The typical standard deviation of the annual return on a stock is 20% and the typical mean

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The typical standard deviation of the annual return on a stock is 20% and the typical mean return is about 12%. The typical correlation between the annual returns of two stocks is about 0.25. Mutual funds often put an equal percentage of their money in a given number of stocks. By choosing a large number of stocks, they hope to diversify away the risk involved with choosing particular stocks. How many stocks does an investor need to own to diversify away the risk associated with individual stocks?
To answer this question, use the above information about “typical” stocks to determine the mean and standard deviation for the following portfolios:
Portfolio 1: Half your money in each of 2 stocks
Portfolio 2: 20% of your money in each of 5 stocks
Portfolio 3: 10% of your money in each of 10 stocks
Portfolio 4: 5% of your money in each of 20 stocks
Portfolio 5: 1% of your money in each of 100 stocks
What
do your answers tell you about the number of stocks a mutual fund needs to invest in to diversify adequately?

Stocks
Stocks or shares are generally equity instruments that provide the largest source of raising funds in any public or private listed company's. The instruments are issued on a stock exchange from where a large number of general public who are willing...
Mutual Funds
Mutual funds are like a pool of funds gathered by different small investors that have simalar investment perspective about returns on their investments. These funds are managed by professional investment managers who act smartly on behalf of the...
Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...
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Data Analysis and Decision Making

ISBN: 978-0538476126

4th edition

Authors: Christian Albright, Wayne Winston, Christopher Zappe

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