SPY Recommendation

SPY is a popular fund that aims to track the S&P 500 Index that is made up of 500 large and mid-cap stocks traded on the U.S. stock market. The stocks that are in the index are carefully chosen to represent the financial health and stability of the economy. The S&P 500 is widely seen as the definitive measurement of the U.S. stock market. Therefore, when you choose to invest in SPY you are basically investing in the stock market as a whole. You can acquire shares of SPY in the form of a stock on the New York Stock Exchange.

To give you some data to look over I calculated the mean and standard deviation of the monthly values of SPY from its inception on February 2, 1993. To do this I used google sheets and made a pivot table with the data from google finance. With that pivot table I was able to separate the month and price and calculate an average rate of return for each month by using the formula ((Next month price-Previous month price)/Previous month price). I then took the average of these returns to get the mean return over the life of SPY and that came out to be 0.78% and I also calculated a standard deviation of 4.56%. With this data we can look at the range of SPY's possibility of return for years to come. Assuming that SPY's monthly returns are normally distributed we can reasonably predict that 68% of the time SPY will produce a monthly return of -3.78% to 5.34%. These percentages were calculated by taking the mean monthly return and doing +/- one standard deviation from the mean. This shows that even if SPY has a bad month the loss you will be taking on will likely not be a harsh one, and it is likely that SPY will recover along with the market in the near future.

Based on this data you can see that SPY will not produce unbelievable returns year in and year out, but it is a safe investment in that over a 28+ year life it has produced on average a positive return with a relatively low standard deviation.

To calculate an estimated return by contributing $500 a month over a 30 year period in SPY in an IRA, I did a random return generator based on the $500 monthly contribution, the mean and standard deviation represented above, and a random function in google sheets. Using this formula I calculated a random amount that the IRA would be at in 30 years one hundred times and took a mean and standard deviation of the results. The mean was $951,633 and the standard deviation of the random sample was $752,511. This means that over 100 simulations, based upon the mean and standard deviation of SPY over its lifetime, and by contributing $500 monthly into SPY over 30 years the average amount in your IRA would be $951,633. Additionally, your IRA could very well have a balance of $1,704,144, the likelihood of this event is quite reasonable as this is only one standard deviation away from the mean!

All of this is exciting news, but before I make my recommendation on SPY I would like to perform the chances of a fat-tail event occurring. A fat-tail event is when an event occurs that is over 3 standard deviations away from the mean, which basically means it is very unlikely to occur. To calculate this chance I will use the data from October 2008, which was SPY's worst monthly return in its existence during the 2008 Financial Crisis.

SPY's monthly return in October of 2008 was -16.33%, to calculate the probability of this fat-tail event I used the normdist(-0.1633, 0.0078, 0.0456) function in google sheets, the probability of this occurring came out to be 0.0083%. To put that number into years I took 1 divided by 0.0083% times 12(number of months in a year) which came out to be about 947 years. This means that this fat-tail event has the chance to occur once every 947 years! So, basically this won't occur again in our lifetime.

To recap, over its lifetime SPY has produced on average a positive rate of return. In addition, if you look at my projection for an IRA, if you invest $500 monthly for 30 years my simulation over 100 random outcomes, calculated an average amount of $951,633 in your IRA at the end of the 30 years. Why wouldn't you want an extra almost $1 million in 30 years? Lastly, per analysis above the probability of a fat-tail event occurring again like the one in October 2008 is only 0.0083%. Therefore, after all of the analysis presented above I would recommend to invest in SPY.