Chapter 2: Q2B (page 284)
Question: After reading about three successful investors in The Wall Street Journal you decide that active investing will also provide you with superior trading results. What sort of behavioral tendency are you exhibiting?
Answer
Representativeness bias
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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?
In forming a portfolio of two risky assets, what must be true of the correlation coefficient between their returns if there are to be gains from diversification? Explain.
We know that the market should respond positively to good news and that good-news events such as the coming end of a recession can be predicted with at least some accuracy. Why, then, can we not predict that the market will go up as the economy recovers?
If the simple CAPM is valid, which of the situations in Problems 13 – 19 below are possible? Explain. Consider each situation independently.
Portfolio | Expected Return | Standard Deviation |
A B | 30% 40 | 35% 25 |
You’ve just decided upon your capital allocation for the next year, when you realize that you’ve underestimated both the expected return and the standard deviation of your risky portfolio by 4%. Will you increase, decrease, or leave unchanged your allocation to risk-free T-bills?
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