Interpretation of Beta Coefficient B 1 Asset has the same systematic risk as

Interpretation of beta coefficient b 1 asset has the

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Interpretation of Beta Coefficient B = 1 → Asset has the same systematic risk as the overall market Β < 1 → Asset has less systematic risks than the overall market B > 1 → Asset has more systematic risks than the overall market Example of Portfolio Beta Security Weight Beta INTC .15 0.98 MO .35 0.50 MCD .50 0.47 Portfolio Beta = 0.15(0.98) + 0.34(0.50) + 0.50(0.47) = 0.552 Total Risk versus Beta Standard Deviation Beta Security C 20% 1.25 Security K 30% 0.95 Security K has greater total risks than Security C but less systematic risks. From the systematic risk principle, security C will have a higher risk premium. Beta and Risk Premium Risk premium = Expected return Risk-free rate The higher the beta, the greater the risk premium should be
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38 Interpretation of Graph ?(?) = ? ? + 𝛽 ( ?(? 𝐴 ) − ? ? 𝛽 𝐴 − 0 ) Slope: Reward-to-Risk Ratio = ( ?(𝑅 𝐴 )−𝑅 ? 𝛽 𝐴 −0 ) = ( ?(𝑅 𝐴 )−𝑅 ? 𝛽 𝐴 ) Security Market Line A positively sloped straight line displaying the relationship between expected return and beta. Representation of market equilibrium. The slope of the SML is the reward-to-risk ratio: ?(𝑅 𝑀 )− 𝑅 ? 𝛽 𝑀 But since the beta for the market is ALWAYS equal to one, the slope can be rewritten Slope = E(R M ) R f = market risk premium Argument for SML Market Equilibrium o In an active and competitive market, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market, in equilibrium. o E.g. If Asset A had a super return to Asset B, people would be attracted to Asset A and away from the Asset B. This would cause A’s price to rise while B’s to fall and will continue until the two assets are plotted on exactly the same line. (i.e. Offer the same reward for bearing risk) ?(? 𝐴 ) − ? ? 𝛽 𝐴 = ?(? ? ) − ? ? 𝛽 ? Market Portfolios SML Slope = Risk-to-reward ratio of overall market = ?(𝑅 𝑀 )− 𝑅 ? 𝛽 𝑀 Since M = 1, SML Slope = ?(? ? ) − ? ? (Also known as the Market Risk Premium )
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39 Capital Asset Pricing Model (CAPM) From the theory, we know that reward-to- risk ratio of an asset will be the same as the overall market’s in equilibrium. Hence: ?(? 𝐴 ) − ? ? 𝛽 𝐴 = ?(? ? ) − ? ? ?(? 𝐴 ) = ? ? + 𝛽 𝐴 [?(? ? ) − ? ? ] Expected Return for a particular asset depends on: Pure time value of money o Measured by R f , as the reward for merely waiting for your money, without taking any risks. Reward for bearing systematic risks o Measured by the market risk premium ( ?(? ? ) − ? ? , which is the reward the market offers for bearing an average amount of systematic risk in addition to waiting. Amount of systematic risks o Measured by 𝛽 𝐴 where beta is the amount of systematic risk present in a particular asset or portfolio, relative to that in an average asset. SML and Cost of Capital Cost of Capital: The minimum required return on a new investment. SML is used to find out the cost of capital for projects by finding systematic risk of that project. Use SML to find the expected return in financial markets corresponding to that level of systematic risk.
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