Sunday, December 3, 2017

Contingency Tables: Tandem Movements


The table below contains contingency tables for daily co-movement of stock prices with the S&P 500.



Co=movement of Stock Price with S&P 500
Company One
Stock Close<Prior Low
Stock Close Between Prior Low and High
Stock Close>Prior High
S&P Close < Prior Low
12
18
4
S&P Close Between Prior Low & High
26
80
28
S&P Close > Prior High
5
31
48
Company Two
Stock Close<Prior Low
Stock Between Prior Low and High
Stock Close>Prior High
S&P Close < Prior  Low
10
21
3
S&P Close
 Between Prior Low & High
19
68
47
S&P Close
> Prior High
14
48
22


Question One:   A stock moves in tandem with the market in three instances --- (1) stock price close is below previous day’s low, (2) stock price close and S&P 500 close are both between prior low and prior high, and (3) S&P close is greater than prior high.   What is the probability these stocks move in tandem with the market? Is the difference in the likelihoods that these two stocks move in tandem significantly different from zero?


Answer to Problem One:  The probability that the stock moves in tandem with the market is (12+80+48)/252 or 0.556 for the first company and (10+68+22)/252 for the second stock.  


The results of the significant test for difference in proportion of observations that move in tandem is presented below.                                                        
                                                                       

Proportion Test Results
Variable
Mean
Std. Err.
z
Company One
0.556
0.031302
Company Two
0.397
0.0308192
diff
0.158
0.0439276
under Ho:
0.044493
3.57


Go back to the contingency table question list for more problems.





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