Null Hypothesis: What Is It and How Is It Used in Investing?

A null Hypothesis is a kind of statistical hypothesis that does not show any relationship between the variables. This hypothesis is considered "true" until proven wrong based on given or experimental data. It is useful in quantitative analysis, where theories related to the market, investing strategies, or economies are required to be tested to check whether an idea is true or false. To provide support to the alternative hypothesis, the null hypothesis must be rejected first.

Understanding Null Hypothesis

The null hypothesis is the statement that states that there is no relationship between the two variables, and the researchers assume this before conducting the research. Here, null means nothing, which defines that no relationship is present between variables.

For example, consider the statement that says, "Increase in the number of cancer patients is not due to increase in pollution level". In that case, it will be said that there is no relationship between the two variables meaning the number of cancer patients is not increasing because of the increase in pollution level. So, it depicts the null hypothesis.

The null hypothesis is typically the opposite of what a researcher predicts or expects. The null hypothesis is tested, and the researcher checks whether the null hypothesis is to be rejected.

The null hypothesis is believed to be true unless it is proved false by the researchers by finding evidence against it. As all the tests are done on the basis of the null hypothesis, in the end, the null hypothesis either gets rejected or not.

Working of Null Hypothesis

Whenever a researcher conducts any research, hypothesis testing is done in the process of such research. The researcher also considers a null hypothesis, and some statistical tests are done to check whether the null hypothesis should be rejected. Statistical tests are conducted to test the hypothesis. A statistical test examines the statement or null hypothesis that the researcher has assumed to make a hypothesis.

Let us understand the working of the null hypothesis with an example. Suppose there is a gambler who wants to know whether the game of chance is fair or not. The gambler takes the null hypothesis into consideration. If the expected earnings for both players come to zero per play, then it is called fair. But, when the expected earning for one player is positive, and for the other player, it is negative, the game is said to be unfair.

The gambler collects data on earnings from many previous games for testing. After the collection of earning data, he calculates the average earnings and checks his null hypothesis, i.e., expecting the earnings of both players are not different from zero.

Suppose the average earning calculated is far more than zero. In that case, the gambler will reject the null hypothesis and look for an alternative hypothesis, stating that the expected earnings per play are different from zero.

But if in case, the average earning is not exactly zero but anywhere around it or close to zero, then in such a case, the gambler will not reject the null hypothesis, and the conclusion will be given that the difference is between zero and the average earning is nothing but by chance.

Whoever the researcher is, his main objective is always to reject the null hypothesis as it strengthens the conclusion or the result of the research. And therefore, to reject a null hypothesis, strong evidence is required, and only chance is not enough to explain.

Suppose the researcher fails to reject the null hypothesis and tries to explain the results by chance. In that case, it is seen as a very weak conclusion and shows that some other factors are present but are not detected by the research. However, they might be affecting the results of the research. It is essential to note that the null hypothesis can only be rejected, not proven.

The Alternative Hypothesis

The null hypothesis is tested because there is an element of doubt that it is not valid. All the information or pieces of evidence which are against the null hypothesis and help in proving the null hypothesis false are recorded in the Alternative Hypothesis. Simply put, the alternative hypothesis refers to a direct contradiction of the null hypothesis.

For example, consider the null hypothesis statement that says- "the mean annual return of the mutual fund is equal to 8% per year".

So, the alternate hypothesis will state that "the mean annual return of the mutual fund is not equal to 8% per year".

Use of Null Hypothesis Testing in Investment

Let's take an example related to the financial market. Suppose Arun believes that the return he is receiving by his investment strategy is higher than the return he gets by simply buying and holding a stock. The null hypothesis in such a condition will be that there is no difference in the two average returns, and Arun must believe this until he gets any other result contradictory to it.

Refuting a null hypothesis requires showing some statistical significance, which can be found through various tests. In this case, the alternative hypothesis will be the opposite of the null hypothesis, and therefore it will state that the investment strategy of Arun will have a higher average return than a traditional buy-and-hold strategy.

P-Value is one of the tools which can be used to determine the statistical significance of the results. P-Value is used to show the probability that the difference between the two average returns can occur because of chance solely. If the p-value is not greater than 0.5 but less than or equal to 0.5, it means that there is some evidence that is against the null hypothesis and that can be used to reject the null hypothesis.

Suppose Arun performs such tests and sees a significant difference between the average returns between his return from the investment strategy and return from the buy and hold strategy, which means the p-value is less than 0.5 or equal to 0.5. In that case, Arun may reject the null hypothesis and conclude the alternative hypothesis.

Uses of Null Hypothesis in Finance

While doing any quantitative analysis in finance, the null hypothesis is often used. A null hypothesis checks against the premise of an investment strategy, market, or economy to conclude whether it is true or false. For example, in the case where the analyst wants to test whether stocks XYZ and ABC are correlated, he may take the null hypothesis, which states that stocks XYZ and ABC are not correlated (i.e., XYZ ≠ ABC).

How are Statistical Hypotheses tested?

To check any statistical hypothesis, there are four steps that need to be followed. They are:

• In the first step, the analyst performing the research need to state two hypotheses so that one of them can be rejected.
• The second step is to make a plan for the evaluation of data correctly.
• The third step is to implement the plan and so the sample data analysis is done physically.
• In the final step, i.e., the fourth step, the results of the tests are analyzed, and the null hypothesis is rejected, or a claim is made to explain that the observed differences are solely because of chance.