Transcript No Slide Title

CHAPTER 5
McGraw-Hill/Irwin
Risk and Return:
Past and Prologue
© 2007 The McGraw-Hill Companies, Inc., All Rights Reserved.
Holding Period Return
P
1  P 0  D1
HPR 
P0
P0  BeginningP rice
P1  EndingPric e
D1  CashDivide nd
5-2
Rates of Return: Single Period
Example
Ending Price =
Beginning Price =
Dividend =
24
20
1
HPR = ( 24 - 20 + 1 )/ ( 20) = 25%
5-3
Data from Table 5.1
1
1.0
.10
Assets(Beg.)
HPR
TA (Before
Net Flows
1.1
Net Flows
0.1
End Assets
1.2
2
1.2
.25
3
2.0
(.20)
4
.8
.25
1.5
0.5
2.0
1.6
(0.8)
.8
1.0
0.0
1.0
5-4
Returns Using Arithmetic and
Geometric Averaging
Arithmetic
ra = (r1 + r2 + r3 + ... rn) / n
ra = (.10 + .25 - .20 + .25) / 4
= .10 or 10%
Geometric
rg = {[(1+r1) (1+r2) .... (1+rn)]} 1/n - 1
rg = {[(1.1) (1.25) (.8) (1.25)]} 1/4 - 1
= (1.5150) 1/4 -1 = .0829 = 8.29%
5-5
Dollar Weighted Returns
Internal Rate of Return (IRR) - the
discount rate that results in present value
of the future cash flows being equal to the
investment amount
Considers changes in investment
Initial Investment is an outflow
Ending value is considered as an inflow
Additional investment is a negative flow
Reduced investment is a positive flow
5-6
Dollar Weighted Average
Using Text Example
Net CFs
$ (mil)
1 2
- .1 - .5
3
.8
4
1.0
Solving for IRR
1.0 = -.1/(1+r)1 + -.5/(1+r)2 + .8/(1+r)3 +
1.0/(1+r)4
r = .0417 or 4.17%
5-7
Quoting Conventions
APR = annual percentage rate
(periods in year) X (rate for period)
EAR = effective annual rate
( 1+ rate for period)Periods per yr - 1
Example: monthly return of 1%
APR = 1% X 12 = 12%
EAR = (1.01)12 - 1 = 12.68%
5-8
Characteristics of Probability
Distributions
1) Mean: most likely value
2) Variance or standard deviation
3) Skewness
* If a distribution is approximately normal,
the distribution is described by
characteristics 1 and 2
5-9
Normal Distribution
s.d.
s.d.
r
Symmetric distribution
5-10
Skewed Distribution: Large Negative
Returns Possible
Median
Negative
r
Positive
5-11
Skewed Distribution: Large Positive
Returns Possible
Median
Negative
r
Positive
5-12
Measuring Mean: Scenario or
Subjective Returns
Subjective returns
E(r) = S p(s) r(s)
s
p(s) = probability of a state
r(s) = return if a state occurs
1 to s states
5-13
Numerical Example: Subjective or
Scenario Distributions
State Prob. of State
1
.1
2
.2
3
.4
4
.2
5
.1
rin State
-.05
.05
.15
.25
.35
E(r) = (.1)(-.05) + (.2)(.05)...+ (.1)(.35)
E(r) = .15
5-14
Measuring Variance or Dispersion of
Returns
Subjective or Scenario
Variance = S p(s) [rs - E(r)]
2
s
Standard deviation = [variance]1/2
Using Our Example:
Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2...+ .1(.35-.15)2]
Var= .01199
S.D.= [ .01199] 1/2 = .1095
5-15
Annual Holding Period Returns
From Table 5.3 of Text
Geom.
Series
Mean%
World Stk 9.41
US Lg Stk 10.23
US Sm Stk 11.80
Wor Bonds 5.34
LT Treas
5.10
T-Bills
3.71
Inflation
2.98
Arith.
Mean%
11.17
12.25
18.43
6.13
5.64
3.79
3.12
Stan.
Dev.%
18.38
20.50
38.11
9.14
8.19
3.18
4.35
5-16
Annual Holding Period Excess Returns
From Table 5.3 of Text
Series
World Stk
US Lg Stk
US Sm Stk
Wor Bonds
LT Treas
Arith.
Mean%
7.37
8.46
14.64
2.34
1.85
Stan.
Dev.%
18.69
20.80
38.72
8.98
8.00
5-17
Figure 5.1 Frequency
Distributions of Holding Period Returns
5-18
Figure 5.2 Rates of Return on Stocks,
Bonds and Bills
5-19
Figure 5.3 Normal Distribution with
Mean of 12.25% and St Dev of 20.50%
5-20
Real vs. Nominal Rates
Fisher effect: Approximation
nominal rate = real rate + inflation premium
R = r + i or r = R - i
Example r = 3%, i = 6%
R = 9% = 3% + 6% or 3% = 9% - 6%
Fisher effect: Exact
r = (R - i) / (1 + i)
2.83% = (9%-6%) / (1.06)
5-21
Figure 5.4 Interest, Inflation and Real
Rates of Return
5-22
Allocating Capital Between Risky &
Risk-Free Assets
Possible to split investment funds
between safe and risky assets
Risk free asset: proxy; T-bills
Risky asset: stock (or a portfolio)
5-23
Allocating Capital Between Risky &
Risk-Free Assets (cont.)
Issues
– Examine risk/ return tradeoff
– Demonstrate how different degrees of risk
aversion will affect allocations between risky
and risk free assets
5-24
Example Using the Numbers in
Chapter 5 (pp 146-148)
rf = 7%
srf = 0%
E(rp) = 15%
sp = 22%
y = % in p
(1-y) = % in rf
5-25
Expected Returns for Combinations
E(rc) = yE(rp) + (1 - y)rf
rc = complete or combined portfolio
For example, y = .75
E(rc) = .75(.15) + .25(.07)
= .13 or 13%
5-26
Figure 5.5 Investment Opportunity
Set with a Risk-Free Investment
5-27
Variance on the Possible Combined
Portfolios
Since
s r = 0, then
f
sc = y s p
5-28
Combinations Without Leverage
If y = .75, then
s c = .75(.22) = .165 or 16.5%
If y = 1
s c = 1(.22) = .22 or 22%
If y = 0
sc = 0(.22) = .00 or 0%
5-29
Using Leverage with
Capital Allocation Line
Borrow at the Risk-Free Rate and invest in
stock
Using 50% Leverage
rc = (-.5) (.07) + (1.5) (.15) = .19
sc = (1.5) (.22) = .33
5-30
Figure 5.6 Investment Opportunity Set with
Differential Borrowing and Lending Rates
5-31
Risk Aversion and Allocation
Greater levels of risk aversion lead to
larger proportions of the risk free rate
Lower levels of risk aversion lead to larger
proportions of the portfolio of risky assets
Willingness to accept high levels of risk for
high levels of returns would result in
leveraged combinations
5-32
Table 5.5 Average Rates of Return,
Standard Deviation and Reward to
Variability
5-33