Imagine that you are holding 6,100 shares of stock, currently selling at $80 per share. you are ready to sell the shares but would prefer to put off the sale until next year due to tax reasons. if you continue to hold the shares until january, however, you face the risk that the stock will drop in value before year-end. you decide to use a collar to limit downside risk without laying out a good deal of additional funds. january call options with a strike price of $85 are selling at $3, and january puts with a strike price of $75 are selling at $5. what will be the value of your portfolio in january (net of the proceeds from the options) if the stock price ends up at $71, $80, $91?

The hawthorne works was a large western electric factory with 45,000 employees. during the 1920s and 1930s, hawthorne works was the site of some well-known industrial studies. in one of the studies, researchers investigated the impact of different working conditions on worker productivity. prior to the start of the study, researchers secretly measured workers' productivity for several weeks. then researchers chose two workers, who then chose their own teams. the teams were separated from the general workforce and completed their work in different experiment rooms where the researchers could observe them more easily. over a 5-year period researchers manipulated the structure of the workday for each team (number and duration of breaks and number of hours per shift). for each of these changes in working conditions, the researchers measured the effect on productivity. for some conditions, such as frequent short breaks, workers rebelled by intentionally decreasing productivity.why did the researchers secretly measure the workers' productivity before creating the two treatment groups? a, to create similar treatment groups so that a cause-and-effect relationship could be establishedb, to draw conclusions about the productivity of all workers in the plant based on the test groupsc, to directly control for confounding variablesd, to provide a baseline for measuring worker productivity