How to Value Bonds

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Recent Trend in Stock Valuation By Charnwut
Roongsangmanoon
Ph.D. (Finance) NTU, Singapore 2005 M.B.A.
(Finance) NIDA, Thailand 1997 B.Eng. (Chemical
Engineering) CU, Thailand 1993
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Outline
INTRODUCTION
1. Basic Equity Valuation 2. Equity Valuation in
a Complex Market 3. Capital Asset Pricing
Model 4. Multifactor Models 5. Implementing an
Integrated Investment Process 6. Conclusions
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1. Basic Equity Valuation
INTRODUCTION
Stock Valuation and Stock Selection - Aim of
equity valuation ? To determine fair price. - Aim
of active equity selection ? To detect
mispricing. This detection provides superior
returns as their prices correct to fair value.
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1.1 Basic Asset Valuation
INTRODUCTION
PV present value of asset CFi net cash
flows at period i ri (required) rate of return
at period i
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1.2 The Present Value of Common Stock
INTRODUCTION
P0 present value of the stock Divi net
cash flows at period i ri (required) rate
of return on the stock at period i
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1.2 The Present Value of Common Stock
INTRODUCTION
Zero Growth Constant Growth Two-Differential
Growth
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Where does r come from?
INTRODUCTION

• r can be divided into two parts
• Dividend yield
• Growth rate (in dividends)
• In practice, a great deal of estimation error
  involves in estimating r.

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1.3 Other Valuation Techniques

• Price/Earning Ratio
• The price earnings ratio is the multiple
• - Calculated as current stock price divided by
  annual EPS

Firms whose shares are in fashion sell at high
multiples. Growth stocks for example. Firms
whose shares are out of favor sell at low
multiples. Value stocks for example.
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1.3 Other Valuation Techniques

• 2. Price/Cash Flow Ratio
• cash flow net income depreciation cash flow
  from operations or operating cash flow
• 3. Price/Sales
• current stock price divided by annual sales per
  share
• 4. Price/Book (or Market to Book Ratio)
• price divided by book value of equity, which is
  measured as assets liabilities

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1.4 Stock Returns

• Dollar Returns
• the sum of the cash received and the change in
  value of the stock, in dollars.

• Percentage Returns
• the sum of the cash received and the change in
  value of the stock divided by the original
  investment.

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1.4 Stock Returns

• Dollar Return Dividend Change in Market Value

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2. Equity Valuation in a Complex Market
INTRODUCTION
The equity market is a complex system Random
systems, e.g. Brownian motion, cannot be modeled
and are unpredictable. Ordered systems are
determined by some variables. The complex system
of equity market can be at least partly modeled,
but only with great difficulty.
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2.1 Return on Size-Ranked Portfolio SET
INTRODUCTION
Data Thai Securities (Apr 2000 Dec
2004) Source MFC Quantitative Research
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2.1 Risk on Size-Ranked Portfolio SET
INTRODUCTION
Data Thai Securities (Apr 2000 Dec
2004) Source MFC Quantitative Research
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2.1 Small Capitalization Performance SET
INTRODUCTION
Source MFC Quantitative Research
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2.2 Why is the equity market complex?
Arbitrage b/w intrinsic valuation and mispricing
due to segment concentration
Different investment styles
Markets tenuous balance
integrating
integrating
This tenuous balance between integration and
segmentation is one dimension of its complexity.
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2.3 What should a smart investor do?
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2.4 Stock Valuation in a Complex Market
INTRODUCTION
Situation Different investment styles cause
market segmentation while other forces (e.g.
arbitrage opportunities) act to integrate
it. Need Investors need an approach that
accounts for broad stock behavior, without losing
sight of significant differences in price
behavior of particular segments.

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3. Capital Asset Pricing Model
INTRODUCTION

• Return and risk of one security
• - Expected return the measure of the
  securitys return.
• - Variance the measure of the securitys risk.
• Return and risk of securities as part of a
  portfolio
• Key The contribution of each security to the
  expected return and the risk of the portfolio.
• - A securitys expected return the measure of
  a securitys contribution to the expected return
  on the portfolio.
• - A securitys beta the measure of a
  securitys contribution to the risk of the
  portfolio.

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Outline of CAPM
INTRODUCTION
3.1 Individual Securities 3.2 Expected Return and
Covariance 3.3 Return and Risk for Portfolios 3.4
Efficient Set for Two Assets 3.5 Efficient Set
for Many Securities 3.6 Riskless Borrowing and
Lending 3.7 Market Equilibrium 3.8 Risk -
Expected Return Relation
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3.1 Individual Securities
INTRODUCTION

• Characteristics of individual securities
• Expected Return
• Variance and Standard Deviation
• Covariance and Correlation

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3.2 Expected Return and Covariance
INTRODUCTION
Consider the following two risky asset world.
There is a 1/3 chance of each state of the
economy and the only assets are a stock fund and
a bond fund.
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3.2 Expected Return and Covariance
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3.2 Expected Return and Covariance
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3.2 Expected Return and Covariance
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3.3 Return and Risk for Portfolios
The rate of return on the portfolio is a weighted
average of the returns on the stocks and bonds in
the portfolio
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3.3 Return and Risk for Portfolios
The expected rate of return on the portfolio is a
weighted average of the expected returns on the
securities in the portfolio.
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3.3 Return and Risk for Portfolios
The variance of the rate of return on the two
risky assets portfolio is
where ?BS is the correlation coefficient between
the returns on the stock and bond funds.
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3.3 Return and Risk for Portfolios
Observe the decrease in risk that diversification
offers. An equally weighted portfolio (50 in
stocks and 50 in bonds) has less risk than
stocks or bonds held in isolation.
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3.4 Efficient Set for Two Assets
100 stocks
100 bonds
Note that some portfolios are better than
others. They have higher returns for the same
level of risk or less.
These compromise the efficient frontier.
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Two-Security Portfolios with Various Correlations
100 stocks
return
? -1.0
? 1.0
? 0.2
100 bonds
?

• Relationship depends on correlation coefficient
• -1.0 lt r lt 1.0
• If r 1.0, no risk reduction is possible
• If r 1.0, complete risk reduction is possible

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Portfolio Risk as a Function of the Number of
Stocks in the Portfolio
In a large portfolio the variance terms are
effectively diversified away, but the covariance
terms are not.
?
Diversifiable Risk Nonsystematic Risk Firm
Specific Risk Unique Risk
Portfolio risk
Nondiversifiable risk Systematic Risk Market
Risk
n
Thus diversification can eliminate some, but not
all of the risk of individual securities.
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3.5 Efficient Set for Many Securities
return
Individual Assets
?P

• Consider a world with many risky assets we can
  still identify the opportunity set of risk-return
  combinations of various portfolios.

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3.5 Efficient Set for Many Securities
return
minimum variance portfolio
Individual Assets
?P

• Given the opportunity set we can identify the
  minimum variance portfolio (MVP).

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3.5 Efficient Set for Many Securities
return
efficient frontier
minimum variance portfolio
Individual Assets
?P

• Efficient frontier is the section of the
  opportunity set above MVP.

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Optimal Portfolio with Risk-Free Asset
return
100 stocks
rf
100 bonds
?

• In addition to stocks and bonds, consider a world
  that also has risk-free securities like T-bills

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3.6 Riskless Borrowing and Lending
CML
return
100 stocks
Balanced fund
rf
100 bonds
?

• Now investors can allocate their money across the
  T-bills and a balanced mutual fund

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3.6 Riskless Borrowing and Lending
CML
return
efficient frontier
rf
?P

• With a risk-free asset available and the
  efficient frontier identified, we choose the
  capital allocation line with the steepest slope

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3.7 Market Equilibrium
return
CML
efficient frontier
M
rf
?P

• With the capital allocation line identified, all
  investors choose a point along the linesome
  combination of the risk-free asset and the market
  portfolio M. In a world with homogeneous
  expectations, M is the same for all investors.

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The Separation Property
CML
return
efficient frontier
M
rf
?P

• The Separation Property states that the market
  portfolio, M, is the same for all investorsthey
  can separate their risk aversion from their
  choice of the market portfolio.

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The Separation Property
CML
return
efficient frontier
M
rf
?P

• Investor risk aversion is revealed in their
  choice of where to stay along the capital
  allocation linenot in their choice of the line.

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3.7 Market Equilibrium
CML
return
100 stocks
Balanced fund
rf
100 bonds
?

• Just where the investor chooses along the Capital
  Asset Line depends on his risk tolerance. The big
  point though is that all investors have the same
  CML.

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Optimal Portfolio with Risk-Free Asset
CML1
CML0
return
100 stocks
Second Optimal Risky Portfolio
First Optimal Risky Portfolio
100 bonds
?

• By the way, the optimal risky portfolio depends
  on the risk-free rate as well as the risky assets.

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Definition of Risk When Investors Hold the Market
Portfolio

• Researchers have shown that the best measure of
  the risk of a security in a large portfolio is
  the beta (b)of the security.
• Beta measures the responsiveness of a security to
  movements in the market portfolio.

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Estimating b with regression
Security Returns
Return on market
Ri a i biRm ei
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Estimates of b for Selected Stocks
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Expected Return on a Security

• This formula is called the Capital Asset Pricing
  Model (CAPM)

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3.8 Risk-Expected Return Relation
Expected return
b
1.0
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INTRODUCTION
4. Multifactor Models
Why do we need multifactor models? CAPM does not
perform well. Examples of Proposed Models -
Three-factor model of FamaFrench Beta, Size
(SML) Book to Market(BTM) - BARRA, Wilshire,
Goldman Sachs etc.
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4.1 Systematic Risk and Betas
INTRODUCTION

• The beta coefficient, b, tells us the response of
  the stocks return to a systematic risk.
• In the CAPM, b measured the responsiveness of a
  securitys return to a specific risk factor, the
  return on the market portfolio.

• We shall now consider many types of systematic
  risk.

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4.2 Portfolios and Factor Models
INTRODUCTION

• Now let us consider what happens to portfolios of
  stocks when each of the stocks follows a
  one-factor model.
• We will create portfolios from a list of N stocks
  and will capture the systematic risk with a
  1-factor model.
• The ith stock in the list has returns

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4.3 Relationship Between the Return on Common
Factor Excess Return
Excess return
If we assume that there is no unsystematic risk,
then ei 0
The return on the factor F
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4.3 Relationship Between the Return on Common
Factor Excess Return
Excess return
Different securities will have different betas
The return on the factor F
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4.4 Portfolios and Diversification

• Portfolio return is the weighted average of
  returns on individual assets in the portfolio

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4.4 Portfolios and Diversification

• The return on any portfolio is determined by
  three sets of parameters

In a large portfolio, the third row of this
equation disappears as the unsystematic risk is
diversified away.
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4.4 Portfolios and Diversification

• So the return on a diversified portfolio is
  determined by two sets of parameters
• The weighed average of expected returns.
• The weighted average of the betas times the
  factor F.

In a large portfolio, the only source of
uncertainty is the portfolios sensitivity to the
factor.
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INTRODUCTION
4.5 Types of Multifactor Models
Three types Statistical factor
models Macroeconomic factor models Fundamental
factor models
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INTRODUCTION
4.6 Statistical factor models
Factor analysis Aim to explain the linear
relation of observed stock returns with factor
realizations. Pro purely statistical
tools Con problem of interpretation Example
principal component analysis
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4.7 Macroeconomic factor models
INTRODUCTION
Aim to determine macroeconomic variables that
are pervasive in explaining historical stock
returns. Example BIRR model (five variables)
confidence, time horizon, inflation, business
cycle and market timing. RAM model (six
variables) economic growth, business cycle,
long-term and short-term interest rate, inflation
shock, change in US dollar.
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4.8 Fundamental factor models
INTRODUCTION
Aim to relate company, industry and market
attributes to cross-section of stock
returns. Example Wilshire Atlas Factor
(seven) E/P, BV/P, market capitalization, net
earning revision reversal, earnings torpedo,
historical beta.
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4.8 Fundamental Factor Models
Return Ranking
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Goldman Sachs CORE risk Model
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MFC Factor Model
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MFC Model Performance Thailand
Source MFC Quantitative Research
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MFC Model Performance Asian Countries
Source MFC Quantitative Research
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5. Implementing an Integrated Investment Process
INTRODUCTION
Aim - to relate risk factors to average stock
returns. - to do stock selection Procedure -
Research - Implementation - Performance
Attribution  - Process Enhancement
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5.1 Procedure
INTRODUCTION
1. Research-Developing the strategy     - Constru
cting the component models - Combining the
models - Statistical evaluation of the models
- Back-testing portfolio simulation 2.
Implementation-Putting it into action
Portfolio construction-Optimization Portfolio
analysis
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5.1 Procedure
INTRODUCTION
3. Performance Attribution-Evaluating the
strategy       Portfolio performance       Model
performance 4. Process Enhancement-Closing the
loop
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6. Conclusions

• An approach to stock selection that has both
  breadth of inquiry and depth of focus can enhance
  the number and goodness of investment insights.
• Although the approach requires more time, effort
  and ability, it will be better positioned to
  capture the complexities of security pricing.

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