Hypothesis Testing in Finance - Explained with Example

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What is hypothesis testing?

Finance is incomplete without statistics and Hypothesis Testing is a method of statistical inference. Too much technical for you?

Basically, it is a method that analysts use to check if the statement (question) about a population parameter (sample selection) is useful or not. Want to check the power of predictions? Hypothesis Testing is a powerful tool for that.

Who uses hypothesis testing?

Well, generally, this statistical tool is used by the financial analysts. But that does not mean that people belonging to other domains cannot use it. If you are an English literature student and have a thorough knowledge of Hypothesis Testing, ain’t nobody stopping you.

Anyway, suppose financial analysts want to predict the mean value that a customer can pay for the product that a firm is manufacturing. The Bugatti La Voiture Noire is in trend so let us assume that. Now, the analyst can formulate a hypothesis like “The average value a billionaire can pay for this car is $5 million.” This is a hypothesis that the firm will now test and that will be hypothesis testing.

Hypothesis testing is a scientific method.

Do you feel like Stephen Hawking right now? Hypothesis Testing is a major part of the scientific methods that is a systematic approach of measuring the theories through visual examination. A good theory is the one that makes accurate predictions. For an analyst who is making predictions about the business, hypothesis testing is a way in which he/she can give statistical support to the predictions. If the analysts say the product is going to fetch $100 million in sales in the first week, hypothesis testing is to check if that is true or not.

How should you conduct hypothesis testing?

1. Begin by stating your null hypothesis. Let us call is H0. Then you state your alternative hypothesis which we should call Ha.
2. After the hypothesis have been declared, identify the statistical assumptions that will be made. The statistical assumption should be evaluated to see if these assumptions are in agreement with the sample chosen.
3. Determine the appropriate probability distribution and select the appropriate test statistic.
4. Select the Significance Level (?). What is that? It is the probability threshold for which the null hypothesis will be rejected.
5. Based on the significance level and on the appropriate test, state the decision rule.
6. Collect the observed sample data and use it to calculate the test statistic.
7. Based on your results you should either reject the null hypothesis or fail to reject the null hypothesis. This is known as the statistical decision.
8. Consider any other economic issues that are applied to the problem. These are non-statistical considerations that need to be considered for a decision. For example, sometimes societal cultural shifts lead to changes in consumer behaviour, this must be taken into consideration in addition to the statistical decision for a final decision.

Explanation with an example.

Will the customers pay an average $5 million for the new Bugatti car?

1. Null hypothesis, H0 <= 5

Alternative hypothesis, Ha > 5

2. The car will be bought by billionaires around the world. There is a huge population of billionaires around the world of various cultural backgrounds. So, the car will be used by a population of the normal distribution.
3. Let us assume that we can survey 100 billionaires and collect observations. Our population choice is right and sufficient population, we will go with z-test.
4. As a financial analyst, one should be confident of the result. Let us take the significance level of ?=5%.
5. After applying formula and stuff, the rejection point becomes 1.645. So, if the z score comes larger than 1.645, we are dumping this hypothesis.
6. The mean price that the customers can pay is $5.02 million. This came from the data of 100 observations. Standard deviation is of $0.10. The z score will be [(5.02 – 5) / ( 0.1/ ?100)] = 2.
7. Z score is greater than 1.645, so we reject our null hypothesis at 5% significance level. So, the alternative hypothesis holds true that the customers will pay on average a price greater than $5 million. And the car was sold for $18 million.

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