Analyzing the Retirement Game

The previous post, “Playing the Retirement Game“, introduced you to a simple financial model for a salaried employee named Sal. If you have not played the Retirement Game yet, you are encouraged to visit github.io and figure out what is the best advice you can give Sal regarding his savings and investments.

To obtain a deeper analysis, I put a wrapper around the game to automatically run it multiple times and generate numbers and charts. Here is my experience with the game.

First observation is that randomness introduced in the game for debt and equity investments causes a large spread in outcomes for a given investment strategy.

Living Purely off Fixed Deposits

When all investments are in fixed deposits, how long does the money last? It depends on the level of savings. Without aggressive saving rates we see a shortfall of 20 to 60 years worth of starting salary. But the good news is that if Sal sets aside a fairly large fraction into savings, he will stay in positive zone.

rg1_exprate_score_purrefd

Score vs expense level, pure FD investment strategy

What I don’t like about fixed deposits is that they lose value with time. So, in one sense, Sal’s scrimping and saving and denying his family the money only goes to support the banker’s lifestyle.

Large Spread in Outcomes with Risky Investments

When the game is run many times with risky investments, most runs will have several loss events, but some lucky runs will have zero or very few loss events. These lucky runs, thanks to the power of compounding, will yield extremely large scores. Conversely, some unlucky runs will yield very low scores. Given below are histograms for pure debt and pure equity strategies.

rg2_puredebt_hist

Pure Debt Investment Strategy, 65% expense rate

Pure debt investment with 65% expense rate (i.e. 35% saving rate) gives a mean score of 1, which is approximately break even. Note that a 35% saving rate with pure debt strategy gives same results as a 50% savings rate with pure FD. To see this in another way, we find that pure debt strategy with 50% saving rate gives a mean score of 30 as against zero for pure FD at same saving rate. Score of 30 means retaining 30 years worth of starting annual salary at the end, a decent sum.

Now let us see what happens with a pure equity strategy. Thanks to the compounding effect, mean score is 3970 at 50% saving, 2624 at 35% saving rate, 380 at 10% saving rate! Thousands of years of annual salary is serious money: Sal can surely take early retirement!

However, there is a downside: although mean scores are high, so is the variability. Here is the histogram for 25% savings rate, which shows that there is a 45% chance that Sal won’t make much with this strategy, but a 35% chance that Sal will do very well, plus  20% chance of doing really really well.

rg3_pureequity_75expratePure Equity strategy with 75% expense rate

Debt to Equity Ratio

How does D/E allocation ratio impact results? We shall approach this question from a different angle: let’s measure only the chances of survival with a given mixed strategy. That is, given a certain allocation strategy, what fraction of trial runs result in a positive score? We will call this fraction the success rate of an allocation strategy.

The figure below charts success rate vs D/E ratio. The curves were generated for varying expense rates. The curves are not smooth because a large enough sample size was not used. This jaggedness is noise and should be ignored.

Debt to Equity ratio is given by a parameter k, D : E :: k : 20-k. Horizontal axis represents k as k varies from 0 to 20. Therefore, leftmost values are for pure equity moving to pure debt at the right.

rg4_successratio_vs_exprate

Success ratio (chance of positive score) vs debt/equity ratio

The figure above is very interesting. We can infer several things:

  • Success ratio is higher for higher saving rates (lower expense ratios). That’s obvious, really: more money Sal puts into savings, more likely will the money last until the end.
  • At lower saving rates, debt tends to reduce survival rate.
  • With higher saving rates, there is a sweet spot. best success rate is at about 60-70% debt. I suspect a mixed strategy tempers equity risk by not wiping out all the capital in less lucky runs (that have many loss years).

Remember, with the way the game is set up, if capital is wiped out post retirement, there is no scope for Sal to earn more money, resulting in an inescapable downward spiral into increasing debt.

Conclusion

I feel this extremely simple model has been successful in delivering several insights — or at least, suggesting some directions on where to explore further, perhaps with more realistic models.

In particular, this game does not allow exploration of a non-constant allocation strategy. Many books and blogs advice starting off with higher risk in earlier years and then shift the portfolio to less risky ones later. A hint of this can be seen in the previous chart — building net worth aggressively in initial years is equivalent to using a higher savings rate in the game.

This is also the right place for a strong disclaimer:

Sal’s world is very simple and in no way matches the complexities of real life. It would be extremely foolhardy to use the numbers presented here to take real life decisions. So don’t do that, and if you still do, don’t blame me!

So for example, Sal can put 50% of his salary in FDs and expect the money to last until age 85. But would you get the same results in real life? Who knows?

Nevertheless, some important lessons can be derived from the Retirement Game (notice these ideas are not at all novel — most financial planning blogs and experts will give similar advice).

  1. Risk free investments do not provide sufficient protection in the long term.
  2. One has to, especially from early on, grow money faster albeit taking on more risk.
  3. Provided you have enough money in play, you can reduce the risk with a mixed portfolio. Although it was not allowed in Sal’s world, one can also use a time-varying strategy: start with high risk high reward strategy but gradually reduce high risk investments in later years.

If nothing more, even if this post encourages you to seriously look at investment options beyond bank fixed deposits, I think this Retirement Game will have served its purpose.

Further Reading

Estimate how much you will need at retirement based on current expenses: https://www.bigdecisions.com/calculators/retirement-spend-calculator

Mathematical models of the stock market – https://www.scientificamerican.com/article/can-math-beat-financial-markets/

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