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Loose-leaf for Principles of Corporate Finance (12th Edition)

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Problem

Market efficiency “The strong form of the efficient-market hypothesis is nonsense. Look at mutual fund X; it has had superior performance for each of the last 10 years.” Does the speaker have a point? Suppose that there is a 50% probability that X will obtain superior performance in any year simply by chance.

a. If X is the only fund, calculate the probability that it will have achieved superior performance for each of the past 10 years.

b. Now recognize that there are nearly 10,000 mutual funds in the United States. What is the probability that by chance there is at least 1 out of 10,000 funds that obtained 10 successive years of superior performance?

Step-by-step solution

Efficient market hypothesis is an investment theory. This theory states that it is impossible to beat the market. This is because; the stock market efficiency causes the shares to reflect all the relevant information.

As per the theory, stocks always trade on fair value on stock exchange. This does not lead to investors buying undervalued or overvalued stock.

Comment

Mutual fund X has superior performance for each year for last 10 years. There is a 50% probability that X will obtain superior performance in any year.

Comment

(a)

Calculate the probability of achieving superior performance.

For one year probability of achieved superior performance is 50% or 0.50.

Mutual fund X being the only fund, calculate the probability of achieving superior performance as follows:

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Therefore, the probability of achieving superior performance is 0.00097656 .

Comment

(b)

Calculate the probability of at least 1 out of 10,000 funds that have obtained 10 successive years of superior performances.

There are 10,000 Mutual Funds in U.S.

Calculate the probability that out of 10,000 funds, none have obtained 10 successive years of superior performances as follows:

Comment

Calculate the probability of at least 1 out of 10,000 funds that have obtained 10 successive years of superior performances as follows:

Therefore, the probability of at least 1 out of 10,000 funds that have obtained 10 successive years of superior performances is 0.99994288 .

Comment

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Step 5 of 5

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Chapter 13, Problem 23P

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Chapter 13, Problem 22P

Market efficiency “The strong form of the efficient- market hypothesis is nonsense. Look at mutual fund X; it has had superior...

See solution

  Textbook Solutions Expert Q&A Practice Study Pack 

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