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Unformatted text preview: lies above the CML, or a portfolio that is more efficient than
one suggested by the CML. If there is a superior portfolio, it will have a lower return than the market portfolio
M, but will lie above CML, or is it not possible to locate a balanced portfolio between rf and M that is more
efficient. 9 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 T HE SHARPE RATIO
The Sharpe Ratio provides a quantitative measure for portfolio performance
evaluation. It is the gradient between a risky portfolio and the risk free portfolio. It is a
risk adjusted return. A portfolio is said to have beat the market if its Sharpe ratio is
larger than that of the market portfolio.
The Sharpe Ratio of an investment in asset i in isolation:
Since the market portfolio is the portfolio with the highest
Sharpe ratio, it cannot be improved by changing the portfolio
weights. This means that no isolated investment can have a
larger Sharpe ratio than any other investment. wi E ri rf S E r rf Er r wi Covri , rM i f Covri , rM The outcome that every investor should be holding the value-weighted market portfolio explains the
popularity of index funds. This outcome also explains why index fund managers have to rebalance their
portfolios whenever there is a major change to the composition of the market index. U NDERSTANDING ASSET BETA The CAPM asserts that every investor should be holding the market portfolio, M. To quantify the amount of
risk 1 of the assets, e.g. Asset C contributes to M, we must consider the variance covariance matrix. Every asset
contributes to 1 row in the matrix.
From that, it is clear that Asset C adds the following amount of risk to the market portfolio:
N Cov wC rC , wM rM CovwC rC , rM wC CovrC , rM M 1 Since Asset C is only one of the many risky assets in the market
portfolio, and the total risk of the market portfolio is σ2M, the
proportion of risk of the market portfolio contributed by CBA = wC CovrC , rM 2
M wC c The beta of a risky asset shows the relative amount of risk the asset contr...
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