Year	S&P 500 (includes dividends)	3-month T.Bill	US T. Bond	Baa Corporate Bond	Real Estate	Gold
1928	43.81%	3.08%	0.84%	3.22%	1.49%	0.10%
1929	-8.30%	3.16%	4.20%	3.02%	-2.06%	-0.15%
1930	-25.12%	4.55%	4.54%	0.54%	-4.30%	0.10%
1931	-43.84%	2.31%	-2.56%	-15.68%	-8.15%	-17.38%
1932	-8.64%	1.07%	8.79%	23.59%	-10.47%	21.28%
1933	49.98%	0.96%	1.86%	12.97%	-3.81%	27.26%
1934	-1.19%	0.28%	7.96%	18.82%	2.91%	31.75%
1935	46.74%	0.17%	4.47%	13.31%	9.77%	0.43%
1936	31.94%	0.17%	5.02%	11.38%	3.22%	0.09%
1937	-35.34%	0.28%	1.38%	-4.42%	2.56%	-0.23%
1938	29.28%	0.07%	4.21%	9.24%	-0.87%	0.17%
1939	-1.10%	0.05%	4.41%	7.98%	-1.30%	-1.23%
1940	-10.67%	0.04%	5.40%	8.65%	3.31%	-1.66%
1941	-12.77%	0.13%	-2.02%	5.01%	-8.38%	0.00%
1942	19.17%	0.34%	2.29%	5.18%	3.33%	0.00%
1943	25.06%	0.38%	2.49%	8.04%	11.45%	0.00%
1944	19.03%	0.38%	2.58%	6.57%	16.58%	0.00%
1945	35.82%	0.38%	3.80%	6.80%	11.78%	2.54%
1946	-8.43%	0.38%	3.13%	2.51%	24.10%	0.00%
1947	5.20%	0.60%	0.92%	0.26%	21.26%	0.00%
1948	5.70%	1.05%	1.95%	3.44%	2.06%	0.00%
1949	18.30%	1.12%	4.66%	5.38%	0.09%	-8.70%
1950	30.81%	1.20%	0.43%	4.24%	3.64%	9.56%
1951	23.68%	1.52%	-0.30%	-0.19%	6.05%	0.00%
1952	18.15%	1.72%	2.27%	4.44%	4.41%	-0.35%
1953	-1.21%	1.89%	4.14%	1.62%	11.52%	0.69%
1954	52.56%	0.94%	3.29%	6.16%	0.92%	0.57%
1955	32.60%	1.72%	-1.34%	2.04%	0.00%	-0.03%
1956	7.44%	2.62%	-2.26%	-2.35%	0.91%	-0.11%
1957	-10.46%	3.22%	6.80%	-0.72%	2.72%	-0.11%
1958	43.72%	1.77%	-2.10%	6.43%	0.66%	0.43%
1959	12.06%	3.39%	-2.65%	1.57%	0.11%	0.00%
1960	0.34%	2.87%	11.64%	6.66%	0.77%	0.48%
1961	26.64%	2.35%	2.06%	5.10%	0.98%	-0.06%
1962	-8.81%	2.77%	5.69%	6.50%	0.32%	-0.06%
1963	22.61%	3.16%	1.68%	5.46%	2.14%	-0.40%
1964	16.42%	3.55%	3.73%	5.16%	1.26%	0.03%
1965	12.40%	3.95%	0.72%	3.19%	1.66%	0.06%
1966	-9.97%	4.86%	2.91%	-3.45%	1.22%	0.03%
1967	23.80%	4.29%	-1.58%	0.90%	2.32%	-0.51%
1968	10.81%	5.34%	3.27%	4.85%	4.13%	12.47%
1969	-8.24%	6.67%	-5.01%	-2.03%	6.99%	5.01%
1970	3.56%	6.39%	16.75%	5.65%	8.22%	-9.45%
1971	14.22%	4.33%	9.79%	14.00%	4.24%	16.69%
1972	18.76%	4.06%	2.82%	11.41%	2.98%	48.78%
1973	-14.31%	7.04%	3.66%	4.32%	3.42%	72.96%
1974	-25.90%	7.85%	1.99%	-4.38%	10.07%	66.15%
1975	37.00%	5.79%	3.61%	11.05%	6.77%	-24.80%
1976	23.83%	4.98%	15.98%	19.75%	8.18%	-4.10%
1977	-6.98%	5.26%	1.29%	9.95%	14.65%	22.64%
1978	6.51%	7.18%	-0.78%	3.14%	15.72%	37.01%
1979	18.52%	10.05%	0.67%	-2.01%	13.74%	126.55%
1980	31.74%	11.39%	-2.99%	-3.32%	7.40%	15.19%
1981	-4.70%	14.04%	8.20%	8.46%	5.10%	-32.60%
1982	20.42%	10.60%	32.81%	29.05%	0.56%	15.62%
1983	22.34%	8.62%	3.20%	16.19%	4.75%	-16.80%
1984	6.15%	9.54%	13.73%	15.62%	4.68%	-19.38%
1985	31.24%	7.47%	25.71%	23.86%	7.47%	6.00%
1986	18.49%	5.97%	24.28%	21.49%	9.61%	18.96%
1987	5.81%	5.78%	-4.96%	2.29%	7.88%	24.53%
1988	16.54%	6.67%	8.22%	15.12%	7.21%	-15.26%
1989	31.48%	8.11%	17.69%	15.79%	4.38%	-2.84%
1990	-3.06%	7.50%	6.24%	6.14%	-0.69%	-3.11%
1991	30.23%	5.38%	15.00%	17.85%	-0.16%	-8.56%
1992	7.49%	3.43%	9.36%	12.17%	0.82%	-5.73%
1993	9.97%	3.00%	14.21%	16.43%	2.16%	17.68%
1994	1.33%	4.25%	-8.04%	-1.32%	2.51%	-2.17%
1995	37.20%	5.49%	23.48%	20.16%	1.80%	0.98%
1996	22.68%	5.01%	1.43%	4.79%	2.42%	-4.59%
1997	33.10%	5.06%	9.94%	11.83%	4.02%	-21.41%
1998	28.34%	4.78%	14.92%	7.95%	6.45%	-0.83%
1999	20.89%	4.64%	-8.25%	0.84%	7.68%	0.85%
2000	-9.03%	5.82%	16.66%	9.33%	9.28%	-5.44%
2001	-11.85%	3.40%	5.57%	7.82%	6.67%	0.75%
2002	-21.97%	1.61%	15.12%	12.18%	9.56%	25.57%
2003	28.36%	1.01%	0.38%	13.53%	9.82%	19.89%
2004	10.74%	1.37%	4.49%	9.89%	13.64%	4.65%
2005	4.83%	3.15%	2.87%	4.92%	13.51%	17.77%
2006	15.61%	4.73%	1.96%	7.05%	1.73%	23.20%
2007	5.48%	4.36%	10.21%	3.15%	-5.40%	31.92%
2008	-36.55%	1.37%	20.10%	-5.07%	-12.00%	4.32%
2009	25.94%	0.15%	-11.12%	23.33%	-3.85%	25.04%
2010	14.82%	0.14%	8.46%	8.35%	-4.12%	29.24%
2011	2.10%	0.05%	16.04%	12.58%	-3.88%	12.02%
2012	15.89%	0.09%	2.97%	10.12%	6.44%	5.68%
2013	32.15%	0.06%	-9.10%	-1.06%	10.72%	-27.61%
2014	13.52%	0.03%	10.75%	10.38%	4.51%	0.12%
2015	1.38%	0.05%	1.28%	-0.70%	5.21%	-12.11%
2016	11.77%	0.32%	0.69%	10.37%	5.31%	8.10%
2017	21.61%	0.93%	2.80%	9.72%	6.21%	12.66%
2018	-4.23%	1.94%	-0.02%	-2.76%	4.53%	-0.93%
2019	31.21%	2.06%	9.64%	15.33%	3.69%	19.08%
2020	18.02%	0.35%	11.33%	10.41%	10.35%	24.17%
2021	28.47%	0.05%	-4.42%	0.93%	18.91%	-3.75%
2022	-18.01%	2.02%	-17.83%	-14.49%	7.30%	0.55%

To maintain a semblance of her prior lifestyle she needs to draw down 50K per year to complement social security and other pension payments. a) Based on actual data (use the random function to select different starting years, sampling 40 times), determine the average number of years she can continue to draw down 50K before she runs out of money.

b) Second, since your client understands distribution (she took this course) and comes from a family of septagenarians, she wants to know what is the maximum she can draw down, with 95% confidence, if she expects to live to 78. She is 65 now.

c) finally, any other advice you would like to offer

FAQ question: wont the answer be different since it will change when i open it answer: i expect that using the random function even a couple of dozen times (since there is only 90 odd years of history) the average will be relatively stable. again i care about the analysis and model and any out of the box thinking you can bring to the issue please dont hesitate if you have any other questions question: how can we set the formuala to get a non-negative number? answer: the random function is used to randomize the retirement year back in history. so a random function may result in your retiring in 1939 or 1972 or 1956 etc.. we need to do a simulation. what happens with your savings if you had invested in the market and the market returned whatever it actually did that year (data provided) figure out how frequently she might be broke before she dies? also see how much the frequency of going broke drops, if the cash spent is reduced hope this helps. this is a very realistic and non-academic assignment. The question is how does one count the number of years till the money goes negative. Answer: please keep in mind that the money invested on the first year of retirement earns a return based on the return of that year in the market. so unless one is unlucky in retiring when thie market is about to crash, the one should be able to make do for many years. a simple example is that if the market returned 10% the year the person retired, then the market paid the retiree $40K on a 400K investment. so even if the drawdown is $50K, it should go a longish while. the purpose of the exercise is to make it vividly clear how much of financial security is random Question: I am wondering for the answer, do we just pick any year to work out an answer or does the answer need to account for all possibilities (starting year ranging from 1928--1998)? Answer: One has to account for more than one year. One can do it for all years (since the sample is not too big) OR use the random function for a few dozen years and take the average of that.. Again, please don't be scared about not having the 'right' answer. In life there is rarely such a thing. I look forward to your best thinking and work, maybe incorporating any tools and material we covered. FAQ question: wont the answer be different since it will change when i open it answer: i expect that using the random function even a couple of dozen times (since there is only 90 odd years of history) the average will be relatively stable. again i care about the analysis and model and any out of the box thinking you can bring to the issue please dont hesitate if you have any other questions question: how can we set the formuala to get a non-negative number? answer: the random function is used to randomize the retirement year back in history. so a random function may result in your retiring in 1939 or 1972 or 1956 etc.. we need to do a simulation. what happens with your savings if you had invested in the market and the market returned whatever it actually did that year (data provided) figure out how frequently she might be broke before she dies? also see how much the frequency of going broke drops, if the cash spent is reduced hope this helps. this is a very realistic and non-academic assignment. The question is how does one count the number of years till the money goes negative. Answer: please keep in mind that the money invested on the first year of retirement earns a return based on the return of that year in the market. so unless one is unlucky in retiring when thie market is about to crash, the one should be able to make do for many years. a simple example is that if the market returned 10% the year the person retired, then the market paid the retiree $40K on a 400K investment. so even if the drawdown is $50K, it should go a longish while. the purpose of the exercise is to make it vividly clear how much of financial security is random Question: I am wondering for the answer, do we just pick any year to work out an answer or does the answer need to account for all possibilities (starting year ranging from 1928--1998)? Answer: One has to account for more than one year. One can do it for all years (since the sample is not too big) OR use the random function for a few dozen years and take the average of that.. Again, please don't be scared about not having the 'right' answer. In life there is rarely such a thing. I look forward to your best thinking and work, maybe incorporating any tools and material we covered