Consider the statement: “If we can identify a portfolio that beats the S&P 500 Index portfolio, then we should reject the single-index CAPM.” Do you agree or disagree? Explain.
They may prove superior to the single-index model but are not practical.
Though it may be true or not, the single index CAPM is a form of correlation equation between two variables.
As of now, there are no tools i.e. index funds or ETFs to directly invest in the 500 index portfolio. These could even be superior to a single index yet they are not practical even for professional investors.
Your investment client asks for information concerning the benefits of active portfolio management. She is particularly interested in the question of whether active managers can be expected to consistently exploit inefficiencies in the capital markets to produce above-average returns without assuming higher risk.
The semi-strong form of the efficient market hypothesis asserts that all publicly available information is rapidly and correctly reflected in securities prices. This implies that investors cannot expect to derive above-average profits from purchases made after information has become public because security prices already reflect the information’s full effects.
a. Identify and explain two examples of empirical evidence that tend to support the EMH implication stated above.
b. Identify and explain two examples of empirical evidence that tend to refute the EMH implication stated above.
c. Discuss reasons why an investor might choose not to index even if the markets were, in fact, semi-strong-form efficient.
Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 30%.
Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3%, and one-half have an alpha of - 3%. The analyst then buys $1 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1 million of an equally weighted portfolio of the negative-alpha stocks.
a. What is the expected profit (in dollars), and what is the standard deviation of the analyst’s profit?
b. How does your answer change if the analyst examines 50 stocks instead of 20? 100 stocks?
Assume that both X and Y are well-diversified portfolios and the risk-free rate is 8%.
In this situation you could conclude that portfolios X and Y:
a. Are in equilibrium.
b. Offer an arbitrage opportunity.
c. Are both under priced.
d. Are both fairly priced.
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