## Personal Finance and Simulation Modeling

CFA studying can be tough, and sometimes you need to take a break; During one of my study breaks, I came up with a Monte Carlo model to estimate my (or your) future net worth. In this posting I explore that model, and take you on a journey of personal finance wonderment.

**The Model**

A Monte Carlo simulation (at least in my model) works by generating random numbers that act as inputs into a predefined model (with appropriate assumptions). Each time the model is taken through an iteration, a different result will occur, driven by these random inputs. When the model is run multiple times, you are able to determine the probabilities that certain outcomes will occur.

Below you can see the results of several of the iterations in my model`[kml_flashembed movie="http://simran.crownpac.net/blog/wp-content/uploads/2006/08/iterationgraph1.swf" height="230" width="450" wmode="transparent" /]`

As mentioned above, each iteration is driven by both inputs and assumptions. The inputs for my model were the return on equity for each of the 40+ years, while the assumptions used are listed below (and are fairly realistic):

- a relatively aggressive but realistic savings level of ~20% of personal income (decreases as a proportion of personal income over time)
- a real return on equity of ~7%
- inflation of ~2%
- borrowing rate at Prime plus 1.5%
- annual return standard deviation of ~10% with returns normally distributed
- implementation of a properly balanced portfolio (approximating “the market” with an overall beta of 1)

**Insights**

As you can see, the results from each iteration appear unique. Although you can anecdotally get a sense of what you might expect to be worth by watching each iteration, the real insight comes when you start to produce a histogram (all values are shown in today’s dollars):

*Probability of Net Worth at Age Seventy*

Interpreting this graph, you can see that you will have a 1% likelihood of being worth $0-$2M, and a 19% chance of being worth $5M-10M. Notice that despite our assumption of a normal distribution of annual returns, the expected value of the portfolio is positively skewed: There are a greater number of very high results, and the most expected result is lower than the average.

What I find more useful than the histogram, however, are the cumulative probabilities as shown below. Interpreting the following graph, you can see that at age 70 (and with no debt in the portfolio), there is an 80% chance you’ll be worth at least $2M-5M, and a 12% chance of being worth at least $12M-15M.

`[kml_flashembed movie="http://simran.crownpac.net/blog/wp-content/uploads/2006/08/leverage1.swf" height="250" width="450" wmode="transparent" /]`

As with any model, the fun part comes when you play with the assumptions. I’ve included some buttons on the above graph to facilitate your play: you can choose the leverage scenario for the portfolio, and see the impact it has on the cumulative probabilities.

Notice that as you increase the debt level, your likelihood of being very rich increases, while the likelihood of being worth less remains the same? Debt in your portfolio, over the long term, is a good thing.

**Downside of Debt**

The graph above shows only the upside of increased leverage. There are, of course, downsides that will ultimately determine the optimal balance of debt and equity for your portfolio. What are the constraints that should limit debt exposure and determine your optimal capital structure? read away:

**Portfolio value variability**- Your personal risk aversion level determines how much you can take. My personal feeling is that many investors are overly cautious when it comes to use of leverage, but not careful enough when it comes to individual stock selection vs asset allocation. Using a monte carlo model can help you quantify the risks, and determine what level you really should be at.**Probability of Bankruptcy**(and associated costs) – Because the costs of personal bankruptcy are so high, any chance of total portfolio loss should be avoided. Fortunately, bankruptcy only becomes an issue at extremely high levels of leverage; well beyond the 65% leverage scenario I included above (I ran a test on the simulation, but have not included it in this posting)**Greater demands on cashflow management**– The impact on the portfolio resulting from margin calls, and portfolio rebalancing adds extra cost and care to managing the portfolio**Greater Need to rebalance portfolio**- Changes to asset class values will be magnified by the use of leverage. Depending on your rebalancing approach, this could add significant costs**Increased borrowing costs at higher debt levels**– This depends on how big you shoot. If you are pushing 8 figures, you might want to read up on some Miller and Modigliani

**Extensions**

There are many more variations we can build off of this model. For instance, if you where interested how soon you could expect to be worth $5,000,000, you could use the following graph:

*Probability of $5MM Net Worth at Various Ages*

With a little bit of work, we could also examine:

- How often periods of low cashflow would occur
- How often Portfolio rebalancing would be necessary
- Likelihood of bankruptcy
- Optimal portfolio construction

Whatever you are interested in, the model can be built to examine your needs.

**Conclusions**

Despite the long post, this is a relatively brief look at what these kinds of models can do for you. Some takeaways:

**Modeling brings Clarity**– Despite the uncertainty around future market returns, you can develop rational expectations on where you will be in the future by using tools like simulation modeling. Combine a knowledgeable financial modeler with powerful computing, and a model can be adapted to address any issue that you might be concerned with.**Time is your Friend**– When you no longer have the ability ski moguls because your knees are titanium, you can take comfort in the fact that you can cruise the Mediterranean, be a philanthropist, or buy a fancy Skoda. You already know that it is good to save, but it is nice to be able to quantify it.**Debt is your Friend**– Assuming you’ve got time (measured in decades), it probably makes sense to bite off some debt. You’ve seen above the result of adding leverage to my model, and the resulting net worth values are*large*. Always remember however that there is a big difference between consumer debt, and leveraged investments; make sure your debt is working for, not against you.

I hope you found this long and flashy post interesting. Let me know if you have any comments or questions.