Let Positive Daily S&P 500 Returns Define Up Days, and Negative

question 32

Essay

Let positive daily S&P 500 returns define up days, and negative daily S&P 500 returns define down days. A stockbroker wants to know if the up and down days of the S&P 500 occur randomly. For 30 trading days, there were 17 up days, 13 down days, four runs of up days, and four runs of down days.
A) Specify the competing hypotheses to determine whether the S&P 500 up and down days occur at random.
B) What is the value of the Wald-Wolfowitz runs test statistic?
C) At the 5% significance level, what is the decision and conclusion?

• A) Specify the competing hypotheses to determine whether the S&P 500 up and down days occur at random.
• B) What is the value of the Wald-Wolfowitz runs test statistic?
• C) At the 5% significance level, what is the decision and conclusion?

---

Definitions:

Respiratory System

The biological system consisting of specific organs and structures used for gas exchange in animals and plants.

Osteoporosis

A condition characterized by weakened bones, making them fragile and more likely to fracture.

Estrogen Levels

The concentration of estrogen hormones in the body, which are crucial to reproductive health and other functions.

Osteogenesis Imperfecta

A genetic disorder characterized by bones that break easily, often with little or no apparent cause, due to a defect in the quality or quantity of collagen.