SAMPLE SECOND QUIZ
with selected numerical answers
Do all the problems. Include calculations and/or explanations in your answers wherever appropriate. More credit will be given for correct reasoning than for correct arithmetic.
- Consider the following scheme for making money in the stock market.
“You are a mathematician specializing in chaos theory. This is still a small branch of mathematics, and there are very few other chaoticians studying the stock market. You have found a very subtle deterministic, chaotic pattern in stock price changes which has been repeating dependably. You use this pattern to predict which stocks are going to rise in price and which are going to fall. Buy stocks when you predict a rise and sell (and sell short) those for which you predict a fall.”
If the market is completely efficient can you make money this way? If your profits require an inefficiency, what kind is it?
2. In January 1, 2004 I held 100 shares of ABC Co. stock, then selling for $40.00 per share. On June 1, when the price was $45.00 the stock paid a $3.00/sh dividend. At the close of trading on Dec. 31 the price was $42.00.
(a) What was the rate of return calculated using the holding period method? 12.5%
(b) What was the rate of return using the reinvestment rate method? 12%
(c) Which rate is higher? Why?
3. I am now 25 and beginning to plan for retirement. I hope to retire at 68 and die actuarially at 83. I am forecasting a rate of return of 6% real during accumulation and 4% in retirement.
(a) If I contribute $3,600 per year during accumulation, what annual income can I expect in retirement? $675,027
(b) If I want a retirement income of $100,000 per year, what annual contribution must I make? $5,930
4. I am now 45 with $75,000 in my retirement plan. I am hoping to retire at 68 with a 15 year retirement. I am forecasting a rate of return of 6% in accumulation and 3% in retirement. I want an annual income of $100,000 in retirement.
(a) What annual contribution must I make in accumulation to finance that retirement? $19,306
(b) Suppose the next week after I have decided what contribution to make in part (a) a big loss in the stock market reduces my $75,000 by 30%. If I continue to make the contributions I calculated in part (a) and retire at 69 with a 15 year retirement, what will my income be in retirement?