Business Context

NorthBridge Asset Management is evaluating whether a simple value factor should be added to its systematic equity model. In systematic investing, a factor is a measurable stock characteristic associated with differences in expected returns.

Problem Statement

You are given monthly returns for a long-short value factor portfolio over the last 24 months. The portfolio goes long cheap stocks and short expensive stocks, where “cheap” and “expensive” are defined using book-to-market. Determine whether the factor has delivered a statistically significant positive average return, and explain what a factor means in systematic investing.

Given Data

Interpret returns in decimal form, so 0.0068 = 0.68% per month.

Requirements

1. Define what a factor is in systematic investing.
2. Name at least four common factors and briefly describe them.
3. State the null and alternative hypotheses for testing whether the value factor has positive expected return.
4. Compute the standard error of the sample mean.
5. Compute the t-statistic and one-sided p-value.
6. Decide whether the factor is statistically significant at the 5% level.
7. Calculate a 95% confidence interval for the mean monthly return.
8. Interpret the result in portfolio-management terms.

Assumptions

• Monthly factor returns are independent and identically distributed.
• The sample is small enough that a t-test is appropriate.
• The historical sample is representative of future factor behavior.