: CAPM/SML
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:
 Dollar terms.
 Percentage terms.
3
An investment costs $1,000 and is sold
after 1 year for $1,100.
Dollar return:
$ Received - $ Invested
$1,100 - $1,000 = $100.
Percentage return:
$ Return/$ Invested
$100/$1,000 = 0.10 = 10%.
4
What is investment risk?
 Typically, investment returns are not known
with certainty.
 Investment risk pertains to the probability of
earning a return less than that expected.
 The greater the chance of a return far below
the expected return, the greater the risk.
5
Probability Distribution: Which stock
is riskier? Why?
Stock A
Stock B
-30 -15 0 15 30 45 60
Returns (% )
6
Consider the Following
Investment Alternatives
Econ. Prob T-Bill Alta Repo Am F. MP
.
- -
Bust 8.0%
0.10 22.0% 28.0% 10.0% 13.0%
Below
8.0 -2.0 14.7 -10.0 1.0
avg. 0.20
Avg. 8.0 20.0 0.0 7.0 15.0

0.40
Above
8.0 35.0 -10.0 45.0 29.0
avg. 0.20
Boom 8.0 50.0 -20.0 30.0 43.0

0.10
7
What is unique about the T-bill
return?
 The T-bill will return 8% regardless of the state
of the economy.
 Is the T-bill riskless? Explain.
8
Alta Inds. and Repo Men vs. the
Economy
 Alta Inds. moves with the economy, so it is
positively correlated with the economy. This is
the typical situation.
 Repo Men moves counter to the economy.
Such negative correlation is unusual.
9
Calculate the expected rate of
return on each alternative.
^r = expected rate of return.

n
^
r = ∑ riPi.
i=1
^r = 0.10(-22%) + 0.20(-2%)
Alta
+ 0.40(20%) + 0.20(35%)
+ 0.10(50%) = 17.4%. 10
Alta has the highest rate of return.
Does that make it best?
^
r
Alta 17.4%
Market 15.0
Am. Foam 13.8
T-bill 8.0
Repo Men 1.7
11
What is the standard deviation
of returns for each alternative?
σ = Standard deviation
σ = √ Variance = √ σ2
= √ ^
∑ (ri – r)2 Pi.
i=1
12
Standard Deviation of Alta
Industries
 = [(-22 - 17.4)20.10 + (-2 - 17.4)20.20

+ (20 - 17.4)20.40 + (35 - 17.4)20.20
+ (50 - 17.4)20.10]1/2
= 20.0%.
13
Standard Deviation of Alternatives
T-bills = 0.0%. Repo = 13.4%.

Alta = 20.0%.Am Foam = 18.8%.
Market = 15.3%.
14
Stand-Alone Risk
 Standard deviation measures the stand-alone
risk of an investment.
 The larger the standard deviation, the higher
the probability that returns will be far below
the expected return.
15
Expected Return versus Risk
Expected
Security return Risk, 
Alta Inds. 17.4% 20.0%
Market 15.0 15.3
Am. Foam 13.8 18.8
T-bills 8.0 0.0
Repo Men 1.7 13.4
16
Coefficient of Variation (CV)
 CV = Standard deviation / expected return
 CVT-BILLS = 0.0% / 8.0% = 0.0.
 CVAlta Inds = 20.0% / 17.4% = 1.1.
 CVRepo Men = 13.4% / 1.7% = 7.9.
 CVAm. Foam = 18.8% / 13.8% = 1.4.
 CVM = 15.3% / 15.0% = 1.0.
17
Expected Return versus Coefficient
of Variation
Expecte
d Risk: Risk:
Security return  CV
Alta Inds 17.4% 20.0% 1.1

Market 15.0 15.3 1.0
Am. Foam 13.8 18.8 1.4
T-bills 8.0 0.0 0.0
Repo Men 18
Return vs. Risk (Std. Dev.):
Which investment is best?
20.0%
18.0% Alta
16.0%
Mkt
14.0% Am. Foam
Return
12.0%
10.0%
8.0% T-bills
6.0%
4.0%
2.0% Repo
0.0%
0.0% 5.0% 10.0% 15.0% 20.0% 25.0%
Risk (Std. Dev.)
19
Portfolio Risk and Return
Assume a two-stock portfolio with

$50,000 in Alta Inds. and $50,000 in
Repo Men.
Calculate ^rp and p.
20
Portfolio Expected Return
^
rp is a weighted average (wi is % of
portfolio in stock i):
n
^ ^
rp = wiri
i=1
^r = 0.5(17.4%) + 0.5(1.7%) = 9.6%.
p
21
Alternative Method: Find portfolio
return in each economic state
Port.=
0.5(Alta)
+
Econom 0.5(Repo
y Prob. Alta Repo )
Bust 0.10 -22.0% 28.0% 3.0%
Below 0.20 -2.0 14.7 6.4
avg.
Average 0.40 20.0 0.0 10.0
Above 0.20 35.0 -10.0 12.5
avg.
Boom 0.10 50.0 -20.0 15.0
22
Use portfolio outcomes to estimate risk
and expected return
^
rp = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40
+ (12.5%)0.20 + (15.0%)0.10 = 9.6%.
p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20

+(10.0 - 9.6)20.40 + (12.5 -9.6)20.20
+ (15.0 - 9.6)20.10)1/2 = 3.3%.
CVp = 3.3%/9.6% = .34.
23
Portfolio vs. Its Components
 Portfolio expected return (9.6%) is between Alta
(17.4%) and Repo (1.7%)
 Portfolio standard deviation is much lower than:
 either stock (20% and 13.4%).
 average of Alta and Repo (16.7%).
 The reason is due to negative correlation (r)
between Alta and Repo.
24
Two-Stock Portfolios
 Two stocks can be combined to form a riskless
portfolio if r = -1.0.
 Risk is not reduced at all if the two stocks have
r = +1.0.
 In general, stocks have r ≈ 0.35, so risk is
lowered but not eliminated.
 Investors typically hold many stocks.
 What happens when r = 0?
25
Adding Stocks to a Portfolio
 What would happen to the risk of an average 1-
stock portfolio as more randomly selected
stocks were added?
 sp would decrease because the added stocks
would not be perfectly correlated, but the
expected portfolio return would remain
relatively constant.
26

Lecture # 3

Uploaded by

Copyright:

Available Formats

Lecture # 3

Uploaded by

Document Information

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Lecture # 3

Uploaded by

Copyright:

Available Formats

Risk and Return

Avg. 8.0 20.0 0.0 7.0 15.0

Boom 8.0 50.0 -20.0 30.0 43.0

^r = expected rate of return.

 = [(-22 - 17.4)20.10 + (-2 - 17.4)20.20

T-bills = 0.0%. Repo = 13.4%.

Alta Inds 17.4% 20.0% 1.1

Risk (Std. Dev.)

Assume a two-stock portfolio with

Calculate ^rp and p.

p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20

You might also like