The post When Can I Retire? Early Retirement Calculator / FIRE Calculator appeared first on Engaging Data.

]]>This early retirement calculator / visualizer is designed to project the number of years until you can retire, based upon a few key inputs such as annual income and spending, income growth rate, expected annual spending in retirement and asset allocation. It is a **pre-retirement** calculator that is useful before you retire to get a sense of how many years it is likely to take to * accumulate enough money to retire*. The three primary modes that are available in the early retirement calculator are: (1) constant, single fixed-percentage real return rates, (2) historical series of real returns are applied to account for likely variability in future returns and (3) monte carlo simulation of the variable returns based upon user-specified input parameters.

– Use this button to generate a URL that you can share a specific set of inputs and graphs. Just copy the URL in the address bar at the top of your browser (after pressing the button).

Your Target Retirement Amount is based upon your **expected annual retirement spending** and your **withdrawal rate**.

`FIRE Target amount = retirement spending / withdrawal rate`

Your money (including the **money you’ve already saved** and the **amount you save each year**) is invested based upon your asset allocation and will grow based upon the following formula annually.

`End of Year Savings = Previous Savings x (1 + GrowthRate) + AnnualSavings `

The growth rate will vary based upon how much of your savings is invested in stocks vs bonds vs cash and the annual growth rate for each of these assets.

Your **savings rate **plays a large role in accumulating enough to retire and improving your savings rate can be done by reducing your annual spending and/or increasing your annual income.

`Savings rate = (Annual (Post-tax) Income - Annual Spending) / Annual (Post-Tax) Income`

**The early retirement calculator determines how many years it takes to reach the FIRE Target.**

There are three primary modes for how this calculator determines returns:

**Fixed percentage**: This mode requires you to enter the expected value for futurestock and bond returns (the default is the US historical average values from 1871 to 2015 of 8.1% and 2.4%). You can see how your retirement time depends on these rates of return.**real****Historical cycles**: This mode uses real stock and bond returns data from the last ~145 years and applies them sequentially to your savings annually to project their growth over time. Each of these chronological series of years starting in a different year is one historical cycle. Each cycle has a different series of stock/bond returns and thus has a different amount of money each year (even with the same annual savings profile).**Monte Carlo simulation**: This mode simulates thousands of possible sets of paths to meet your target and calculates the probability of different trajectories for your retirement investments. You can use the historical distribution of returns for your draws (8.1% real return for stocks and 2.4% for bonds) or you can specify a different average return for each set of assets. This enables you to run for optimistic or pessimistic scenarios.

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When the calendar uses probabilistic outcomes from a series of model runs (i.e. the historical cycles approach and Monte Carlo simulation), the graph shows several bands, the 10th to 90th percentiles, the 25th to 75th percentiles and the median. Some definitions may be helpful for many folks here:

**10th to 90th percentile**– if you have a number of results or observations that you have put in order from smallest to largest, the 10th percentile is the result that is higher than 10% of the other results, while the 90th percentile is higher than 90% of the results. The range from 10th to 90th percentile encompasses 80% of the results and ignores the extreme outliers in the data.**25th to 75th percentile**– similarly, ordering results or observations from smallest to largest, the 25th percentile is the result that is higher than 25% of the other results, while the 75th percentile is higher than 75% of the results. This range encompasses the middle 50% of the results and ignores the lowest and highest results.**Median**– the median is the data point that is in the middle of the ordered data; exactly half of the results are below and half are above.

A * sensitivity analysis* is also included to help you understand the implications of reducing (or increasing) your spending. The calculator runs different spending cases between -20% and +20% spending to show you how your time to retirement changes with these spending amounts.

When using the **Historical cycles** or **Monte Carlo** projection, you can view a * histogram* showing the distribution and variation in the number of years until retirement. Each of these individual runs has it’s own value for when your total invested savings surpasses the FIRE target.

While the frequency of events occurring in the past does not necessarily reflect the future probability, this distribution of outcomes gives a sense of the potential variation in number of years until retirement depending on whether there are a good or bad series of stock market returns

One of the key takeaways is that early on in your journey towards retirement, savings plays a larger role than investment returns. This highlights the importance of having a high savings rate if you would like to minimize the amount of time it takes to achieve your FIRE target.

I hope that is tool will be useful for anyone trying to achieve financial independence. As always, any comments, suggestions or feedback will be greatly appreciated.

**Calculator Update** – I added a button to generate a URL for a specific scenario that you can share with others.

**Data source and Tools** Historical Stock/Bond and Inflation data comes from Prof. Robert Shiller. Javascript, HTML and CSS are used to build the interface and javascript is used to calculate, process and aggregate the retirement balance results over all historical cycles and the results are graphed using Plot.ly javascript graphing library.

**Privacy and Data statement**: None of the information entered into the calculator is transmitted to our server or anywhere else. All of the data stays on your computer and all of the calculations are made within your browser (rather than on this site’s server).

The post When Can I Retire? Early Retirement Calculator / FIRE Calculator appeared first on Engaging Data.

]]>The post Post-Retirement Calculator: Will My Money Survive Early Retirement? Visualizing Longevity Risk appeared first on Engaging Data.

]]>**You may notice that additional features have been added to the calculator (taxes, investment fees, and ability to add other income sources (e.g. social security) and other expenses to the calculator). **

One of the key issues with retiring is the question of outliving your money. This is also known as **Longevity Risk** and is especially important if you want to retire early, since your retirement could be 50 years long (or more). This interactive * post-retirement* calculation and visualization looks at the question of whether your retirement savings can last long enough to support your retirement spending and combines it with average US life expectancy values to get a fuller picture of the likelihood of running out of money before you die.

It helps to answer the question: **If I start out with $X dollars at the beginning of my retirement, will I run out of money before I die?**

The graph shows the likelihood of your balance being at different levels during each year of your retirement (and compares it to the probability of dying during this time). Red indicates failure (i.e. you’ve run out of money) and green indicates success (i.e. you haven’t run out of money). The probabilities are calculated based upon looking at stock, bond and cash returns from historical cycles between 1871 and 2016. If you expect to retire for 50 years, one historical cycle would be from 1871 to 1922, another one from 1872 to 1923, and so on until 1965 to 2016. Thus 95 different historical cycles are considered (in this case). It is important to note that these frequencies in the past are not the same as actual probabilities. Just because an outcome happened once in history doesn’t mean that there is a one in 95 chance (1.05%) of this same thing happening in the future. However, if your retirement portfolio survives most historical cycles, there is a good chance that it’ll survive in the future without any major black swan events. If something crazy occurs (e.g. a major nuclear war), your retirement balance may be the least of your worries, so we can safely ignore this, since there’s very little way to prepare for it financially.

The fields are all pre-filled but you should modify the numbers to suit your situation or to explore other options. Press ‘Enter’ or ‘tab’ after you enter the value into the input box.

- Hover over the input labels for more info.
- Enter your expected spending per year in retirement and the savings amount you expect to have at retirement.
- Enter your age at retirement and how long you expect to live (you can estimate on the longer side since the calculator will include life expectancy).
- Enter your target asset allocation for retirement.
- Enter your sex.
- Enter your average expected tax rate (not your marginal rate) – this will be applied to your annual spending and any additional income.
- Enter your average investment fees (e.g. expense ratios).
- Enter any additional income sources or expenses that aren’t applicable for the entire model period, and indicate both the starting and ending ages. If you have multiple income or expense streams, you can enter them all separated by a semi-colon (;).

You can also modify a few graph elements (to help you focus on different parts of the graph):

- Show or hide the death probability wedge. Hiding it helps you investigate the portfolio balances with greater resolution for later years.
- Show or hide different categories of success (green wedges). Success is defined as any outcome where you are not broke (i.e. balance <0). Additional categories of success include
*balances that are below your initial retirement balance (but still above zero)*and*balances that are more than double your initial retirement balance*. - You can download an PNG image of your graph (click on the camera icon in the lower right).

**Huge tip of the hat to maizeman** who first developed this type of graph and was helpful in putting these graphs together. Thanks! Here is maizeman’s github repo. It is also inspired by many hours of playing with cFIREsim and FIRECalc.

One of the most valuable things about these sorts of interactive graphs is that it allows you to understand how the results vary as you modify the inputs (asset allocation and length of retirement). So I encourage you to play with the inputs to calculator and the ways to visualize and see how the results and hopefully your understanding of the processes change.

One of the key takeaways from this is how large the ‘Wedge of Death’ gets as you get older and how the likelihood of dying is much higher than running out of money.

Another important takeaway is that if your retirement has a large likelihood of success (e.g. 4% or lower withdrawal rate), your retirement balance is most likely to be large (more than 2x your initial balance).

As mentioned earlier, it is important to remember that past performance does not predict future performance.

**Data source and Tools** Historical Stock/Bond and Inflation data comes from Prof. Robert Shiller. Life expectancy data is from the Social Security Administration. Javascript is used to process and aggregate the retirement balance results over all historical cycles and graphed using Plot.ly javascript graphing library.

**Update:** – I’ve gotten alot of really good feedback on this tool. I’m really happy that people find it useful and informative. I’ve also gotten a long list of suggested additions to the calculator, so come back and check to see if I’ve implemented any.

**First update: **I added the ability to toggle between looking at nominal and inflation-adjusted success values. i.e. if we are looking at 2x the original starting balance, 2x can be in nominal dollars (i.e. $2M on a $1M starting balance) or 2x in inflation adjusted dollars (i.e. more than $2M, whose exact value depends on the historical inflation for a particular cycle). You’ll notice that the success bands look worse when comparing to the inflation-adjusted (real) starting balance rather than the nominal starting balance.

**2nd update: **I added a few requested features. The first two are the ability to specify you annual tax rate on income and also fees (like expense ratios) on your investments. The main addition is the ability to add multiple income and expense streams with specified starting and end dates to the calculation. This is useful for adding income streams like social security or pensions and temporary expenses like a mortgage or childrens’ college expenses.

The post Post-Retirement Calculator: Will My Money Survive Early Retirement? Visualizing Longevity Risk appeared first on Engaging Data.

]]>The post Should You Invest (Or Wait) When The Stock Market Is At An All-Time-High? appeared first on Engaging Data.

]]>The stock market has been on a bull run (hitting numerous all time highs) for the last 8+ years and it’s not clear when it will end. Whenever there’s been an extended bull run, one question that comes to mind “Should I invest in the market now, or wait until a pullback?” The question comes about because of fear and loss aversion: fear that the market will drop right after they invest and the observation that people want to avoid losses more than they value gains. However, historically, the correct answer, at least over the last 68 years, has been to invest and not to try to time the market.

This was also demonstrated in the **Market Timing Game**; that people are pretty bad at predicting the direction of the markets and given the upward trend of the market, it’s simpler and more likely than not, better to just stay invested in the market. The corollary to this is that when you have additional money to invest (e.g. from regular savings from your paycheck or a one-time event like the sale of a house), it makes sense to invest the money and not worry about whether the market is at a high or low point. Some graphs that look at the distribution of returns when the market is at an all time high (ATH) can help answer this question of whether you expect to see worse returns than investing at other times.

The graph below shows two histograms plotted together. The first histogram (in blue) shows the distribution of returns for the S&P500 over a specified period (one week to ten years) for every single day between 1950 and 2018 (68 years). The second histogram (in orange) shows a similar distribution of returns for the S&P500 but only from days in which the S&P500 index was at an all-time-high (i.e. the index was higher than any previous day). There have been approximately 1200 days where the index was at an all-time-high, out of the more than 17000 market trading days since 1950.

You can select which periods you’d like to investigate and also whether to look at the histogram in terms of raw counts of data points or fraction of the distribution.

What is remarkable about the graph for any period you choose, is that the returns after hitting an all-time-high are very similar to the returns for all days in the market. In most cases the statistics about the two distributions are very similar (mean, median and 25th to 75th percentile vales). In some cases, the distribution of returns are actually higher starting from an all time high point compared to starting from a random point.

It is important to note that this distribution is not a probability moving forward (i.e. if the market is at an all time high, you don’t know if your more likely in the future to get this set of returns). All it tells you is that this is what happened in the past. If you think the markets in the future will resemble those of the past (with bull markets and recessions and recoveries) then it’s reasonable to assume that you should have results that are at least within the range of what’s happened in the past. If you think there’ll be a nuclear war with North Korea, then obviously all bets are off and why are you reading this site in the first place.

The second graph shows the S&P500 market index price over the past 68 years (1950-2018), with color coding to indicate how close to the all-time-high (ATH) the index is. There is, of course, only one point where the price is highest for any given period, but in this case, the ATH is when the index price is higher than any point before it (i.e. if you were invested in the market at that time, the index would be the highest it had been in history). You can resize the graph (click and drag) to zoom in to look at a specific period/point in history as well.

What you can see is that the S&P500 has risen quite a bit in the last 68 years and as a result, much of the time the index is at or near its ATH (over 36% of the 17,000+ days when the index is within 1% of the ATH). There are also always some dips thrown in there where can drop 10%, 20% or even more, accounting for less than 50% of market days.

The key takeaway is that in the past several generations of investing, the market has done well and most of the time, the market is within 5% of its ATH. If you waited for a large dip to invest, you could be waiting for a long time and you would have missed out on a large amount of the gains.

**Data and Tools**: the data is the same as used for the Market Timing Game, daily, historical dividend adjusted prices for the S&P500 stock index (between 1950 and 2018) were downloaded from Yahoo! Finance. The data for the visualizations and graphs were calculated using a program written in Javascript using the Plot.ly engine to create the graphs.

The post Should You Invest (Or Wait) When The Stock Market Is At An All-Time-High? appeared first on Engaging Data.

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