Question

The analyst also tells you that shares in Chris Mining plc have no systematic risk, in other words that the returns on its shares are completely unrelated to movements in the market. The value of beta and its standard error are calculated to be 0.214 and 0.186, respectively. The model is estimated over thirty-eight quarterly observations. Write down the null and alternative hypotheses. Test this null hypothesis against a two-sided alternative.

Answer 1

We want to use a two-sided test to test the null hypothesis that shares in Chris Mining are completely unrelated to movements in the market as awhole. In other words, the value of beta in the regression model would be zero so that whatever happens to the value of the market proxy, ChrisMining would be completely unaffected by it.The null and alternative hypotheses are therefore:

H₀: = 0

H₁: 0

The test statistic has the same format as before, and is given by:

where

We want to find a value from the t-tables for a variable with

38-2=36 degrees of freedom,

and we want to look up the value that puts 2.5% of the distribution in each tail since we are doing a two-sided test and we want to have a 5% size of test over all:

The critical t-value is therefore 2.03.Since the test statistic is not within the rejection region, we do not reject the null hypothesis. We therefore conclude that we have no statistically significant evidence that Chris Mining has any systematic risk. In other words, we have no evidence that changes in the company’s value are driven by movements in the market.