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Equilibrium in the Asset Market

# Equilibrium in the Asset Market - i s m cost of risk =...

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Equilibrium in the Asset Market Risk adjusted return equals the expected return minus the cost of risk. In equilibrium, all assets should have the same risk-adjusted rate of return. If one asset had a higher risk-adjusted rate of return than another, everyone would want to hold the asset with the higher risk-adjusted return. In equilibrium the risk-adjusted rates of return must be equalized. Let E(R m ) = expected return on the market portfolio of risky assets s m = standard deviation of the market return R f = rate of return on the risk-free asset p = price of risk (measures the tradeoff between return and risk) B i = beta for asset i (7) p = [E(R m ) - R f ]/s m B i gives the relative amount of risk in asset i. The total amount of risk in asset i is B
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Unformatted text preview: i s m . cost of risk = total amount of risk x price of risk cost of risk = B i s m p cost of risk = B i s m [E(R m ) - R f ]/s m (8) cost of risk = B i (E(R m ) - R f ) Consider two assets i and j that have expected returns E(R i ) and E(R j ) and betas B i and B j . Then in equilibrium (9) E(R i ) - B i (E(R m ) - R f = E(R j ) - B j (E(R m ) - R f This equilibrium condition must also hold between asset i and the risk-free asset with B f = 0: (10) E(R i ) - B i (E(R m ) - R f = R f ) Rearranging (10): (11) E(R i ) = R f + B i (E(R m ) - R f )...
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