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Unformatted text preview: ibutes to the market portfolio, and is
mathematically defined as the covariance of returns between the asset and the market portfolio divided by
the variance of returns of the market portfolio.
The conclusion that every investor should hold the market portfolio means that the risk of an individual asset
is best described by its beta rather than the SD of returns. The beta equation above also suggests that the
higher the weight (i.e. with a larger market capitalisation), the higher the contribution to a larger proportion of
risk to the market portfolio.
Also, note that the beta of the market portfolio must add up to 1. 10 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 D ERIVING THE SML
I NCREMENTAL REWARD PER UNIT OF INCREMENTAL RISK
For a rational mean-variance optimiser, the basis of comparison between investing a borrowed sum of money
into a market portfolio, or an asset C, is the incremental return per unit of incremental risk. If the market is in
equilibrium, both investments should offer the same incremental return per unit of incremental risk. Invest further in market portfolio () ( Invest in Asset C ) ( () )
( ) If 1 invest offers a larger reward per unit of incremental risk, the homogeneous expectations assumptions
implies that all investors know about this information. They will rush to bid up prices, which will then push
down the expected return, until both reward per unit of incremental risk are equal. Thus, asset C will be at
equilibrium, only when the 2 expressions above are =. After rearranging, this derives to: () ( )− This equation suggests:
• The expected return of a risky asset is linearly related to its beta
Investors are rewarded for the risk that an asset adds to the market portfolio (measured by asset
beta), rather than the total risk of the asset (measured by the asset’s standard deviation of returns)
E(rM)-rf = market risk premium = amount of return in excess of the risk free return required to
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