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Unformatted text preview: Session 10: Comparing the Performance of Funds A.
Appraisal Ratio Yankee
0.1740 Dow Jones
0.0016 B. The Sharpe index measures the slope of a capital allocation line which summarises the
risks and expected returns of balanced portfolios formed by combining the risk free asset
and a portfolio of risky assets in different proportions. In hindsight, these balanced
portfolios are formed at the beginning of, rather than during, the evaluation period.
C. One may apply the Sharpe index, Treynor index, Jensen alpha, appraisal ratio or
any other measures to rank portfolios. A portfolio is said to have beaten another
one if this portfolio has a larger performance measure. Alternatively, this
portfolio has earned a larger excess return per unit of risk.
D. Among all the portfolio of risky assets lying on the efficient frontier, the capital
asset pricing model asserts that the market portfolio offers the largest excess
return per unit of risk (see the CML) and should be chosen by all investors. An
investor who can tolerate more (less) risk than that of the market portfolio may
borrow (lend) risk-free to achieve other efficient risk-return combinations. Thus
the market portfolio is the benchmark against which all portfolios of risky assets
should be compared. Since the excess return per unit of risk is in fact the Sharpe
ratio and the above performance evaluation has not compared the Sharpe ratios of
the managed portfolio with that of the market index portfolio, the finding is
insufficient to convince me to invest in the fund.
E. The result suggests that the fund manager has demonstrated his/her skills to
consistently include under-valued stocks in the portfolio, i.e., stocks were
purchased at their lows before the market realises the mispricing. However, you
should be aware of the following before committing your money to this fund:
• superior past performance does not necessary imply superior future
• ensure that the manager has not been head-hunted by other institutions
• you must be satisfied with the level of unsystematic risk, as reflected by the
fund’s residual variance, as a result of the weighting bias towards the
F. When a fund manager shifts funds towards a group of securities that are believed to be
underpriced, the fund manager has effectively sacrificed diversification and raised the
level of unsystematic risk of the portfolio for the sake of demonstrating his/her ability to
pick underpriced securities. Therefore, the appraisal ratio, which is defined as alpha
divided by the portfolio residual variance, may be used to rank the two portfolios. A
larger appraisal ratio is preferred because this reflects the ability of the fund manager to
select and invest in a larger number of underpriced securities so as to keep the
unsystematic risk down. 1 ...
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