CML Vs SML
1.Capital Market Line (CML) actually represents the expected returns if the efficient portfolios as a function of their volatility which is measured by the standard deviation of their returns whereas the Security Market Line (SML) represents the expected returns of the individual asset as a function of its sensitivity to market fluctuations.
2.CML gives the risk/return relationship for efficient portfolios whereas SML , also part of the CAPM, gives the risk/return relationship for individual stocks.
3.The measure of risk used in CML is standard deviation whereas in SML it is the beta coefficient.
Monday, September 29, 2008
Sunday, September 28, 2008
Efficient frontier and Capital Market Line (CML)
Efficient Frontier
It is possible to calculate the risk/return ratio for every possible portfolio at any given time. This ratio for the stock market portfolio is composed from the risk/return ratio of all stocks in the portfolio AND the risk/return ratio of the stocks to each other. The right combination of stocks can substantially minimize the risk of a portfolio. It becomes possible to compare portfolios with each other. Each dot in the image represents one possible portfolio. As this graph clearly shows, there is only a certain range with regard to the relationship of risk and return, where portfolios can be situated. If the topmost points are connected, a line becomes visible: the efficient frontier line. All portfolios on this line have the optimum combination of stocks, meaning an optimum risk/return ratio.
All those portfolios give the highest return for the amount of risk an investor is willing to take - or defined in another way, have the lowest risk for the return to be achieved. As you can see in the risk return portfolio graph, at a certain level the gradient of the efficient market frontier line drops. At this level you have to risk more for the same profit increase in percentage terms.
Capital Market Line
The method to determine the best position on the efficient frontier line is the capital market line (CML). The capital market line is, graphically, a tangent line that can be drawn on a graph, connecting the return of risk-free-asset with the efficient market frontier. An investor is only willing to accept higher risk if the return rises proportionally. The CML shows where the most efficient portfolio lies on the efficient frontier line.
It is possible to calculate the risk/return ratio for every possible portfolio at any given time. This ratio for the stock market portfolio is composed from the risk/return ratio of all stocks in the portfolio AND the risk/return ratio of the stocks to each other. The right combination of stocks can substantially minimize the risk of a portfolio. It becomes possible to compare portfolios with each other. Each dot in the image represents one possible portfolio. As this graph clearly shows, there is only a certain range with regard to the relationship of risk and return, where portfolios can be situated. If the topmost points are connected, a line becomes visible: the efficient frontier line. All portfolios on this line have the optimum combination of stocks, meaning an optimum risk/return ratio.
All those portfolios give the highest return for the amount of risk an investor is willing to take - or defined in another way, have the lowest risk for the return to be achieved. As you can see in the risk return portfolio graph, at a certain level the gradient of the efficient market frontier line drops. At this level you have to risk more for the same profit increase in percentage terms.
Capital Market Line
The method to determine the best position on the efficient frontier line is the capital market line (CML). The capital market line is, graphically, a tangent line that can be drawn on a graph, connecting the return of risk-free-asset with the efficient market frontier. An investor is only willing to accept higher risk if the return rises proportionally. The CML shows where the most efficient portfolio lies on the efficient frontier line.
Few Useful Terms
Risk Free Return:
Before understanding Risk free assets, let us understand what a risky asset is. A risky asset is one which gives uncertain future returns. This uncertainty can be measured by the variance or the standard deviation of the expected future returns.
Risk free assets are assets whose expected risk is fully certain and thus the standard deviation of such expected returns comes to zero.
Alpha:
The α (alpha) of a security or fund is its outperformance over the return adjusted for risk, with risk measured by β (beta).
α= (r - rf) - (β×(rm - rf))
where rf is the risk free rate
rm is the (forecast) market rate of return
and rm the return on a fund or security r.
Beta :
The Beta coefficient, in terms of finance and investing, is a measure of a stock's (or portfolio's) volatility in relation to the rest of the market. Beta is calculated for individual companies using regression analysis.
The beta coefficient is a key parameter in the capital asset pricing model (or CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio.
• Beta < 0: Negative Beta - not likely.
• Beta = 0: Cash in the bank.
• Beta Between 0 and 1: Low-volatility
• Beta = 1: Matching the market.
• Beta > 1: More volatile than the market.
Example of use: A fund with a beta of 1 is deemed to have the same volatility as the S&P 500; therefore a fund with a beta of 4 is four times more volatile than the S&P 500, and a fund with a beta of .25 is 25% as volatile as the S&P 500.
This means that a fund with a beta of 4 would rise 40% if the S&P 500 rose 10% (the same is true of a drop).
The three basic interpretations of Beta are as follows:
Econometric Beta: The primary risk factor for the CAPM. Relevant to pricing and not valuation.
Graphical Beta: The slope coefficient of the characteristic line.
Statistical Beta: The measure of systematic risk in the CAPM.
Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the asset's sensitivity of the asset's returns to market returns, its non-diversifiable risk, its systematic risk or market risk. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. On a portfolio level, measuring beta is thought to separate a manager's skill from his or her willingness to take risk.
Variance :
Variance measures the variability (volatility) from an average. Volatility is a measure of risk, so this statistic can help determine the risk an investor might take on when purchasing a specific security.
Standard Deviation
The standard deviation is a measure of how spread out a set of numbers is. It is the square root of variance.
The most common use of the standard deviation in finance is to measure the risk of holding a security or portfolio.
Covariance
The covariance of two variables (numbers measuring something) is a measure of the relationship between them. It closely related to the correlation and calculated as an intermediate step in calculating the correlation.
The covariance of two numbers is the arithmetic mean, over all values of x1, and the corresponding values of x2, of:
(x1 - μ1)(x2 - μ2)
where x1 is the value of one variable
x2 is the value of the other variable
μ1 is the arithmetic mean of of x1 and
μ2 is the arithmetic mean of of x2.
The correlation of x1 and x2 is:
(cov(x1,x2))/(σ1σ2)
where cov(x1,x2) is the covariance of x1 and x2
σ1 is the standard deviation of x1 and
σ2 is the standard deviation of x2.
Coefficient of correlation
A coefficient of correlation is a mathematical measure of how much one number (such as a share price) can expected to be influenced by changes in another (such as an index). It is closely related to covariance (see below).
A correlation coefficient of 1 means that the two numbers are perfectly correlated: if one grows so does the other, and the change in one is a multiple of the change in the other.
A correlation coefficient of -1 means that the numbers are perfectly inversely correlated. If one grows the other falls. The growth in one is a negative multiple of the growth in the other.
A correlation coefficient of zero means that the two numbers are not related.
A non-zero correlation coefficient means that the numbers are related, but unless the coefficient is either 1 or -1 there are other influences and the relationship between the two numbers is not fixed. So if you know one number you can estimate the other, but not with certainty. The closer the correlation coefficient is to zero the greater the uncertainty, and low correlation coefficients means that the relationship is not certain enough to be useful.
Before understanding Risk free assets, let us understand what a risky asset is. A risky asset is one which gives uncertain future returns. This uncertainty can be measured by the variance or the standard deviation of the expected future returns.
Risk free assets are assets whose expected risk is fully certain and thus the standard deviation of such expected returns comes to zero.
Alpha:
The α (alpha) of a security or fund is its outperformance over the return adjusted for risk, with risk measured by β (beta).
α= (r - rf) - (β×(rm - rf))
where rf is the risk free rate
rm is the (forecast) market rate of return
and rm the return on a fund or security r.
Beta :
The Beta coefficient, in terms of finance and investing, is a measure of a stock's (or portfolio's) volatility in relation to the rest of the market. Beta is calculated for individual companies using regression analysis.
The beta coefficient is a key parameter in the capital asset pricing model (or CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio.
• Beta < 0: Negative Beta - not likely.
• Beta = 0: Cash in the bank.
• Beta Between 0 and 1: Low-volatility
• Beta = 1: Matching the market.
• Beta > 1: More volatile than the market.
Example of use: A fund with a beta of 1 is deemed to have the same volatility as the S&P 500; therefore a fund with a beta of 4 is four times more volatile than the S&P 500, and a fund with a beta of .25 is 25% as volatile as the S&P 500.
This means that a fund with a beta of 4 would rise 40% if the S&P 500 rose 10% (the same is true of a drop).
The three basic interpretations of Beta are as follows:
Econometric Beta: The primary risk factor for the CAPM. Relevant to pricing and not valuation.
Graphical Beta: The slope coefficient of the characteristic line.
Statistical Beta: The measure of systematic risk in the CAPM.
Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the asset's sensitivity of the asset's returns to market returns, its non-diversifiable risk, its systematic risk or market risk. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. On a portfolio level, measuring beta is thought to separate a manager's skill from his or her willingness to take risk.
Variance :
Variance measures the variability (volatility) from an average. Volatility is a measure of risk, so this statistic can help determine the risk an investor might take on when purchasing a specific security.
Standard Deviation
The standard deviation is a measure of how spread out a set of numbers is. It is the square root of variance.
The most common use of the standard deviation in finance is to measure the risk of holding a security or portfolio.
Covariance
The covariance of two variables (numbers measuring something) is a measure of the relationship between them. It closely related to the correlation and calculated as an intermediate step in calculating the correlation.
The covariance of two numbers is the arithmetic mean, over all values of x1, and the corresponding values of x2, of:
(x1 - μ1)(x2 - μ2)
where x1 is the value of one variable
x2 is the value of the other variable
μ1 is the arithmetic mean of of x1 and
μ2 is the arithmetic mean of of x2.
The correlation of x1 and x2 is:
(cov(x1,x2))/(σ1σ2)
where cov(x1,x2) is the covariance of x1 and x2
σ1 is the standard deviation of x1 and
σ2 is the standard deviation of x2.
Coefficient of correlation
A coefficient of correlation is a mathematical measure of how much one number (such as a share price) can expected to be influenced by changes in another (such as an index). It is closely related to covariance (see below).
A correlation coefficient of 1 means that the two numbers are perfectly correlated: if one grows so does the other, and the change in one is a multiple of the change in the other.
A correlation coefficient of -1 means that the numbers are perfectly inversely correlated. If one grows the other falls. The growth in one is a negative multiple of the growth in the other.
A correlation coefficient of zero means that the two numbers are not related.
A non-zero correlation coefficient means that the numbers are related, but unless the coefficient is either 1 or -1 there are other influences and the relationship between the two numbers is not fixed. So if you know one number you can estimate the other, but not with certainty. The closer the correlation coefficient is to zero the greater the uncertainty, and low correlation coefficients means that the relationship is not certain enough to be useful.
Thursday, September 25, 2008
Top Down or Bottom Up Approach
Top Down Approach
A top-down investor lays more emphasis on sector, industry or theme rather than individual blue-chip stocks. Investors study the economic trends, and determine the industries and companies that are likely to benefit most of them.
Top-down investors will first look at the entire forest instead of specific trees and try to identify the main market theme ahead of the market in general. They believe that picking individual companies comes second because if the economic conditions are not right for the industry that that a company operates in, it will be difficult for the company to generates profits, regardless of how efficient it is. Nevertheless, such investors may sometimes miss good companies that are still performing well, even in depressed sector.
Bottom Up Approach
Bottom up investors conduct extensive research on individual companies. As long as the company’s prospect look strong, the economic, market or industry cycles are of no concern. In fact, the downturn in the stock market may provide investors with a good margin of safety to buy stocks at depressed levels and ride them up to big gains.
Thus, bottom up managers will buy stocks even though the macroeconomic and industry outlooks look uncertain. When the industry may be out of favour and most investors are ignoring the true earning of companies, bottom-up managers ca detect good and well-managed ones selling at prices that are far lower than their intrinsic worth.
Combination Approach
The top down and bottom up approaches are two distinct and fundamentally very different approaches to investing. Investors can combine the two approaches by applying top-down analysis on asset allocation decisions while using a bottom-up approach to select the individual securities in the portfolio.
As there is prediction and practice of major market crashes occurring every 10 to 15 years, the top-down approach may be more appropriate.
A top-down investor lays more emphasis on sector, industry or theme rather than individual blue-chip stocks. Investors study the economic trends, and determine the industries and companies that are likely to benefit most of them.
Top-down investors will first look at the entire forest instead of specific trees and try to identify the main market theme ahead of the market in general. They believe that picking individual companies comes second because if the economic conditions are not right for the industry that that a company operates in, it will be difficult for the company to generates profits, regardless of how efficient it is. Nevertheless, such investors may sometimes miss good companies that are still performing well, even in depressed sector.
Bottom Up Approach
Bottom up investors conduct extensive research on individual companies. As long as the company’s prospect look strong, the economic, market or industry cycles are of no concern. In fact, the downturn in the stock market may provide investors with a good margin of safety to buy stocks at depressed levels and ride them up to big gains.
Thus, bottom up managers will buy stocks even though the macroeconomic and industry outlooks look uncertain. When the industry may be out of favour and most investors are ignoring the true earning of companies, bottom-up managers ca detect good and well-managed ones selling at prices that are far lower than their intrinsic worth.
Combination Approach
The top down and bottom up approaches are two distinct and fundamentally very different approaches to investing. Investors can combine the two approaches by applying top-down analysis on asset allocation decisions while using a bottom-up approach to select the individual securities in the portfolio.
As there is prediction and practice of major market crashes occurring every 10 to 15 years, the top-down approach may be more appropriate.
Monday, September 22, 2008
Modern Portfolio Theory
Modern portfolio theory, or MPT, is an attempt to optimize the risk-reward of investment portfolios. Created by Harry Markowitz, who earned a Nobel Prize in Economics for the theory, modern portfolio theory introduced the idea of diversification as a tool to lower the risk of the entire portfolio without giving up high returns.
The key concept in modern portfolio theory is Beta. Modern portfolio theory constructs portfolios by mixing stocks with different positive and negative Betas to produce a portfolio with minimal Beta for the group of stocks taken as a whole. What makes this attractive, at least theoretically, is that returns do not cancel each other out, but rather accumulate.
Modern portfolio theory uses the Capital Asset Pricing Model, or CAPM, to select investments for a portfolio. Using Beta and the concept of the risk-free return CAPM is used to calculate a theoretical price for a potential investment. If the investment is selling for less than that price, it is a candidate for inclusion in the portfolio.
While impressive theoretically, modern portfolio theory has drawn severe criticism from many quarters. The principle objection is with the concept of Beta; while it is possible to measure the historical Beta for an investment, it is not possible to know what its Beta will be going forward. Without that knowledge, it is in fact impossible to build a theoretically perfect portfolio. This objection has been strengthened by numerous studies showing that portfolios constructed according to the theory don't have lower risks than other types of portfolios.
Modern portfolio theory also assumes it is possible to select investments whose performance is independent of other investments in the portfolio. Market historians have shown that there are no such instruments; in times of market stress, seemingly independent investments do, in fact, act as if they are related.
The key concept in modern portfolio theory is Beta. Modern portfolio theory constructs portfolios by mixing stocks with different positive and negative Betas to produce a portfolio with minimal Beta for the group of stocks taken as a whole. What makes this attractive, at least theoretically, is that returns do not cancel each other out, but rather accumulate.
Modern portfolio theory uses the Capital Asset Pricing Model, or CAPM, to select investments for a portfolio. Using Beta and the concept of the risk-free return CAPM is used to calculate a theoretical price for a potential investment. If the investment is selling for less than that price, it is a candidate for inclusion in the portfolio.
While impressive theoretically, modern portfolio theory has drawn severe criticism from many quarters. The principle objection is with the concept of Beta; while it is possible to measure the historical Beta for an investment, it is not possible to know what its Beta will be going forward. Without that knowledge, it is in fact impossible to build a theoretically perfect portfolio. This objection has been strengthened by numerous studies showing that portfolios constructed according to the theory don't have lower risks than other types of portfolios.
Modern portfolio theory also assumes it is possible to select investments whose performance is independent of other investments in the portfolio. Market historians have shown that there are no such instruments; in times of market stress, seemingly independent investments do, in fact, act as if they are related.
Friday, September 19, 2008
Capital Asset Pricing Model
William Sharpe published the capital asset pricing model (CAPM). Parallel work was also performed by Treynor and Lintner. CAPM extended Harry Markowitz’s portfolio theory to introduce the notions of systematic and specific risk
CAPM considers a simplified world where:
1. There are no taxes or transaction costs.
2. All investors have identical investment horizons.
3. All invetors have identical opinion about expected returns, volatilities and correlations of available investments
CAPM decomposes a portfolio's risk into systematic and specific risk. Systematic risk is the risk of holding the market portfolio. As the market moves, each individual asset is more or less affected. To the extent that any asset participates in such general market moves, that asset entails systematic risk. Specific risk is the risk which is unique to an individual asset. It represents the component of an asset's return which is uncorrelated with general market moves.
According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be diversified away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification, the investor's net exposure is just the systematic risk of the market portfolio.
Systematic risk can be measured using beta. According to CAPM, the expected return of a stock equals the risk-free rate plus the portfolio's beta multiplied by the expected excess return of the market portfolio.
r = Rf + beta x ( Km - Rf )
where,
r is the expected return rate on a security;
Rf is the rate of a "risk-free" investment, i.e. cash;
Km is the return rate of the appropriate asset class.
Beta measures the volatility of the security, relative to the asset class. The equation is saying that investors require higher levels of expected returns to compensate them for higher expected risk. You can think of the formula as predicting a security's behavior as a function of beta: CAPM says that if you know a security's beta then you know the value of r that investors expect it to have.
CAPM considers a simplified world where:
1. There are no taxes or transaction costs.
2. All investors have identical investment horizons.
3. All invetors have identical opinion about expected returns, volatilities and correlations of available investments
CAPM decomposes a portfolio's risk into systematic and specific risk. Systematic risk is the risk of holding the market portfolio. As the market moves, each individual asset is more or less affected. To the extent that any asset participates in such general market moves, that asset entails systematic risk. Specific risk is the risk which is unique to an individual asset. It represents the component of an asset's return which is uncorrelated with general market moves.
According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be diversified away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification, the investor's net exposure is just the systematic risk of the market portfolio.
Systematic risk can be measured using beta. According to CAPM, the expected return of a stock equals the risk-free rate plus the portfolio's beta multiplied by the expected excess return of the market portfolio.
r = Rf + beta x ( Km - Rf )
where,
r is the expected return rate on a security;
Rf is the rate of a "risk-free" investment, i.e. cash;
Km is the return rate of the appropriate asset class.
Beta measures the volatility of the security, relative to the asset class. The equation is saying that investors require higher levels of expected returns to compensate them for higher expected risk. You can think of the formula as predicting a security's behavior as a function of beta: CAPM says that if you know a security's beta then you know the value of r that investors expect it to have.
Tuesday, September 16, 2008
Subscribe to:
Posts (Atom)