Question

Allen Young has always been proud of his personal investment strategies and has done very well over the past several years. He invests primarily in the stock market. Over the past several months, however, Allen has become very concerned about the stock market as a good investment. In some cases, it would have been better for Allen to have his money in a bank than in the market. During the next year, Allen must decide whether to invest $10,000 in the stock market or in a certificate of deposit (CD) at an interest rate of 5%. If the market is good, Allen believes that he could get a 15% return by investing in stocks. With a fair market, he expects to get a 6% return. If the market is bad, he will most likely to get a 5% loss.

(a) Develop a table of opportunity losses.

(b) Allen estimates that the probability of a good market is p and the probability of a fair market is q. He thinks that CD is the best option given the probabilities. Now, Allen is thinking about paying for a stock market newsletter, which could predict very accurately how the market would be. He determines that he would at most pay $500 for the newsletter. Please offer an upper bound and a lower bound for Allen’s estimate of p.

Answer 1

		good market	Bad Market	Worst Market
	Investment	10,000	10,000	10,000
	Return on shares	15%	6%	-5%
	Return on CD	5%	5%	5%
	Cost of Newsletter	500	500	500
A.	Opportunity loss when invested in CD (%)	-10%	-1%	0%
	Opportunity loss when invested in CD ($)	-1,000	-100	-
B.	Upper Bound of good market probability	1,693
	Lower Bound of good market probability	307
	Condifence Interval	693
	STDV	500
	Sample Size	1500	0.5
		500	0.5