## 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 ClosePrior 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 ClosePrior 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.