Playing the Retirement Game

How do I get out of the salary trap?

As should be clear from the previous posts, especially the ones titled Salary Curve, Life Expectancy, and Middle Class Saving Mantras, almost all of us middle class people are squarely in a salary trap. The trap has four walls:

  • Limited (and declining) real income from salary
  • Long remaining  life span after salary income stops
  • Lack of know-how on how to grow one’s net worth
  • Limiting mindset regarding financial matters

The question, of course, is this: is there a way out of the salary trap? Well, there must be at least four ways out of the salary trap — one path for each of the four walls listed above!

Most people will focus on breaking through the first two walls:

  • Increase salary income: job hopping / industry hopping / retraining / second job
  • Continue working beyond normal retirement age

Although these two walls may be pushed back a bit, so to speak, they are very difficult to truly break through.

In this post, we shall focus on the third wall, and examine the effect of increasing one’s know-how regarding savings growth. Please note that this post does not tell you how to increase your know-how. Instead, the focus is on analyzing the impact on one’s life if better saving decisions are taken from the beginning.

To that end, let us look at a simple simulation, what we shall call the Retirement Game. The Retirement Game is an extremely simple financial model of a salaried person named Sal. In the game, you are Sal’s financial advisor and must help Sal get out of the salary trap by advising him on his investment decisions.

An F-minus cartoon

You will basically provide Sal an allocation strategy: what fraction of Sal’s net worth is to be held in each asset class (more details below). At the end of each year, Sal’s portfolio is rebalanced so as to continue adherence to the allocation strategy. This means, for example, if one asset class grows very well, its value as a fraction of total worth will exceed the value decided in the allocation strategy. Then Sal books profits to bring this asset class fraction back to the desired level and buys more of the underrepresented asset class.

Based on your investment suggestions, Sal’s savings will grow or shrink. After retirement, Sal lives off his savings for the rest of his lifespan.

A game needs a way to keep score. The score is the amount of real savings (inflation-adjusted) that Sal has left over at the end of the game. If Sal runs out of money, he will live off borrowed money, then his net worth may become negative at the end. Notice that once Sal gets into debt after retirement, he has no chance to recover, and his net worth will keep spiraling downward.

The objective of the Retirement Game is to understand the impact of taking different investment decisions over Sal’s lifetime.

Now let us get into the details of the game. Remember, we want to keep the game as simple as possible to meet its objective, but no simpler. So most parameters are kept constant, although they will not be constant in real life. Also unlike real life, Sal does not face shocks to his expenses such as sending a child abroad for education, children’s marriages, or expensive illness in family. Nevertheless, with a simpler model, we hope to get improved understanding of the shape of the solution.

Thus, there are just a few knobs and levers to operate in the game.

Constant Parameters

Sal gets a job at age 20, his career plateaus at 40, he retires at 60, and has a natural life span of 85.

Starting post-tax salary is 3,00,000 per year. Salary grows at 15% pa for first 20 years, then grows at 2.5% pa less than inflation rate for the remaining part of his career. Actually, starting salary gets factored out from the final score, so don’t agonize over the starting salary being too low or too high.

Inflation is 7.5% throughout. Cost of borrowing money is 10% pa.

There are only three Investment options with fixed risks and returns (% returns are post-tax). That is, there are no long term boom-bust economic cycles in this game.

  1. Bank Fixed Deposits, 5.5% pa, zero risk
  2. Debt instruments, expected yield 8% pa, risk of 10% loss
  3. Equity, expected yield 15% pa, risk of 30% loss

Yields and risks for Debt and Equity need to be explained. The model is as follows:

An investment may either give a bad return of x2 < 1.0 or a good return of x1 > 1.0 with probability of p and 1-p, respectively, per year. Then

(1 + expected yield) = (1-p) * x1 + p * x2

Or,

x1 = [(1 + expected yield) – p * x2 ]/(1-p)

Now,  expected yield and x2 are known. As value of p is varied (higher p represents more volatility), x1 will be change correspondingly to keep expected yield at the set level. For example,

1.15  = 0.90 * x1 + 0.10 * 0.70,  then x1 = 1.20 (i.e 20% profit)

1.15 = 0.80 * x1 + 0.20 * 0.70,  then x1 = 1.2625 (i.e. 26.25% profit)

By keeping p as the independent variable, we can better study the effect of market volatility on playing the retirement game.

We also need to model expenses incurred by Sal every year. The model we will use is not too complicated, but should reflect some of the ups and downs in expenditure that happen in real life.

We start with fixing a base level of expenditure at the start of the game, when Sal starts out a bachelor, but over the next 20 years his expenditure grows at the same rate as his salary does, that is, at 15%. However, after age 40 Sal switches to a constant lifestyle, so until retirement his expenses just keep pace with the inflation rate. At retirement, Sal cuts down his lifestyle by 50%. However, with time, expenses again rise with inflation. Since level of savings is an important decision, base level of expenditure is a tunable parameter. Yes, I agree, this is an extremely simplistic model!

Knobs and Levers

You can set the following knobs at the beginning of the game:

  1. Base level of expenditure, as a percentage of starting salary.
  2. Investment allocation decisions. What percent is put in Fixed Deposits, Debt and Equity. In this simple game, allocation strategy is constant throughout.
  3. Number of runs. Since debt and equity investments have randomized returns, play the game many times to get a better understanding.

There is only one lever: hit the [start] button to start the runs!

Note: Although one could chose a design where the expenditure and investment decisions can be changed every year, I have chosen to keep them constant for two reasons. First, it keeps the game simple so it’s easier to measure the effectiveness of a particular strategy that is applied consistently. Second, because random elements are involved, a proper analysis will require the same game to be run many times, which is easy to do when all the knobs are set only once at the start of the game.

Running the Game

We run the game in one year time steps.

At the end of each time step, do the following:

  • Compute changes for one time step
    • Case positive net worth: Calculate returns on existing investments
    • Case negative net worth: calculate interest on borrowings
    • Add gains or losses into current net worth
  • Compute current savings = salary – expenses
  • Compute new net worth = current net worth + current savings.

Note that current savings and net worth can each be negative. Returns on investments may also be negative.

End the game at age 85.

At end of the game, compute score as the following dimensionless number.

score = real net worth / starting salary  , or, in other words,

score = net worth adjusted for inflation / starting salary

Note: Since this game always ends at age 85, we did not really need to discount net worth. But if we ever make the lifespan variable, inflation-adjusted net worth will be required. Also, inflation-adjusted values are easier to understand.

One can interpret a score of N as ending at age 85 with a net worth equal to N years of annual starting salary.

Play the Game

The Retirement Game is hosted at github.io.Please visit this site where you will find the link for playing the retirement game.

If you want to study the code and perhaps modify it, it is also available for download:  download and unzip RetirementGame.zip to get a folder named RetirementGame. Its major functionality is in the associated JavaScript file.

In a few days, I shall publish the next piece, which analyzes the Retirement Game using more powerful tools.

Acknowledgments

Many thanks to:

Manas Sathe provided invaluable help with detailed review and a critique of the model.

Sandeep Ranade pointed me to Github Pages where the Retirement Game could be hosted (WordPress effectively does not allow JavaScript).

 

 

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