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Security Analysis & Portfolio
Management
Risk & Return
What is Investment?
Forgoing one now. For many in future.
What is Risk?
• The chance that an investment's
actual return will be different than expected.
Risk includes the possibili...
What is Return?
• The gain or loss of a security in a particular
period. The return consists of the income and
the capital...
Investment Avenues
• Fixed deposits
• Equity
• Fixed income
• Mutual funds
Price and Value
Price is determined by:
Value
• Value of any asset is the amount of cash it can
generate in its future, discounted to present.
Time Value of Money
Discounting Single Period
Discounting Multi-period
Discounting Multi-period
How do you value each?
Probability Distribution of Stock
Returns
Measures of Risk in Academics
1. Absolute Measures
• Variance
• Standard deviation
2. Relative Measures
• Covariance
• Cor...
Variance of Return
• Variance is used in statistics for probability
distribution. Since variance measures the variability
...
Standard Deviation
• Standard deviation is a statistical
measurement that sheds light on historical
volatility. For exampl...
Formula
• Variance:
• Standard deviation:
Covariance
• A measure of the degree to which returns on
two risky assets move in tandem. A positive
covariance means that...
Correlation
• Correlation is computed into what is known as the correlation
coefficient, which ranges between -1 and +1. P...
Covariance & Correlation Formula
Example
Years HUL Nestle Covar Corr
2006 12% 6% 0.012016 73.00%
2007 15% 21%
2008 -22% -6%
2009 6% 23%
2010 23% 15%
Modern Portfolio Theory
Modern Portfolio Theory
– Modern portfolio theory (MPT)—or portfolio theory—
was introduced by Harry Markowitz with his pa...
Applications of MPT
• Asset Allocation
• Asset-liability management
• Optimal Manager Selection
• Index funds/Mutual funds...
Modern Portfolio Theory - In Nut Shell
• Due to scarcity of resources, all economic decisions are made in the
face of trad...
Assumptions of
Markowitz Portfolio Theory
• Investors consider each investment alternative as
being presented by a probabi...
Markowitz Portfolio Theory
• Quantifies risk
• Derives the expected rate of return for a portfolio of
assets and an expect...
Covariance of Returns
• A measure of the degree to which two variables “move
together” relative to their individual mean v...
Covariance and Correlation
• The correlation coefficient is obtained by
standardizing (dividing) the covariance by the
pro...
Correlation Coefficient
• It can vary only in the range +1 to -1.
• A value of +1 would indicate perfect positive correlat...
Portfolio Standard Deviation
Calculation
• Any asset of a portfolio may be described by
two characteristics:
– The expecte...
Portfolio Standard Deviation Formula
ji



ijij
ij
2
i
i
port
n
1i
n
1i
ijj
n
1i
i
2
i
2
iport
rCovwhere
j,andiasset...
Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ...
Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ...
Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ...
Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ...
Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ...
• Suppose two securities have perfect negative
Correlation. Would it make sense to invest in
these two securities only?
Efficient Frontier
for Alternative Portfolios
Efficient Frontier
A
B
C
E(R)
Standard Deviation of Return
MARKOV’S TRILIMMA...
The Efficient Frontier
• The efficient frontier represents that set of
portfolios with the maximum rate of return for
ever...
The Efficient Frontier
and Investor Utility
• An individual investor’s utility curve specifies
the trade-offs he is willin...
Selecting an Optimal Risky Portfolio
)E( port
)E(Rport
X
Y
U3
U2
U1
U3’
U2’
U1’
• The optimal portfolio has the highest u...
The MPT Investment Process
Expected Return
Model
Volatility & Correlation
Estimates
Constraints on
Portfolio Choice
Optima...
Implementation of MPT
• Though the theory is straight forward ….
Implementation is a complication process.
Estimation Issues
• Results of portfolio allocation depend on
accurate statistical inputs
• Estimates of
– Expected return...
The Proof Is In the Pudding
• The MPT has been around for 40 years and is
still going strong
– But, it has flaws
• There a...
An Introduction to Capital Asset
Pricing Model
• The capital asset pricing model is an idealized
portrayal of how financia...
Capital Asset Pricing Model
Risk-Free Asset
• An asset with zero standard deviation
• Zero correlation with all other risky assets
• Provides the risk...
Risk-Free Asset
• Covariance between two sets of returns is


n
1i
jjiiij )]/nE(R-)][RE(R-[RCov
Because the returns for...
Combining a Risk-Free Asset
with a Risky Portfolio
• Expected return
• the weighted average of the two returns
))E(RW-(1(R...
Combining a Risk-Free Asset
with a Risky Portfolio
• The expected variance for a two-asset
portfolio is
211,221
2
2
2
2
2
...
Combining a Risk-Free Asset
with a Risky Portfolio
• Given the variance formula 22
RF
2
port )w1()E( i 
22
RFport )w1(...
Combining a Risk-Free Asset
with a Risky Portfolio
Since both the expected return and the standard deviation of
return for...
Combining a Risk-Free Asset
with a Risky Portfolio
)E( port
)E(Rport
RFR
M
C
A
B
D
Since both the expected return and the...
Combining a Risk-Free Asset
with a Risky Portfolio
)E( port
)E(R port
RFR
M
C
A
B
D
Since both the expected return and th...
Portfolio Possibilities Combining the Risk-Free
Asset and Risky Portfolios on the Efficient
Frontier
)E( port
)E(R port
R...
• Suppose you pay a higher rate of Interest to
buy stock on margin than you receive when
you invest at the risk free rate....
The Market Portfolio
• Because portfolio M lies at the point of tangency, it has
the highest portfolio possibility line
• ...
Statement of CAPM
A model that describes the relationship between
risk and expected return and that is used in the
pricing...
Systematic Risk
• Only systematic risk remains in the market
portfolio
• Systematic risk is the variability in all risky
a...
Number of Stocks in a Portfolio and the
Standard Deviation of Portfolio Return
Standard Deviation of Return
Number of Stoc...
SML
Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of ...
Slope of SML
• Given the SML reflects the return on a given
investment in relation to risk, a change in the slope of
the S...
Properties of any asset on , above or
below the SML
• On the line assets are fairly valued.
• Above the line they are unde...
Assumptions of CAPM
• Aim to maximize economic utilities (Asset quantities are given and
fixed).
• Are rational and risk-a...
Arbitrage Pricing Theory
The arbitrage pricing theory (APT) describes the price where a
mispriced asset is expected to be....
Competition may be
stronger or weaker
than anticipated
Exchange rate
and Political risk
Projects may
do better or
worse th...
Multi-factor Model
• Multi factor models explain risk/reward
relationships based on two or more factors:
Alternatives
– Single Index Market Model
• With assumption that stock returns can be
described by a single market model, t...
Efficient Market Hypothesis
Random Walk Theory
The idea that stocks take a random and unpredictable
path. A follower of the random walk theory believe...
Implications of Randomness
• The fact that the deviations from true value are random implies, in a rough
sense, that there...
What is an efficient market?
• Efficient market is one where the market price is an unbiased
estimate of the true value of...
Definitions of Market Efficiency
• Definitions of market efficiency have to be specific not only about the market
that is ...
Information and Market Efficiency
• Under weak form efficiency, the current price reflects the information
contained in al...
Implications of Market Efficiency
• No group of investors should be able to consistently beat the market using a
common in...
What market efficiency does not
imply..
• An efficient market does not imply that –
– (a) stock prices cannot deviate from...
Necessary Conditions for Market
Efficiency
• Markets do not become efficient automatically. It is the actions of investors...
Efficient Markets and Profit-seeking Investors:
The Internal Contradiction
• There is an internal contradiction in claimin...
Anomalies
• Firm size effect
• January effect
• Monday Effect
Firm Size Effect
The theory holds that smaller companies have a greater
amount of growth opportunities than larger compani...
Monday Effect
A theory that states that returns on the stock
market on Mondays will follow the prevailing
trend from the p...
January Effect
The January effect is said to affect small caps more
than mid or large caps. This historical trend,
however...
Portfolio Performance Measures
Sharpe Ratio
• Sharpe ratio= (Rp-Rf)/standard deviation of
the portfolio
• Rp is portfolio return
• Rf is risk free rate o...
Treynor Portfolio
Performance Measure
• Treynor recognized two components of risk
– Risk from general market fluctuations
...
Treynor Portfolio
Performance Measure
• The numerator is the risk premium
• The denominator is a measure of risk
• The exp...
Treynor Portfolio
Performance Measure
• Comparing a portfolio’s T value to a similar measure for the market
portfolio indi...
Treynor Portfolio
Performance Measure
• Comparison to see whether actual return of
portfolio G was above or below expectat...
Sharpe Portfolio
Performance Measure
• Risk premium earned per unit of risk
i
i
i
RFRR
S



Treynor versus Sharpe Measure
• Sharpe uses standard deviation of returns as the
measure of risk
• Treynor measure uses be...
Jensen Portfolio
Performance Measure
• Also based on CAPM
• Expected return on any security or portfolio is
    RFRR...
Jensen Portfolio
Performance Measure
• Also based on CAPM
• Expected return on any security or portfolio is
Where: E(Rj) =...
Application of Derivatives
• Hedging
• Arbitrage
• Speculation
What is Hedging?
What is Arbitrage?
What is Speculation?
Investment Policy Statement
• Objectives
• Constrains
Objectives
• Return Objective
• Risk Objective
Constrains
• Liquidity
• Regulatory and legal
• Taxation
• Time horizon
• Unique
Is this the right way?
Isn't this better?
Constrains leads Objectives follow
What do you need to have to do what
the lady is doing?
Ability Willingness
WACC
Fundamental Analysis
Security Analysis and Portfolio Management
Security Analysis and Portfolio Management
Security Analysis and Portfolio Management
Security Analysis and Portfolio Management
Security Analysis and Portfolio Management
Security Analysis and Portfolio Management
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Security Analysis and Portfolio Management

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Security Analysis and Portfolio Management

  1. 1. Security Analysis & Portfolio Management
  2. 2. Risk & Return
  3. 3. What is Investment? Forgoing one now. For many in future.
  4. 4. What is Risk? • The chance that an investment's actual return will be different than expected. Risk includes the possibility of losing some or all of the original investment.
  5. 5. What is Return? • The gain or loss of a security in a particular period. The return consists of the income and the capital gains relative on an investment. It is usually quoted as a percentage.
  6. 6. Investment Avenues • Fixed deposits • Equity • Fixed income • Mutual funds
  7. 7. Price and Value
  8. 8. Price is determined by:
  9. 9. Value • Value of any asset is the amount of cash it can generate in its future, discounted to present.
  10. 10. Time Value of Money
  11. 11. Discounting Single Period
  12. 12. Discounting Multi-period
  13. 13. Discounting Multi-period
  14. 14. How do you value each?
  15. 15. Probability Distribution of Stock Returns
  16. 16. Measures of Risk in Academics 1. Absolute Measures • Variance • Standard deviation 2. Relative Measures • Covariance • Correlation
  17. 17. Variance of Return • Variance is used in statistics for probability distribution. Since variance measures the variability (volatility) from an average or mean, and volatility is a measure of risk, the variance statistic can help determine the risk an investor might take on when purchasing a specific security. • A variance value of zero indicates that all values within a set of numbers are identical; all variances that are non-zero will be positive numbers. A large variance indicates that numbers in the set are far from the mean and each other, while a small variance indicates the opposite.
  18. 18. Standard Deviation • Standard deviation is a statistical measurement that sheds light on historical volatility. For example, a volatile stock will have a high standard deviation while the deviation of a stable blue chip stock will be lower. A large dispersion tells us how much the return on the fund is deviating from the expected normal returns.
  19. 19. Formula • Variance: • Standard deviation:
  20. 20. Covariance • A measure of the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means returns move inversely.
  21. 21. Correlation • Correlation is computed into what is known as the correlation coefficient, which ranges between -1 and +1. Perfect positive correlation (a correlation co-efficient of +1) implies that as one security moves, either up or down, the other security will move in lockstep, in the same direction. Alternatively, perfect negative correlation means that if one security moves in either direction the security that is perfectly negatively correlated will move in the opposite direction. If the correlation is 0, the movements of the securities are said to have no correlation; they are completely random. • In real life, perfectly correlated securities are rare, rather you will find securities with some degree of correlation.
  22. 22. Covariance & Correlation Formula
  23. 23. Example Years HUL Nestle Covar Corr 2006 12% 6% 0.012016 73.00% 2007 15% 21% 2008 -22% -6% 2009 6% 23% 2010 23% 15%
  24. 24. Modern Portfolio Theory
  25. 25. Modern Portfolio Theory – Modern portfolio theory (MPT)—or portfolio theory— was introduced by Harry Markowitz with his paper "Portfolio Selection," which appeared in the 1952 Journal of Finance. 38 years later, he shared a Nobel Prize with Merton Miller and William Sharpe for what has become a broad theory for portfolio selection. – MPT has had most influence in the practice of portfolio management – MPT commonly referred to as Mean – Variance Analysis – MPT is a normative theory – In its simplest form, MPT provides a framework to construct and select portfolios based on the expected performance of the investments and the risk appetite of the investors.
  26. 26. Applications of MPT • Asset Allocation • Asset-liability management • Optimal Manager Selection • Index funds/Mutual funds • Fund of Funds
  27. 27. Modern Portfolio Theory - In Nut Shell • Due to scarcity of resources, all economic decisions are made in the face of trade-offs • Markowitz identified the trade-off facing the investor : risk versus return • The investment decision is not merely which securities to own, but how to divide investor’s wealth amongst securities – the problem of portfolio selection • Markowitz extends the techniques of linear programming to develop the critical line algorithm • The critical line algorithm identifies portfolios that minimize risk for a given level of expected return • MPT quantified the age old wisdom of diversification by introducing the statistical notion of covariance or correlation. MPT and CAPM
  28. 28. Assumptions of Markowitz Portfolio Theory • Investors consider each investment alternative as being presented by a probability distribution of expected returns over some holding period. • For a given risk level, investors prefer higher returns to lower returns. Similarly, for a given level of expected returns, investors prefer less risk to more risk. • Your portfolio includes all of your assets and liabilities
  29. 29. Markowitz Portfolio Theory • Quantifies risk • Derives the expected rate of return for a portfolio of assets and an expected risk measure • Shows that the variance of the rate of return is a meaningful measure of portfolio risk • Derives the formula for computing the variance of a portfolio, showing how to effectively diversify a portfolio
  30. 30. Covariance of Returns • A measure of the degree to which two variables “move together” relative to their individual mean values over time • For two assets, i and j, the covariance of rates of return is defined as: • Covij = E{[Ri - E(Ri)][Rj - E(Rj)]}
  31. 31. Covariance and Correlation • The correlation coefficient is obtained by standardizing (dividing) the covariance by the product of the individual standard deviations • Correlation coefficient varies from -1 to +1 jt iti ij Rofdeviationstandardthe Rofdeviationstandardthe returnsoftcoefficienncorrelatiother :where Cov r     j ji ij ij   
  32. 32. Correlation Coefficient • It can vary only in the range +1 to -1. • A value of +1 would indicate perfect positive correlation. This means that returns for the two assets move together in a completely linear manner. • A value of –1 would indicate perfect correlation. This means that the returns for two assets have the same percentage movement, but in opposite directions
  33. 33. Portfolio Standard Deviation Calculation • Any asset of a portfolio may be described by two characteristics: – The expected rate of return – The expected standard deviations of returns • The correlation, measured by covariance, affects the portfolio standard deviation • Low correlation reduces portfolio risk while not affecting the expected return
  34. 34. Portfolio Standard Deviation Formula ji    ijij ij 2 i i port n 1i n 1i ijj n 1i i 2 i 2 iport rCovwhere j,andiassetsforreturnofratesebetween thcovariancetheCov iassetforreturnofratesofvariancethe portfolioin thevalueofproportionby thedeterminedareweights whereportfolio,in theassetsindividualtheofweightstheW portfoliotheofdeviationstandardthe :where Covwww          
  35. 35. Portfolio Risk-Return Plots for Different Weights - 0.05 0.10 0.15 0.20 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Standard Deviation of Return E(R) Rij = +1.00 1 2 With two perfectly correlated assets, it is only possible to create a two asset portfolio with risk- return along a line between either single asset
  36. 36. Portfolio Risk-Return Plots for Different Weights - 0.05 0.10 0.15 0.20 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Standard Deviation of Return E(R) Rij = 0.00 Rij = +1.00 f g h i j k 1 2 With uncorrelated assets it is possible to create a two asset portfolio with lower risk than either single asset
  37. 37. Portfolio Risk-Return Plots for Different Weights - 0.05 0.10 0.15 0.20 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Standard Deviation of Return E(R) Rij = 0.00 Rij = +1.00 Rij = +0.50 f g h i j k 1 2 With correlated assets it is possible to create a two asset portfolio between the first two curves
  38. 38. Portfolio Risk-Return Plots for Different Weights - 0.05 0.10 0.15 0.20 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Standard Deviation of Return E(R) Rij = 0.00 Rij = +1.00 Rij = -0.50 Rij = +0.50 f g h i j k 1 2 With negatively correlated assets it is possible to create a two asset portfolio with much lower risk than either single asset
  39. 39. Portfolio Risk-Return Plots for Different Weights - 0.05 0.10 0.15 0.20 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Standard Deviation of Return E(R) Rij = 0.00 Rij = +1.00 Rij = -1.00 Rij = +0.50 f g h i j k 1 2 With perfectly negatively correlated assets it is possible to create a two asset portfolio with almost no risk Rij = -0.50
  40. 40. • Suppose two securities have perfect negative Correlation. Would it make sense to invest in these two securities only?
  41. 41. Efficient Frontier for Alternative Portfolios Efficient Frontier A B C E(R) Standard Deviation of Return MARKOV’S TRILIMMA - CASE
  42. 42. The Efficient Frontier • The efficient frontier represents that set of portfolios with the maximum rate of return for every given level of risk, or the minimum risk for every level of return • Frontier will be portfolios of investments rather than individual securities – Exceptions being the asset with the highest return
  43. 43. The Efficient Frontier and Investor Utility • An individual investor’s utility curve specifies the trade-offs he is willing to make between expected return and risk • These two interactions will determine the particular portfolio selected by an individual investor
  44. 44. Selecting an Optimal Risky Portfolio )E( port )E(Rport X Y U3 U2 U1 U3’ U2’ U1’ • The optimal portfolio has the highest utility for a given investor • It lies at the point of tangency between the efficient frontier and the utility curve with the highest possible utility
  45. 45. The MPT Investment Process Expected Return Model Volatility & Correlation Estimates Constraints on Portfolio Choice Optimal Portfolio Investor Objectives Risk-Return Efficient Frontier PORTFOLIO OPTIMIZATION
  46. 46. Implementation of MPT • Though the theory is straight forward …. Implementation is a complication process.
  47. 47. Estimation Issues • Results of portfolio allocation depend on accurate statistical inputs • Estimates of – Expected returns – Standard deviation – Correlation coefficient • Among entire set of assets • With 100 assets, 4,950 correlation estimates • Estimation risk refers to potential errors
  48. 48. The Proof Is In the Pudding • The MPT has been around for 40 years and is still going strong – But, it has flaws • There are alternatives, but none has yet to prove itself better 54
  49. 49. An Introduction to Capital Asset Pricing Model • The capital asset pricing model is an idealized portrayal of how financial markets price securities and thereby determine expected return on capital investments. • The model provides a methodology for quantifying risk and translating that risk into estimates of expected return on equity.
  50. 50. Capital Asset Pricing Model
  51. 51. Risk-Free Asset • An asset with zero standard deviation • Zero correlation with all other risky assets • Provides the risk-free rate of return (RFR) • Will lie on the vertical axis of a portfolio graph
  52. 52. Risk-Free Asset • Covariance between two sets of returns is   n 1i jjiiij )]/nE(R-)][RE(R-[RCov Because the returns for the risk free asset are certain, 0RF  Thus Ri = E(Ri), and Ri - E(Ri) = 0 Consequently, the covariance of the risk-free asset with any risky asset or portfolio will always equal zero. Similarly the correlation between any risky asset and the risk-free asset would be zero.
  53. 53. Combining a Risk-Free Asset with a Risky Portfolio • Expected return • the weighted average of the two returns ))E(RW-(1(RFR)W)E(R iRFRFport  This is a linear relationship
  54. 54. Combining a Risk-Free Asset with a Risky Portfolio • The expected variance for a two-asset portfolio is 211,221 2 2 2 2 2 1 2 1 2 port rww2ww)E(   Substituting the risk-free asset for Security 1, and the risky asset for Security 2, this formula would become iRFiRF  iRF,RFRF 22 RF 22 RF 2 port )rw-(1w2)w1(w)E(  Since we know that the variance of the risk-free asset is zero and the correlation between the risk-free asset and any risky asset i is zero we can adjust the formula 22 RF 2 port )w1()E( i 
  55. 55. Combining a Risk-Free Asset with a Risky Portfolio • Given the variance formula 22 RF 2 port )w1()E( i  22 RFport )w1()E( i The standard deviation is i)w1( RF Therefore, the standard deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio.
  56. 56. Combining a Risk-Free Asset with a Risky Portfolio Since both the expected return and the standard deviation of return for such a portfolio are linear combinations, a graph of possible portfolio returns and risks looks like a straight line between the two assets
  57. 57. Combining a Risk-Free Asset with a Risky Portfolio )E( port )E(Rport RFR M C A B D Since both the expected return and the standard deviation of return for such a portfolio are linear combinations, a graph of possible portfolio returns and risks looks like a straight line between the two assets
  58. 58. Combining a Risk-Free Asset with a Risky Portfolio )E( port )E(R port RFR M C A B D Since both the expected return and the standard deviation of return for such a portfolio are linear combinations, a graph of possible portfolio returns and risks looks like a straight line between the two assets To attain a higher expected return than is available at point M (in exchange for accepting higher risk) either invest along the efficient frontier beyond point M, such as point D or, add leverage to the portfolio by borrowing money at the risk-free rate and investing in the risky portfolio at point M
  59. 59. Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier )E( port )E(R port RFR M
  60. 60. • Suppose you pay a higher rate of Interest to buy stock on margin than you receive when you invest at the risk free rate. What does the efficiency frontier look like?
  61. 61. The Market Portfolio • Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line • Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML • Therefore this portfolio must include ALL RISKY ASSETS • Because the market is in equilibrium, all assets are included in this portfolio in proportion to their market value • Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away
  62. 62. Statement of CAPM A model that describes the relationship between risk and expected return and that is used in the pricing of risky securities.
  63. 63. Systematic Risk • Only systematic risk remains in the market portfolio • Systematic risk is the variability in all risky assets caused by macroeconomic variables • Systematic risk can be measured by the standard deviation of returns of the market portfolio and can change over time
  64. 64. Number of Stocks in a Portfolio and the Standard Deviation of Portfolio Return Standard Deviation of Return Number of Stocks in the Portfolio Standard Deviation of the Market Portfolio (systematic risk) Systematic Risk Total Risk Unsystematic (diversifiable) Risk
  65. 65. SML Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk An investor with a low risk profile would choose an investment at the beginning of the security market line. An investor with a higher risk profile would thus choose an investment higher along the security market line.
  66. 66. Slope of SML • Given the SML reflects the return on a given investment in relation to risk, a change in the slope of the SML could be caused by the risk premium of the investments. Recall that the risk premium of an investment is the excess return required by an investor to help ensure a required rate of return is met. If the risk premium required by investors was to change, the slope of the SML would change as well. • Risk premium=Rm-Rf
  67. 67. Properties of any asset on , above or below the SML • On the line assets are fairly valued. • Above the line they are undervalued. • Below the line they are overvalued.
  68. 68. Assumptions of CAPM • Aim to maximize economic utilities (Asset quantities are given and fixed). • Are rational and risk-averse. • Are broadly diversified across a range of investments. • Are price takers, i.e., they cannot influence prices. • Can lend and borrow unlimited amounts under the risk free rate of interest. • Trade without transaction or taxation costs. • Deal with securities that are all highly divisible into small parcels (All assets are perfectly divisible and liquid). • Have homogeneous expectations. • Assume all information is available at the same time to all investors.
  69. 69. Arbitrage Pricing Theory The arbitrage pricing theory (APT) describes the price where a mispriced asset is expected to be. It is often viewed as an alternative to the capital asset pricing model (CAPM), since the APT has more flexible assumption requirements. Whereas the CAPM formula requires the market's expected return, APT uses the risky asset's expected return and the risk premium of a number of macro-economic factors. Arbitrageurs use the APT model to profit by taking advantage of mispriced securities. A mispriced security will have a price that differs from the theoretical price predicted by the model. By going short an over priced security, while concurrently going long the portfolio the APT calculations were based on, the arbitrageur is in a position to make a theoretically risk-free profit.
  70. 70. Competition may be stronger or weaker than anticipated Exchange rate and Political risk Projects may do better or worse than expected Entire Sector may be affected by action Interest rate, Inflation & News about economy Firm-specific Market A Break Down of Risk Actions/Risk that Affect only one firm Affects few firms Affects many firms Actions/Risk that affect all investments
  71. 71. Multi-factor Model • Multi factor models explain risk/reward relationships based on two or more factors:
  72. 72. Alternatives – Single Index Market Model • With assumption that stock returns can be described by a single market model, the number of correlations required reduces to the number of assets • Single index market model: imiii RbaR  bi = the slope coefficient that relates the returns for security i to the returns for the aggregate stock market Rm = the returns for the aggregate stock market
  73. 73. Efficient Market Hypothesis
  74. 74. Random Walk Theory The idea that stocks take a random and unpredictable path. A follower of the random walk theory believes it's impossible to outperform the market without assuming additional risk. Critics of the theory, however, contend that stocks do maintain price trends over time - in other words, that it is possible to outperform the market by carefully selecting entry and exit points for equity investments.
  75. 75. Implications of Randomness • The fact that the deviations from true value are random implies, in a rough sense, that there is an equal chance that stocks are under or over valued at any point in time, and that these deviations are uncorrelated with any observable variable. • For instance, in an efficient market, stocks with lower PE ratios should be no more or less likely to under valued than stocks with high PE ratios. • If the deviations of market price from true value are random, it follows that no group of investors should be able to consistently find under or over valued stocks using any investment strategy
  76. 76. What is an efficient market? • Efficient market is one where the market price is an unbiased estimate of the true value of the investment. • Implicit in this derivation are several key concepts – – Market efficiency does not require that the market price be equal to true value at every point in time. All it requires is that errors in the market price be unbiased, i.e., that prices can be greater than or less than true value, as long as these deviations are random. – Randomness implies that there is an equal chance that stocks are under or over valued at any point in time.
  77. 77. Definitions of Market Efficiency • Definitions of market efficiency have to be specific not only about the market that is being considered but also the investor group that is covered. • It is extremely unlikely that all markets are efficient to all investors, but it is entirely possible that a particular market (for instance, the New York Stock Exchange) is efficient with respect to the average investor. • It is possible that some markets are efficient while others are not, and that a market is efficient with respect to some investors and not to others. • This is a direct consequence of differential transactions costs, which confer advantages on some investors relative to others.
  78. 78. Information and Market Efficiency • Under weak form efficiency, the current price reflects the information contained in all past prices, suggesting that charts and technical analyses that use past prices alone would not be useful in finding under valued stocks. • Under semi-strong form efficiency, the current price reflects the information contained not only in past prices but all public information (including financial statements and news reports) and no approach that was predicated on using and massaging this information would be useful in finding under valued stocks. • Under strong form efficiency, the current price reflects all information, public as well as private, and no investors will be able to consistently find under valued stocks.
  79. 79. Implications of Market Efficiency • No group of investors should be able to consistently beat the market using a common investment strategy. • An efficient market would also carry very negative implications for many investment strategies and actions that are taken for granted – – In an efficient market, equity research and valuation would be a costly task that provided no benefits. – The odds of finding an undervalued stock should be random (50/50). At best, the benefits from information collection and equity research would cover the costs of doing the research. – In an efficient market, a strategy of randomly diversifying across stocks or indexing to the market, carrying little or no information cost and minimal execution costs, would be superior to any other strategy, that created larger information and execution costs. – There would be no value added by portfolio managers and investment strategists. – In an efficient market, a strategy of minimizing trading, i.e., creating a portfolio and not trading unless cash was needed, would be superior to a strategy that required frequent trading.
  80. 80. What market efficiency does not imply.. • An efficient market does not imply that – – (a) stock prices cannot deviate from true value; in fact, there can be large deviations from true value. The deviations do have to be random. – no investor will 'beat' the market in any time period. To the contrary, approximately half of all investors, prior to transactions costs, should beat the market in any period. – no group of investors will beat the market in the long term. Given the number of investors in financial markets, the laws of probability would suggest that a fairly large number are going to beat the market consistently over long periods, not because of their investment strategies but because they are lucky. – In an efficient market, the expected returns from any investment will be consistent with the risk of that investment over the long term, though there may be deviations from these expected returns in the short term.
  81. 81. Necessary Conditions for Market Efficiency • Markets do not become efficient automatically. It is the actions of investors, sensing bargains and putting into effect schemes to beat the market, that make markets efficient. • The necessary conditions for a market inefficiency to be eliminated are as follows – • The market inefficiency should provide the basis for a scheme to beat the market and earn excess returns. For this to hold true – – (a) The asset (or assets) which is the source of the inefficiency has to be traded. – (b) The transactions costs of executing the scheme have to be smaller than the expected profits from the scheme. • There should be profit maximizing investors who – (a) recognize the 'potential for excess return' – (b) can replicate the beat the market scheme that earns the excess return – (c) have the resources to trade on the stock until the inefficiency disappears
  82. 82. Efficient Markets and Profit-seeking Investors: The Internal Contradiction • There is an internal contradiction in claiming that there is no possibility of beating the market in an efficient market and then requiring profit- maximizing investors to constantly seek out ways of beating the market and thus making it efficient. • If markets were, in fact, efficient, investors would stop looking for inefficiencies, which would lead to markets becoming inefficient again. • It makes sense to think about an efficient market as a self-correcting mechanism, where inefficiencies appear at regular intervals
  83. 83. Anomalies • Firm size effect • January effect • Monday Effect
  84. 84. Firm Size Effect The theory holds that smaller companies have a greater amount of growth opportunities than larger companies. Small cap companies also tend to have a more volatile business environment, and the correction of problems - such as the correction of a funding deficiency - can lead to a large price appreciation. Finally, small cap stocks tend to have lower stock prices, and these lower prices mean that price appreciations tend to be larger than those found among large cap stocks.
  85. 85. Monday Effect A theory that states that returns on the stock market on Mondays will follow the prevailing trend from the previous Friday. Therefore, if the market was up on Friday, it should continue through the weekend and, come Monday, resume its rise.
  86. 86. January Effect The January effect is said to affect small caps more than mid or large caps. This historical trend, however, has been less pronounced in recent years because the markets have adjusted for it. Another reason the January effect is now considered less important is that more people are using tax- sheltered retirement plans and therefore have no reason to sell at the end of the year for a tax loss.
  87. 87. Portfolio Performance Measures
  88. 88. Sharpe Ratio • Sharpe ratio= (Rp-Rf)/standard deviation of the portfolio • Rp is portfolio return • Rf is risk free rate of return
  89. 89. Treynor Portfolio Performance Measure • Treynor recognized two components of risk – Risk from general market fluctuations – Risk from unique fluctuations in the securities in the portfolio • His measure of risk-adjusted performance focuses on the portfolio’s undiversifiable risk: market or systematic risk
  90. 90. Treynor Portfolio Performance Measure • The numerator is the risk premium • The denominator is a measure of risk • The expression is the risk premium return per unit of risk • Risk averse investors prefer to maximize this value • This assumes a completely diversified portfolio leaving systematic risk as the relevant risk   i i RFRR T   
  91. 91. Treynor Portfolio Performance Measure • Comparing a portfolio’s T value to a similar measure for the market portfolio indicates whether the portfolio would plot above the SML • Calculate the T value for the aggregate market as follows:   m m m RFRR T   
  92. 92. Treynor Portfolio Performance Measure • Comparison to see whether actual return of portfolio G was above or below expectations can be made using:    RFRRRFRRE miG  
  93. 93. Sharpe Portfolio Performance Measure • Risk premium earned per unit of risk i i i RFRR S   
  94. 94. Treynor versus Sharpe Measure • Sharpe uses standard deviation of returns as the measure of risk • Treynor measure uses beta (systematic risk) • Sharpe therefore evaluates the portfolio manager on the basis of both rate of return performance and diversification • The methods agree on rankings of completely diversified portfolios • Produce relative not absolute rankings of performance
  95. 95. Jensen Portfolio Performance Measure • Also based on CAPM • Expected return on any security or portfolio is     RFRRERFRRE mjj  
  96. 96. Jensen Portfolio Performance Measure • Also based on CAPM • Expected return on any security or portfolio is Where: E(Rj) = the expected return on security RFR = the one-period risk-free interest rate j= the systematic risk for security or portfolio j E(Rm) = the expected return on the market portfolio of risky assets     RFRRERFRRE mjj  
  97. 97. Application of Derivatives • Hedging • Arbitrage • Speculation
  98. 98. What is Hedging?
  99. 99. What is Arbitrage?
  100. 100. What is Speculation?
  101. 101. Investment Policy Statement • Objectives • Constrains
  102. 102. Objectives • Return Objective • Risk Objective
  103. 103. Constrains • Liquidity • Regulatory and legal • Taxation • Time horizon • Unique
  104. 104. Is this the right way?
  105. 105. Isn't this better?
  106. 106. Constrains leads Objectives follow
  107. 107. What do you need to have to do what the lady is doing? Ability Willingness
  108. 108. WACC
  109. 109. Fundamental Analysis

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