Transcript How to measure returns?

Salaar - Finance
INVESTMENTS
BBA
SUMMER Semester 2010
Lahore School of Economics
Salaar farooq – Assistant Professor
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RISK & RETURN
of
Investing
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Returns & Risks from Investing
Learning Objectives
 What is return?
 What is risk?
 Sources of risk?
 Types of risk?
 How to measure risk?
 How to measure returns?
 Realized returns & risks from investing
 Practice Problems
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Returns
Objective of Investors ?
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Returns
Objective of Investors
 To maximize expected returns
 Constraint: risk
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Returns
Components of investment returns ?
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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
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Returns
Components of investment returns
 Total Return = Yield + Price Change (CG)
Yield can be 0 or +
CG can be 0,+ or -
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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?
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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
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What is Risk?
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What is Risk?
UNCERTAINTY OF FUTURE OUTCOMES
Definition of Risk:
Risk is the Probability…
ACTUAL OUTCOME will be different from EXPECTED OUTCOME.
Which outcome are we discussing?
Future Returns
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Risk exposure involves Future time
RISK of deviation
Expected Outcome
1,2…n (return)
Decision
T= Future
T=0
Risk Calculation is on Historical Data
T=-n
T=0
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What are the Sources of Risk?
An Overview
– Price risk
– Interest Rate risk
– Market risk
– Inflation risk
– Business risk
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What are the Sources of Risk?
An Overview
– 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
(interest rates)
– Business risk
Variability in ER due to exposure to a particular industry
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What are the Sources of Risk?
An Overview
– Financial risk
– Liquidity risk
– Exchange rate risk
– Country risk (political risk)
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What are the Sources of Risk?
An Overview
– Financial risk
Arises due to debt financing.
Variability in ER due to leverage
– Liquidity risk
Variability in ER due to inability to trade in secondary
mkts.
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.
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What are the Sources of Risk?
Summary
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Price risk
Interest Rate risk (affects market value & resale price)
Market risk (overall market effects)
Inflation risk (purchasing power variability)
Business risk (unique risk)
Financial risk (tied to debt financing)
Liquidity risk (time & price concession to sell securities)
Exchange rate risk (fx)
Country risk (political risk)
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What Types of Risk are there?
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What Types of Risk are there?
– 2 Main Types
– Systematic risk: (MKT)
also called market risk or non-diversifiable risk.
Caused by the market as a whole
– Non-Systematic risk: (COMPANY)
also called non-market risk or diversifiable risk.
This risk is caused by factors unique to the company
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Types of Risk
Average annual
standard deviation (%)
49.2
Diversifiable risk (unique risk)
23.9
19.2
Non-diversifiable
risk (market risk)
1
10
20
30
40
1000
Number of stocks
in portfolio
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How do we measure Risk?
• Probability distributions
Probability distributions combine
outcomes to probabilities
Multiply possible returns by associated probabilities
and sum them
The probabilities must sum to 1.0
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Prob.
Returns
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How do we measure Risk?
The risk for a security can be calculated
using
Standard Deviation measure
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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
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How do we use information regarding risk?
Analytical Development
• In Finance, decision rules are based on benchmark or
alternative comparisons.
E.g. consider the statement:
• A: an investment (IND: X) has an ER of 35% with SD of 30%
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How do we use this information regarding risk?
Analytical Development
• In Finance, decision rules are based on benchmark or
alternative comparisons.
E.g. consider the statement:
• A: an investment (IND: X) has an ER of 35% with SD of 30%
• B: an investment (IND: X) has an ER of 35% with SD of 15%
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How do we use this information regarding risk?
Analytical Development
• In Finance, decision rules are based on benchmark or alternative
comparisons.
E.g. consider the statement:
• A: an investment (IND: X) has an ER of 35% with std dev of 30%
• B: an investment (IND: X) has an ER of 35% with std dev of 15%
• C: IND X has an industry AR of 50% with std dev of 15%.
Given the alternatives, & ATE both A & B are inferior.
• Therefore, one question you must always ask regarding risk is
“what are the alternatives or benchmarks to compare with?”
M-10
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SUMMARY STATISTICS FOR RETURNS
 Arithmetic mean : The mean return
 Geometric mean
Compounded rate of return over time – r at which end value is obtained.
G = (1+TR)^(1/n) – 1
1+TR = RR is used since –ve TR’s cannot be used for G
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SUMMARY STATISTICS FOR RETURNS
Arithmetic mean vs geometric mean
 When should you use the AM or GM?
 AM:
A) better measure of average performance over single periods.
B) Best estimate of ER for next period
 GM:
a) better measure of the change in wealth over multiple periods
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Risk Premiums
 Risk Premium
 Equity Risk Premium
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Risk Premiums
 Risk Premium
Additional Compensation for assuming risk
 Equity Risk Premium
Difference between return on stocks & the risk-free rate (t-bills)
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Risk Premiums
 Equity Risk Premium
ERP = ( (1+TR stock) / (1+Rf) ) – 1
M6
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PROBLEM # 9 Calculating ERP
Common stocks had a return of 10.0466% over 80yrs. Tbills had a return of 4.0358% over the same period.
a) What is the historical Equity Risk Premium?
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PROBLEM # 9
Calculating ERP
Common stocks had a return of 10.0466% over
80yrs. T-bills had a return of 4.0358% over the
same period.
a)What is the historical Equity Risk
Premium?
ERP = 1.100466/1.040358 – 1 = .0578 = 5.78%
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Part II
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MEASURING RETURNS
TOTAL RETURN
 Total return (TR)
A %age relating ALL C/F’s received by an investor to the
purchase price during a period.
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MEASURING RETURNS
TR
FORMULA
 Total return (TR)
TR = (All C/F’s + Price Changes) / purchase Px.
Or
TR = C + (P.e – P.b) / Pb
E = end period b= beginning period
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MEASURING RETURNS
Advantages of TR
 Gives a measure of return in %
 Allows comparison b/w different assets
 Includes realized & unrealized gains
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PROBLEM # 1
Example TR
Suppose you purchase a 10% coupon Bond at
$960. After a year you sell it for $1020.
a)What is the TR?
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PROBLEM # 1
Example TR
Suppose you purchase a 10% coupon Bond at
$960. After a year you sell it for $1020.
a)What is the TR?
TR = 100+(1020-960) / 960 = 100+60 / 960 =
0.1667 or 16.67%
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PROBLEM # 2
Example TR
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.
a)What is the TR?
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PROBLEM # 2
Example TR
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.
a)What is the TR?
2 + (26-30) / 30 = 2 + (-4) / 30 = -0.0667 = (6.67%)
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MEASURING RETURNS
RETURN RELATIVE
 Return Relative (RR)
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 which cannot use –ve returns
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MEASURING RETURNS
Return Relative - Formula
 RR
RR = TR in decimal + 1.0
Therefore,
TR in decimal = RR – 1.0
Since its expressed as 1 base, modified TR
RR = (C+ Pe) / Pb
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PROBLEM # 3
Example RR
If the TR is 10%, & -9.07% then,
a)What is the RR?
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PROBLEM # 3
Example RR
If the TR is 10%, & -9.07% then,
a)What is the RR?
10% TR,
-9.07% TR,
RR = TR + 1 = 0.1 + 1 = 1.1
RR = TR + 1 = -.0907 + 1 = 0.9093
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PROBLEM # 4
Example RR
If the Dividend is 13.79 & the security price is
615.93. One year earlier it was 459.27,
a)What is the RR?
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PROBLEM # 4
Example RR
If the Dividend is 13.79 & the security price is
615.93. One year earlier it was 459.27,
a)What is the RR?
RR = (615.93 – 459.27 + 13.79) / 459.27 = 1.3711
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MEASURING RETURNS
Cumulative Wealth Index
 CWI
Cumulative wealth over time, given an initial wealth & a series of
returns on an asset.
WHY?
TR tracks changes in wealth, CWI measures LEVELS of wealth,
rather than changes.
Measures the effect of returns on the wealth.
Uses $1 as the beginning base amount for convenience.
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MEASURING RETURNS
CWI - Formula
 CWI
CWI = WI.(1+TR1).((1+TR2) … n
where,
CWI = end of period wealth
WI = beginning index value usually 1
TRn = Periodic TR’s in decimal form
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PROBLEM # 5
Example of CWI
The values of the S&P were as follows:
1990 = 330.22
& TR= -3.14%
1991 = 417.09
= 30%
1992 = 435.71
= 7.43%
1993 = 466.45
= 9.94%
a)
b)
What are the Return Relatives?
What is the CWI?
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PROBLEM # 5 Example of CWI
The values of the S&P were as follows:
1990 = 330.22 & TR = -3.14%
1991 = 417.09
= 30%
1992 = 435.71
= 7.43%
1993 = 466.45
= 9.94%
a) What are the Return Relatives?
RR’s = -.0314+1=0.969, 0.3+1=1.3, 0.0743+1=1.0743,
0.0994+1=1.0994
b) What is the CWI? 1(.969)(1.3)(1.0743)(1.0994) = 1.4878
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MEASURING RETURNS
CWI - NOTE
 Calculating TR’s from CWI
TRn = (CWI n / CWI n-1) – 1
TRn = total return for period n
CWI = cumulative wealth index at n
TRn = Periodic TR’s in decimal form
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PROBLEM # 6
Getting TR from CWI
Suppose CWI,2005 = 1.4878 & CWI,2006 = 2.5787,
a)what’s the TR?
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PROBLEM # 6
Getting TR from CWI
Suppose CWI,2005 = 1.4878 & CWI,2006 = 2.5787,
a)what’s the TR?
2.5787/1.4878 – 1 = 1.7332 – 1 = 73.32%
M11
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TAKING A GLOBAL PERSPECTIVE
 Investing Internationally
 Exchange rate risk?
 Calculating TR for foreign positions
NOTE: Foreign currency is stated in domestic terms
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MEASURING RETURNS
Formula – Fx Positions TR
 TR return in domestic terms
TRd = (RR x Ending Value Fx/Begin Value Fx) -1
TRd = total return in domestic terms
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PROBLEM # 8
FX returns
Suppose you are in Pk & invest in Walmart at $ 50
when the value of 1 dollar in Rs. is 60. One year
later, Walmart is $55 & there is no dividend. The
dollar is now Rs. 57, which means the Rs
appreciated against the dollar.
a)Calculate the RR for Walmart?
b)What is your TR in Rs after currency
adjustment?
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PROBLEM # 8
FX returns
Suppose you are in Pk & invest in Walmart at $ 50
when the value of 1 dollar in Rs. is 60. One year
later, Walmart is $55 & there is no dividend. The
dollar is now Rs. 57, which means the Rs
appreciated against the dollar.
a)Calculate the RR for Walmart?
RR = 55/50 = 1.10
b) What is your TR in Rs(domestic) after
currency adjustment?
1.1 x (57/60) – 1 = 1.1*.95 = 1.045 – 1 = .045 = 4.5%.
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Some Realities of risk in the real world
Realized Returns Over Long Periods
(1920-2002)
• Some benchmarks for Returns & Risks on major assets
over long periods:
– Common stocks--approx 13% std dev 20% (more risky)
– AAA corporates—approx 6% std dev 9%
– Treasury bonds—approx 5.4% std dev 8%
– T-bills—
approx 4% std dev 3%
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Summary
We have learnt the following about Risk:
•
•
•
•
What is Risk? Uncertainty about future outcomes
How do we define it? The chance of Actual VS Expected
How do we measure it? Standard Deviation
How do we use this information to make financial
decisions? (benchmarks)
• What are the sources of risk? Price,market,interest rate, etc
• How many types of risk are there? Unique & Market
• What are benchmark Realities of Risk? Stocks, Bonds, T-bills
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• END