Transcript A: An investment

BSC/BBA III
Summer Semester 2010
Lahore School of
Economics
Chap 06
Risks & Returns from
Investing
Risk and Return
Overview & Background
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Investing involves decisions for the future
Key variable with future = Uncertainty
Expected Returns is basis of Investments
Biggest Threat: UNCERTAINTY = RISK
Uncertainty represents RISK conceptually
Investors must estimate & manage Risk
Risk & Return are opposite sides of the same coin
R&R involve a trade-off with each other
Returns
Objective of Investors ?
Returns
Objective of Investors
 To maximize expected returns
 Constraint: risk
Returns
Components of investment returns ?
Returns
Components of investment returns
 Yield
Income component of a security’s return from cash flows
Relates the C/F’s to the price of the security
 Capital gain (loss)
Change in price of a security over time
Returns
Components of investment returns
Total Return = Yield + Price Change (CG)
Yield can be 0 or +
CG can be 0,+ or -
Returns
Examples of components
 A Bond purchased at par held to maturity: ?
 A Bond purchased for $800 & held till maturity?
 A non-dividend stock?
 A dividend paying stock?
Returns
Examples of components
 A Bond purchased at par held to maturity? Yield only
 A Bond purchased for $800 & held till maturity? Y+PG
 A non-dividend stock? PG only
 A dividend paying stock? Y+PG
What is Risk?
What is Risk?
 UNCERTAINTY OF FUTURE OUTCOMES
Definition of Risk:
Risk is the Probability (chance) the ACTUAL
OUTCOME will be different from the
EXPECTED OUTCOME.
 Which outcome are we discussing?
Specifically, investors are worried the actual outcome (of
returns from their investments) will be less than the
expected returns.
Finance involves Future time
Decision
RISK of deviation
UNCERTAINTY
Expected
Outcome 1,2…n
(return)
T= Future
T=0
Risk Calculation is based on Historical Data
T=-n
T=0
What are the Sources of Risk?
An Overview
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Price risk
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Interest Rate risk
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Market risk
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Inflation risk
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Business risk
What are the Sources of Risk?
An Overview
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Price risk
Variability in security’s returns due to price
fluctuations
Interest Rate risk
Variability in ER due to changes in interest rates
Market risk
Variability in ER due to changes in overall market
Inflation risk
Variability in ER due to changes in purchasing
power
Business risk
Variability in ER due to exposure to a particular
industry
What are the Sources of Risk?
An Overview
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Liquidity risk
Variability in ER due to inability to trade in
secondary markets.
Time & price concession required to sell securities
Exchange rate risk
Variability in ER due to currency fluctuations.
Country risk (political risk)
Variability in ER due to instability of the political
system.
Financial Risk
Effects of Financial Leverage?..
 Financial Leverage refers to the extent to which a firm
relies on Debt.
 More Debt means MORE leverage
 The larger the proportion of assets financed by debt,
the larger the variability in returns, other things being
equal.
Financial Risk - Example
 We consider case of company X which has no debt & is
considering restructuring to include debt in its capital
structure.
 We look at DEBT & NO DEBT situations
 Taxes are ignored
Financial Risk - Example
Current
Assets
Proposed
$8,000,000
$8,000,000
0
4,000,000
8,000,000
4,000,000
0
1
Share Price
20
20
# of Shares
400,000
200,000
10%
10%
Debt
Equity
Debt-Equity
Ratio
Interest Rate
Financial Risk - Example
Current Capital Structure: No Debt
Recession
EBIT
Normal
Expansion
$500,000 $1,000,000 $1,500,000
Interest
?
?
?
Net Income
?
?
?
ROE
?
?
?
EPS
?
?
?
Financial Risk - Example
Current Capital Structure: No Debt
Recession
EBIT
Normal
Expansion
$500,000 $1,000,000 $1,500,000
0
0
0
500,000
1,000,000
1,500,000
ROE
6.25%
12.5%
18.75%
EPS
1.25
2.50
3.75
Interest
Net Income
Financial Risk - Example
Proposed Capital Structure: Debt - $4
Million
Recession
EBIT
Normal
Expansion
$500,000 $1,000,000 $1,500,000
Interest
?
?
?
Net Income
?
?
?
ROE
?
?
?
EPS
?
?
?
Financial Risk - Example
Proposed Capital Structure: Debt - $4
Million
Recession
EBIT
Normal
Expansion
$500,000 $1,000,000 $1,500,000
Interest
400,000
400,000
400,000
Net Income
100,000
600,000
1,100,000
ROE
2.50%
15.50%
27.50%
EPS
0.50
3.00
5.50
MEASURING RETURNS
 Total return
 Return relative
 Cumulative wealth index
 Inflation adjusted returns
TOTAL RETURN
The Total Return for a given time period is a decimal number
(or a percentage) relating all the cash flows received by an
investor during designated time period to the purchase price
of the Asset.
TR = Any Cash Payment Received + Price change over time period
Price at which the Asset is Purchased
Or
TR = CFt + (P.e – P.b)
PB
=
CFT + PC
PB
Total Return - Advantages
1. It is all inclusive
2. Allows comparison b/w different assets
3. Includes realized & unrealized gains
Total Return - Example
Suppose you purchase a 10% coupon Bond at $960. After
a year you sell it for $1020. What is the TR?
Total Return - Example
Suppose you purchase a 10% coupon Bond at $960. After
a year you sell it for $1020. What is the Total Return?
TR = {100 + (1020-960)} / 960
= {100 + 60 }/ 960
= 0.1667 or 16.67%
Total Return - Example
Suppose you purchase 100 shares of JNJ at $30 per
share. After a year you sell for $26. A dividend of $2 is
paid during the year. What is the TR?
Total Return - Example
Suppose you purchase 100 shares of JNJ at $30 per
share. After a year you sell for $26. A dividend of $2 is
paid during the year. What is the TR?
TR = {2 + (26-30)}/ 30
= {2 + (-4)} / 30
= -0.0667 or (6.67%)
RETURN RELATIVE
Total return of an investment for a given period expressed
on a base of 1.0
Why?
To calculate cumulative wealth index OR geometric means,
both of which cannot use negative returns.
RR = TR in decimal + 1.0
= {C + PE}/PB
Or,
TR = RR – 1.0
RETURN RELATIVE Example
If the TR is 10% & -9.07% then, What is the RR?
RETURN RELATIVE Example
If the TR is 10% & -9.07% then, What is the RR?
CASE 1:
TR = 10%
RR
= TR + 1
= 0.1 + 1
= 1.1
Case 2:
TR= -9.07%
RR
= TR + 1
= -.0907 + 1
= 0.9093
RETURN RELATIVE Example
If Dividend paid is 13.79 & the security price is 615.93.
One year earlier it was 459.27, What is the RR?
RETURN RELATIVE Example
If Dividend paid is 13.79 & the security price is 615.93.
One year earlier it was 459.27, What is the RR?
RR = (615.93 + 13.79) / 459.27
= 1.3711
Cumulative Wealth Index
Cumulative wealth index measures the cumulative
effect of returns over time, given some stated beginning
dollar amount invested, which typically is shown as $1
for convenience.
WHY?
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TR tracks changes in wealth, CWI measures LEVELS
of wealth, rather than changes.
Measures ending wealth (cumulative wealth) over
some period on the base of beginning $ 1.
Cumulative Wealth Index
CWI = WI0(1+TR1)(1+TR2) … (1 + TRN)
where,
CWI
WI0
TRN
= end of period wealth
= beginning index value usually $1
= Periodic TR’s in decimal form
Cumulative Wealth Index Example
Values & Total Returns for S&P500 for past few years
were as follows:
Values
Total Return
1990: 330.22
-3.14%
1991: 417.09
30%
1992: 435.71
7.43%
1993: 466.45
9.94%
What is the CWI?
Cumulative Wealth Index Example
Values & Total Returns for S&P500 for past few years
were as follows:
Values
Total Return
1990: 330.22
-3.14%
1991: 417.09
30%
1992: 435.71
7.43%
1993: 466.45
9.94%
What is the CWI?
CWI
= 1(.969)(1.3)(1.0743)(1.0994)
= 1.4878
Cumulative Wealth & Total
return
TRN
= (CWIN / CWI N-1) – 1
Where,
TRN
= Total Return for period N
CWIN-1 = Cumulative Wealth Index at
period N - 1
CWIN = Cumulative Wealth Index at
period N
Cumulative Wealth & Total
return - Example
Suppose CWI in 2005 = 1.4878 &
CWI in 2006 = 2.5787, what’s the TR in year 2006?
Cumulative Wealth & Total
return - Example
Suppose CWI in 2005 = 1.4878 &
CWI in 2006 = 2.5787, what’s the TR in year 2006?
TR2006
= (2.5787/1.4878) – 1
= 1.7332 – 1
= 73.32%
International Returns &
Currency Risk
Currency Risk is the Risk that the change in the value of
the domestic & the foreign Currency involved will be
unfavorable.
When investors buy & sell assets in other countries, they
must consider exchange rate or Currency Risk.
Why?
International Returns &
Currency Risk
When investors buy & sell assets in other countries,
they must consider exchange rate or Currency Risk.
Why?
When investors invest in Assets denominated in
Foreign currency, they are actually investing in two
Assets:
1.
Financial security in Foreign Country
2.
Foreign Currency
Thus,
They need to be concerned with the Risks & Returns
of both Assets!
Currency Adjusted RETURNS
1.
2.
As investors have invested in two Assets, their Total
Return will also comprise of the returns that they are
able to earn on both investments:
Return on Foreign Asset
Return on Foreign Currency
Currency Adjusted RETURNS
1.
2.
As investors have invested in two Assets, their Total
Return will also comprise of the returns that they are
able to earn on both investments:
Return on Foreign Asset
Return on Foreign Currency
Thus,
TR in Domestic terms = Return earned on Foreign Asset +
Return earned on Foreign
Currency Investment
Currency Adjusted RETURNS
Thus,
TR in Domestic terms (Approximately)
=
[{CFT + (PE – PB)}/PB]
Plus
{Change in Foreign Currency
Beginning Value of Foreign Currency}]
Where,
Foreign Currency is stated in DC/FC Units
Currency Adjusted RETURNS
Or,
Total Return in Domestic Terms (Exactly)
= {RR earned on Foreign Asset
Multiplied by
(Ending Value of Foreign Currency/ Beginning
Value of
Foreign
Currency)}
Minus
1
Currency Adjusted RETURNS Example
An investor in Pakistan invests in Walmart at $50 when
exchange rate was Rs.60/$. One year later, Walmart is
$55 & there is no dividend. The Exchange rate is now Rs.
57/$. Calculate Approximate Total Return for a
Pakistani investor?
Currency Adjusted RETURNS Example
An investor in Pakistan invests in Walmart at $50 when
exchange rate was Rs.60/$. One year later, Walmart is
$55 & there is no dividend. The Exchange rate is now Rs.
57/$. Calculate Approximate Total Return for a
Pakistani investor?
TR
= Return on Walmart + Return on FC
Return on Walmart = (55 – 50)/50
= 10%
Return on FC
= (57 – 60)/60
= -5%
TR
= 10% + (-5%)
= 5%
Currency Adjusted RETURNS Example
An investor in Canada invests in Walmart (US Co.) at
$35 when exchange rate was US$ 1.27/C$. One year
later, Walmart is $45 & there was $5 dividend. The
Exchange rate is now US$ 1.77/C$. Calculate
Approximate Total Return for a Canadian investor?
Currency Adjusted RETURNS Example
An investor in Canada invests in Walmart (US Co.) at
$35 when exchange rate was US$ 1.27/C$. One year
later, Walmart is $45 & there was $5 dividend. The
Exchange rate is now US$ 1.77/C$. Calculate
Approximate Total Return for a Canadian investor?
TR
= Return on Walmart + Return on FC
Return on Walmart = (45 – 35+5)/35
= 42.86%
Return on FC
= (0.5650 – 0.7874)/0.7874
= -28.24%
TR
= 42.86% + (-28.24%)
= 14.61%
Currency Adjusted RETURNS Example
An investor in Canada invests in Walmart (US Co.) at
$35 when exchange rate was Pak Re 60/US$ & Pak Re
75/C$. One year later, Walmart is $45 & there was $5
dividend. The Exchange rate is now Pak Re 65/US$ &
Pak Re 75/C$. Calculate Approximate Total Return for a
Canadian investor?
Currency Adjusted RETURNS Example
An investor in Canada invests in Walmart (US Co.) at
$35 when exchange rate was Pak Re 60/US$ & Pak Re
75/C$. One year later, Walmart is $45 & there was $5
dividend. The Exchange rate is now Pak Re 65/US$ &
Pak Re 75/C$. Calculate Approximate Total Return for a
Canadian investor?
TR
= Return on Walmart + Return on FC
Return on Walmart = (45 – 35+5)/35
= 42.86%
Return on FC
= (0.8667 – 0.80)/0.80
= 8.34%
TR
= 42.86% + 8.34%
= 51.2%
Summary Statistics for
returns
Investment analysis needs statistics that are used to
describe a series of returns. Two such Measures
include:
1.
2.
Arithmetic Mean
Geometric Mean
Arithmetic Mean
Arithmetic Mean = X
X = Sum of all Values
Number of Observations
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
Arithmetic Mean is a better measure of performance
over single periods.
It is the best estimate of the expected return for next
period.
Geometric Mean
When percentage changes in value over time are
involved, as a result of compounding, Geometric mean is
needed to describe accurately the true average return
over multiple periods.
G = [(1+TR1)(1+TR2) …. (1+TRN)]1/N – 1
The Geometric Mean Returns measures the compound
growth of returns over time (Multiple periods).
Arithmetic Mean Vs
Geometric Mean - Example
Calculate Geometric & Arithmetic Mean using following
data:
Year
Stock 1
1
10%
2
15%
3
-5%
4
7%
5
10%
6
-5%
Arithmetic Mean Vs
Geometric Mean - Example
Arithmetic Mean
= (10 + 15 – 5 +7 + 10 – 5)/6
= 5.33%
Geometric Mean
=[(1+0.1)(1+.15)(1+(0.05))(1+0.07)(1+.10)(1+(-0.05) ] 1/6 – 1
= 5.05%
Inflation adjusted returns

Nominal Returns

Real Returns
Inflation adjusted returns
Nominal Returns
Quoted money returns without inflation adjustments
NOTE: Purchasing power is not adjusted or expressed
Real Returns
Inflation adjusted returns
Nominal returns adjusted for inflation.
Real Return = [(1+ TR)/(1+IF)] – 1
IF = inflation rate
Inflation adjusted returns Example
Suppose the nominal return on a stock is 28.5731%
and the inflation rate is 1.6119%. What is the real
return (Inflation adjusted Return)?
Inflation adjusted returns Example
Suppose the nominal return on a stock is 28.5731%
and the inflation rate is 1.6119%. What is the real
return (Inflation adjusted Return)?
Real Return
= (1.2857/1.0161) - 1
= 1.2653 – 1
= 26.53%
How do we measure Risk?
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
The risk for one security can be calculated using the
standard deviation measure.
Why? Std deviation is the measure of dispersion of a
data set. So, in terms of returns, std deviation actually
represents RISK of that investment.
The standard deviation is a reliable measure of
variability
The standard deviation is a measure of the total risk of
an asset or portfolio.
Variance of return
 R  R 
N
Var R  = σ =
2
i =1
2
i
N 1
where N is the number of returns
Standard deviation of return
SDR = σ = VarR
Measuring Risk- Example
Year
Stock 1
1
10%
2
15%
3
-5%
4
7%
5
10%
6
-5%
Measuring Risk- Example
Step 1:
Calculate Expected Return
Exp. Return = Average of
Past Returns
= 32/6
= 5.33%
Year
Stock 1
1
10%
2
15%
3
-5%
4
7%
5
10%
6
-5%
Measuring Risk- Example
Year
Stock 1
(X – X)
(X – X)2
1
10%
4.67
21.81
2
15%
9.67
93.51
3
-5%
-10.33
106.71
4
7%
1.67
2.79
5
10%
4.67
21.81
6
-5%
-10.33
106.71
Sum of (X – X)2= 353.34
Variance
= 353.34/5 = 70.66
Standard Deviation= (70.66)1/2= 8.41%
How do we use this
information regarding risk?
Analytical Development
In Finance, decision rules are based on benchmark or
alternative comparisons.
Consider the statement:

A: An investment (IND: X) has an ER of 35% with
standard deviation of 30%
How do we use this
information regarding risk?
Analytical Development
In Finance, decision rules are based on benchmark or
alternative comparisons.
Consider the statement:

A: An investment (IND: X) has an ER of 35% with
standard deviation of 30%

B: An investment (IND: X) has an ER of 35% with
standard dev of 15%
How do we use this
information regarding risk?
Analytical Development
In Finance, decision rules are based on benchmark or
alternative comparisons.
Consider the statement:

A: An investment (IND: X) has an ER of 35% with
standard deviation of 30%

B: An investment (IND: X) has an ER of 35% with
standard dev of 15%

C: Investment A & B has an industry AR of 50% with
standard dev of 15%.
Given the alternatives, both A & B are inferior.

Therefore, one question you must always ask regarding
risk is “what are the alternatives or benchmarks to
compare with?”
Risk premiums
A risk premium is the additional return investors expect
to receive by taking on increasing amounts of risk for
example Time Premium, Default Premium, Equity Risk
Premium.
ERP = [(1+TR common stock) / (1+RF)] – 1
Risk premiums - Example
Common stocks had a return of 10.0466% over past 10
years. T-bills had a return of 4.0358% over the same
period. What is the historical Equity Risk Premium?
Risk premiums - Example
Common stocks had a return of 10.0466% over past 10
years. T-bills had a return of 4.0358% over the same
period. What is the historical Equity Risk Premium?
ERP
= (1.100466/1.040358) – 1
= .0578 or 5.78%
Realized Returns & Risks
from Investing
Realized Returns & Risks
from Investing
Thank You for your
Time & Patience 
Assignment # 6 (10 Questions)
Q1: Using the following data, calculate your ending wealth
at the end of year 5, had you initially invested $2500:
Year
Dividend
Beginning
Price
Ending
Price
1
$3
25
45
2
$5
35
40
3
$0
40
45
4
$2
45
36
5
$4
$36
$30
Q2:Assuming EBIT of $2 Million, 2.5 million & 3 million
under Recession, normal & Expansionary economic
environment & using the following data explain how
financial leverage is going to lead to more variability in ER?
Current
Assets
Proposed
$10,000,000
$10,000,000
0
5,000,000
10,000,000
5,000,000
0
1
Share Price
20
20
# of Shares
500,000
250,000
12%
12%
Debt
Equity
Debt-Equity
Ratio
Interest Rate
Assignment # 6 (10 Questions)
Q3:
CWI in year 1 = 1.05643, CWI in year 2 =
1.2568, CWI in year 3 = 1.5878, CWI in
year 4 = 2.3580, TR in Year 5 = 12%, CWI
in year 5 = ?
Q4: Suppose you invest in two Bonds when
Bond A is trading at $950 with a coupon rate of
12% & Bond B is trading at 1150 with a
coupon rate of 8%. After 1 year, you sell Bond
A for $900 & Bond B for $1200, Calculate
Relative Return for two Bonds.
Assignment # 6 (10 Questions)
Q5:
An investor in Canada invests in Walmart Equity at
$45 when exchange rate was $60/C$. One year
later, Walmart is $55 & there is a dividend of $5.
The Exchange rate is now $57/C$. Calculate Exact
Total Return for a Canadian investor?
Q6:
An investor in Japan invests in Canadian Company
at C$350 when exchange rate was Euro60/C$ & Euro
35/Japanese Yen. One year later, Canadian Company is
$355 & there is no dividend. The Exchange rate is now
Euro57/C$ & Euro 45/Japanese yen. Calculate
Approximate Total Return for a Japanese investor?
Assignment # 6 (10 Questions)
Q7:
In year 1, An investor in England invests in 12%
Bond of Japanese Company at Japanese yen 950 when
exchange rate was Euro20/UK pound & Euro
75/Japanese Yen. One year later, British Investor sold
the bond at Japanese Yen 900 when The Exchange rate
was Euro27/UK Pound & Euro 75/Japanese yen. At the
same time, he bought a zero coupon Bond for Japanese
Yen750 & a year later, sold it for Japanese Yen 800
when Exchange Rate was Euro27/UK Pound & Euro
65/Japanese yen Calculate CWI at the end of year 2
using approximate total Returns for British investor
assuming initial investment was Japanese Yen 4750?
Assignment # 6 (10 Questions)
Q8:
In year 1, An investor in Pakistan invests in 10%
Bond of Japanese Company at Japanese yen 950 when
exchange rate was US$ 8.75/Pakistani Re & US$
5.67/Japanese Yen. One year later, British Investor sold
the bond at Japanese Yen 1000 when The Exchange rate
was US$7.25/Pakistani Re & US$ 6.67/Japanese yen. At
the same time, he bought a zero coupon Bond for
Japanese Yen775 & a year later, sold it for Japanese Yen
850 when Exchange Rate was US$8.35/Pakistani Re &
US$ 6.50/Japanese yen Calculate CWI at the end of
year 2 using EXACT total Returns for Pakistani investor
assuming initial investment was Pakistani Rs 5500?
Assignment # 6 (10 Questions)
Q8: Calculate Geometric & Arithmetic Mean & Risk using
following data:
Year
Stock 1
1
8%
2
12%
3
-5%
4
17%
5
12%
6
-15%
Assignment # 6 (10 Questions)
Q9:
Common stocks had a return of 12.0866% over
past 10 years. T-bills had a return of 7.0958% over
the same period. What is the historical Equity Risk
Premium?
Q10:
An investor in India invests in Apple’s 13% Bond at
$875 when exchange rate was $60/Indian Re. One
year later, Bond is trading at is $955. The Exchange
rate is now $67/Indian Re. Calculate Exact Total
Return for a Indian investor? Assuming that
inflation Rate during the year was 12% in India &
in USA it was 5%, also calculate inflation adjusted
Returns for Indian investor?