Question

1. A financial analyst is trying to use changes in real interest rate to predict changes in a stock price index. She is using data from the last 1000 business days out of which the stock price index declined for 560 business days and it increased for the rest of the business days in the sample. According these data, the real interest rate declined on 490 of the business days in the sample and it increased for rest of the business days in the sample. Out of the 440 business days on which the stock price index increased, the real interest rate also increased only on 50 business days and it decreased on the rest. Please answer the following questions based on the given data.

a. If the real interest rate is expected to rise on the next business day, what is the probability that the stock price index will also rise that day? Please show your work. [2 points]

b. If the real interest rate is expected to rise the next business day, what is the probability that the stock price index will fall that day? Please show your work.           [2 points]

c. What is the probability that both the real interest rate and the stock price index will fall the next business day? Please show your work.                                           [1 point]

d. What is the probability that the real interest rate or the stock price index will rise on the next business day? Please show your work.                                            [1 point]

Answer 1

Answer:

given that

A financial analyst is trying to use changes in real interest rate to predict changes in a stock price index.

consider the events

A: stock price index increase

B: real interest rate increase

P(A) = 440/1000 = 0.44

P(B) = 490/ 1000=0.49

P(ANB) = 50/440

=0.1136
=stock price and real interest both are increase

$P(A\cap B^{1}) =390/440$ = stock price increase and real interest rate decrease

$P(A^{1}\cap B)=$real rate increase and stock price decrease =$P(B) - P(A\cap B) =$

a) required probability =

by definition of conditional probability

$P(A/B)=\frac{P(A\cap B)}{P(B)}=\frac{0.1136}{0.49}= 0.2318$

b) required probability =$P(A^{1}\cap B)$

$P(A^{1}/B)= \frac{P(A^{1}\cap B)}{P(B)}=$$\frac{0.3764}{0.49}$

c) required probability $=P(A\cap B)=0.1136$

d) required probability $=P(A\cup B)=P(A)+P(B)-P(A\cap B)=$ $=0.8164$