Annuity Simulator
The purpose of the Annuity Simulator is to help you compare the monthly payments you might get from an annuity with the monthly cash you might be able to withdraw from an account invested in stocks.
The most straightforward example of an annuity is an immediate fixed annuity. You pay an insurance company a lump sum upfront. In return the insurance company pays you a fixed monthly amount, starting after one month and continuing until you die. If you die before you have received as much as you originally paid in, your heirs receive the balance. Otherwise, they receive nothing. The size of the monthly payments is determined by the size of your upfront payment.
There are a number of variations.
- Joint lifetime: The payments continue until the second of two people dies.
- Deferred annuity: The monthly payments do not start immediately but sometime later.
- Variable annuity: This is a type of deferred annuity. The upfront payment is invested, usually in mutual funds until it is time for the monthly payments to start. At that time what happens in effect is that the investment, which presumably has grown in value, is liquidated and the proceeds used to buy an immediate fixed annuity. The variable annuity is said to become “annuitized.” If you die before the annuity is annuitized, your heirs receive the value of the investment.
- Death benefit: If you die before the variable annuity is annuitized, the value of the investment may be less than the amount originally paid for it. A death benefit is a guarantee that your heirs will receive a higher amount.
There are many optional benefits and guarantees that can be added to an annuity. There is a fee attached to each one. The fee is not necessarily obvious to the buyer of the annuity, but each fee has the effect of reducing the size of the monthly payments.
Many people consider buying annuities in order to be guaranteed not to run out of money before dying. This guarantee comes at a price, however. Insurance companies charge healthy fees for that guarantee. The purpose of the Annuity Simulator is to help you compare the monthly payments you might get from an annuity with the monthly cash you might be able to withdraw from an account invested in stocks.
Suppose you are considering buying an annuity, but you ask yourself whether you can get the same or better results by some other method. One possibility would be to take the money you would use to buy the annuity and buy an equity mutual fund instead. Then, each month for the rest of your life you would hope to withdraw from this mutual fund investment some amount of cash. In this way you would simulate an annuity. The hope is that you would receive monthly amounts at least as great as the annuity would pay and still have money at the end to leave your heirs. There is good reason to think such a strategy might work. The stock market has done very well over many years, averaging annual returns in the neighborhood of 10%, much greater than the returns an annuity might offer. This is why the insurance company can offer you a guaranteed income. It gets a better return on its investments than what the annuity would pay you. On the other hand, there is also reason to recognize that this strategy may fail. Although the stock market has gone up over the long run, it sometimes goes down for fairly long periods. The simulated annuity includes no guarantee.
How can we judge the likelihood of succeeding with an equity mutual fund strategy? One way to do it is to simulate future mutual fund returns and see how the strategy would work in various simulated scenarios. (Thus, our term Annuity Simulator plays on two senses of the word simulate.)
No one can know what the stock market will do in the future. We can assume, rightly or wrongly, that it will continue to behave somewhat as it has behaved in the past. Looking at past stock market returns we see that monthly returns are virtually uncorrelated. There is no pattern in past returns that helps us to predict what the next month’s return will be. It is as if each month’s return were drawn at random from a long list of possible returns.
To simulate future returns we do just that. We take a list of plausible returns and pick one at random for each month going forward. The list we use is the list of past returns actually observed over a period of years. We can be sure that the actual future path of stock market returns will turn out to be different from our simulated path, but our simulated path will share two important characteristics with the history of the stock market. First, the size of the returns, positive and negative, will be in a range similar to those of the past. Second, successive monthly returns will be uncorrelated. We can repeat the simulation many times to get a collection of possible future paths. Looking at this collection can give us a feel for the range of possible future outcomes. The critical assumption is that the size of future returns will be in the same range as past returns. (The Annual Drag can be used to modify this assumption.)
The simulations are based on a mutual fund that has existed for more than 40 years, and a money market account with a user-defined rate of return. The mutual fund is designed to track the S&P 500 Index. The user chooses the relative amounts of money to be invested in the mutual fund and the money market account. Past monthly returns are calculated for the portfolio chosen, keeping the balance constant. These calculated monthly portfolio returns are used for the simulation.
Step 1: Basic Information
Step 2: Desired Payments
Step 3: Asset Allocation
Example: Simulate One Scenario
Simulating one scenario at a time allows you to get a feel for what happens when the simulation runs.
Scenario Summary
The following are the results for one simulated -year period.
Remaining Principal By Month
The graph of Remaining Principal by Month shows the value of the portfolio at the end of each month.
Payment by Year
The graph of Payment by Year shows the total amount paid each year next to the total amount of desired payments for the year.
Results: Simulate Scenarios
Summary
Total Present Value of Desired Payments
Success Rate
Results
Results are ranked by Total Present Value of Payments, then Present Value of Final Principal. The graphs of Remaining Principal by Month and Payment by Year for the 10th percentile show the results for the particular replication that ranked 500th worst. Similarly for the Median and 90th percentile graphs.
Remaining Principal by Month
The graph of Remaining Principal by Month shows the value of the portfolio at the end of each month.
Payment by Year
The graph of Payment by Year shows the total amount paid each year next to the total amount of desired payments for the year.