capm and the characteristic line. the characteristic line total risk of any asset can be assessed...
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CAPM and the Characteristic Line
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The Characteristic Line
Total risk of any asset can be assessed by measuring variability of its returns
Total risk can be divided into two parts—diversifiable risk (unsystematic risk) and non-diversifiable risk (systematic risk)
The characteristic line is used to measure statistically the undiversifiable risk and diversifiable risk of individual assets and portfolios
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Characteristic line for the ith asset is:ri,t = ai + birm,t + ei,t OR
ri,t = birm,t + ai + ei,t
Take Variance of both sides of Equation VAR (ri,t) = VAR(birm,t ) +VAR(ai) + VAR(ei,t) VAR(birm,t ) = VAR (ri,t) - VAR(ei,t) OR VAR(ei,t) = VAR(ri,t) - VAR(birm,t )
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Beta Coefficients
An index of risk
Measures the volatility of a stock (or portfolio) relative to the market
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Beta Coefficients Combine
The variability of the asset’s return
The variability of the market return
The correlation between
–the stock's return and
–the market return
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Beta Coefficients
Beta coefficients are the slope of the regression line relating
–the return on the market (the independent variable) to
–the return on the stock (the dependent variable)
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Beta Coefficients
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Interpretation of the Numerical Value of Beta
Beta = 1.0 Stock's return has same volatility as the market return
Beta > 1.0 Stock's return is more volatile than the market return
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Interpretation of the Numerical Value of Beta
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Interpretation of the Numerical Value of Beta
Beta < 1.0 Stock's return is less volatile than the market return
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Interpretation of the Numerical Value of Beta
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High Beta Stocks
More systematic market risk
May be appropriate for high-risk tolerant (aggressive) investors
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Low Beta Stocks
Less systematic market risk
May be appropriate for low-risk tolerant (defensive) investors
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Individual Stock Betas
May change over time
Tendency to move toward 1.0, the market beta
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Portfolio Betas
Weighted average of the individual asset's betas
May be more stable than individual stock betas
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How Characteristic Line leads to CAPM?
The characteristic regression line of an asset explains the asset’s systematic variability of returns in terms of market forces that affect all assets simultaneously
The portion of total risk not explained by characteristic line is called unsystematic risk
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Assets with high degrees systematic risk must be priced to yield high returns in order to induce investors to accept high degrees of risk that are undivesifiable in the market
CAPM illustrates positive relationship between systematic risk and return on an asset
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Capital Asset Pricing Model (CAPM)
For a very well-diversified portfolio, beta is the correct measure of a security’s risk.
All investments and portfolios of investments must lie along a straight-line in the return-beta space
Required return on any asset is a linear function of the systematic risk of that asset
E(ri) = rf + [E(rm) – rf] i
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The Capital Asset Pricing Model (CAPM)
The CAPM has
–A macro component explains risk and return in a portfolio context
–A micro component explains individual stock returns
–The micro component is also used to value stocks
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Beta Coefficients and The Security Market Line
The return on a stock depends on
–the risk free rate (rf)
–the return on the market (rm)
–the stock's beta
–the return on a stock:k= rf + (rm - rf)beta
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Beta Coefficients and The Security Market Line
The figure relating systematic risk (beta) and the return on a stock
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Beta Coefficients and The Security Market Line
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CAPM can be used to price any asset provided we know the systematic risk of that asset
In equilibrium, every asset must be priced so that its risk-adjusted required rate of return falls exactly on the straight line
If an investment were to lie above or below that straight line, then an opportunity for riskless arbitrage would exist.
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Examples of CAPM
Stocks Expected Return Beta
A 16% 1.2
B 19% 1.3
C 13%0.75
E(rm) = 18%rf = 14%
Which of these stocks is correctly priced?
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Example of CAPM
Given the following security market line
E(ri) = 0.07 + 0.09I
What must be the returns for two stocks assuming their betas are 1.2 and 0.9?