Let R denote the simple monthly return on Microsoft stock and let W0 denote initial wealth to be invested over the month. Assume that R N(0:05;(0:12)2 ) and that W0 = $100,000. Determine the 1% and 5% value-at-risk (VaR) over the month on the investment. That is, determine the loss in investment value that may occur over the next month with 1% probability and with 5% probability. Determine the 1% and 5% expected shortfall (ES) over the month on the investment.

What are the positive environmental trends seen today? many industries are taking measures to reduce the use( _gold,carbon dioxide,ozone_) of -depleting substances and are turning to(_scarce,renewable,non-recyclable_) energy sources though they may seem expensive. choose one of those 3 option to fill the

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x,y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.

Sales at a fast-food restaurant average $6,000 per day. the restaurant decided to introduce an advertising campaign to increase daily sales. to determine the effectiveness of the advertising campaign, a sample of 49 days of sales were taken. they found that the average daily sales were $6,300 per day. from past history, the restaurant knew that its population standard deviation is about $1,000. if the level of significance is 0.01, have sales increased as a result of the advertising campaign? multiple choicea)fail to reject the null hypothesis.b)reject the null hypothesis and conclude the mean is higher than $6,000 per day.c)reject the null hypothesis and conclude the mean is lower than $6,000 per day.d)reject the null hypothesis and conclude that the mean is equal to $6,000 per day.expert answer