A theory about the S&P 500 index is that if it increases during the first five t

Question

A theory about the S&P 500 index is that if it increases during the first five trading days of the year, itis likely to increase during the entire year. From 1950 through 2005, the S&P 500 index had these early gains in 35 years. In 30 of these 35 years, the S&P 500 index increased.

Assuming that this indicator is a random event with no predictive value, you would expect that the indicator would be correct 50% of the time. What is the probability of the S&P 500 index increasing in 30 or more years if the true probability of an increase in the S&P 500 index is?

a. 0.50?

b. 0.70?

c. 0.90?

d. Based on the results of (a) through (c), what do you think is the probability that the S&P 500 index will increase if there is an early gain in the first five trading

days of the year? Explain

Explanation / Answer

(a) Here if p = 0.50 where p =  true probability of an increase in the S&P 500 index is

so, Pr(X >= 30) = BIN(X >= 30 ; 35; 0.50) = 1 - BINOMIAL (X < 30 ; 35 ; 0..50) = 1 - 0.999989 = 0.000011

(b) if p = 0.70 then

Pr(X >= 30) = BIN(X >= 30 ; 35; 0.70) = 1 - BINOMIAL (X < 30 ; 35 ; 0.70) = 1 - 0.9731 = 0.0269

(c) if p = 0.90 then

Pr(X >= 30) = BIN(X >= 30 ; 35; 0.90) = 1 - BINOMIAL (X < 30 ; 35 ; 0.90) = 1 - 0.1316= 0.8684

(d) Here as we see that the probability of that indicator would be in between 0.70 and 0.90 which is approximately 30/35 = 6/7 = 0.85.

Here it can be explained as random experiment with success in 30 out of 35 events.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.