Sensitivity Studies and the Reality Checker

Here is an example that uses the Reality Checker prototype. It drives home a key point. Use a sensitivity study to help you interpret results.

The Reality Checker

The Reality Checker automates the Scenario Surfer. It generates 100 runs and presents the confidence levels.

Because of the limited number of runs, it still shows granularity. I do not mind this. Others may find it bothersome. I like the idea of showing the randomness in the data. Others like smooth curves. I believe that showing randomness gets one away from over dependence on a particular answer. It emphasizes the need to run sensitivity studies.

I made these runs on the prototype of the Reality Checker.

Data

I use Idiot Switching as an example. I selected the P/E10=14 Bear Market (today’s market) and entered an initial balance of $100000. I selected 2% TIPS. I allocated 100% of the portfolio to stocks when P/E10 fell below threshold. I allocated nothing into stocks when P/E10 was above threshold. I used a withdrawal amount of $4500. This is 4.5% of the initial balance. This amount increases to match inflation. Here are the results at the 5% and 20% chance of failure levels (bottom of the Red and Yellow levels, respectively).

Here are the Year 15 and Year 30 balances with a 4.5% withdrawal rate

Threshold, Year 15 5% balance, Year 15 20% balance.

P/E10=11, 41790, 75930
P/E10=12, 36556, 67994
P/E10=13, 41561, 77857
P/E10=14, 45984, 71702

Threshold, Year 30 5% balance, Year 30 20% balance.

P/E10=11, 16515, 76178
P/E10=12, 7951, 66731
P/E10=13, 32584, 86225
P/E10=14, -9484, 80455

I selected P/E10=13 as optimal. Others may choose differently.

Here are the Year 15 and Year 30 balances with a 4.7% withdrawal rate

Threshold, Year 15 5% balance, Year 15 20% balance.

P/E10=11, 42318, 63047
P/E10=12, 32421, 65362
P/E10=13, 41629, 59157
P/E10=14, 27910, 59157

Threshold, Year 30 5% balance, Year 30 20% balance.

P/E10=11, -3853, 51547
P/E10=12, -50985, 33832
P/E10=13, 6487, 61295
P/E10=14, -46423, 55267

Once again, I selected P/E10=13 as optimal. Others may choose differently.

Here are the Year 15 5% and 20% balances at different withdrawal rates when P/E10=13

4.5%, 40495, 64694
4.6%, 43145, 71289
4.7%, 43079, 68415
4.8%, 35874, 59394

Here are the Year 30 5% and 20% balances at different withdrawal rates when P/E10=13

4.5%, -1049, 60852
4.6%, 4513, 75699
4.7%, -6006, 73525
4.8%, -38773, 50522

Remarks

Everything might have seemed easy and straightforward until I varied withdrawal rates. Quite clearly, the probability of failure will never increase with lower withdrawal amounts. What we see in the second set of runs gives us a good idea of the randomness remaining in the data. A withdrawal rate in the broad range of 4.5% to 4.7% is likely to last to Year 29 or 30. Withdrawing 4.8% is too high.

This is likely to alter our interpretation of the first set of runs. Much of what we see is randomness in the data. A threshold of P/E10=13 is not that much superior to other thresholds.

While we are at it, we should reconsider which data set to use. Obviously, the Year 30 results are convenient. But there is the issue of turning points. The market is unlikely to remain a long lasting (secular) Bear Market for another thirty years. It is likely to revert to a Normal Market by Year 15. This is why I like to look at Years 10 and 15. Balances in this region are more reliable than those later on.

The presence of a threshold makes a big difference. The exact threshold level does not.

Have fun.

John Walter Russell
January 17, 2009