Anyone feel like doing a financial Monte Carlo simulation?

Had an email argument at work on the subject of whether to buy a house with cash if you can. I argued that it was stupid to do so when you could get a mortgage and put the money in the stock market earning a higher return. They said that was risky. I say BS, because your investment is liquid, and you are not highly leveraged (each years payment is a small portion of the whole fund).

It would be interesting to do a Monte Carlo simulation of this. Let's say the question is whether to put 20% down on a $1M house, and put $800K in the stock market, or to put all $1M in the house. We'd need a schedule of payments for, say, a 30-year fixed loan for $800K. Then we'd need the alpha and beta (EV and variance) for a reasonable portfolio. Start out ignoring taxes. The questions would be: how often does the fund run out of money before the mortgage is paid off? What is the distribution of money still owed when you run out? And on the upside, what is the distribution of money in the account when the loan is paid off?

Taxes are a mixed bag - you pay less for the mortgage, and you earn less. I'm pretty sure that it lowers your final EV (because you have more taxed earnings than tax-saving mortgage payments), but lowers your 'risk of ruin' - because when you have stock market disasters, you end up not having to pay taxes for years while recovering.

UPDATE: Forget it, I just went ahead and wrote it. Will write up the results over the next few days, and post it. The risk is higher than I thought, but the average return is huge.

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Instead of running a Monte

Instead of running a Monte Carlo simulation, what about a simulation that uses actual market returns over several different periods? Go get the last 100 years of stock market data and go to town with it, using some index fund(s).

Good Point Rob^5.

Good Point Rob^5.

You should also consider the

You should also consider the appreciation of the house. If I put 20% down and the house increases in value by 5%, that is a 25% ROI. If I put 100% down it is only a 5% ROI. Of course, if the house loses 50% of its value and I only put 20% down, I'm now in the hole.

Look up the CAPM - Capital

Look up the CAPM - Capital Asset Pricing Model. You can get any level of risk-and-return that you want simply by holding the appropriate combination of just two assets: a risk-free asset and a market-rate asset. Higher risk means higher return, lower risk means lower return. You decide what balance you want, and distribute your money between the two accordingly.

Both you and your friend are right: you could put your money in the market and get a higher return, and it is risky to do so. Whether it's smart or stupid is not a useful question. The question is how much risk do you want to take on? There is no generally correct answer to that. People are usually more risk-prone when they are younger (and rightly so), but there are plenty of other circumstances that would suggest taking on more or less risk, and the largest reason of all is really just personal preference.

All of finance boils down to return and risk and people willing to exchange one for the other. Everything else is just flavoring and fancy special effects.

As far as predicting what the risks and returns on housing vs. the stock market are... whose predictive powers do you greater confidence in: yours, your friends, or the market's?

Patri- Does the average


Does the average return in the stock market beat the 30y mortgage rate? Isn't that the basic determinant of whether you're going to make or lose money on the situation?

Brian - that's exactly what

Brian - that's exactly what determines whether the average return is better. But it doesn't answer the question of risk. People were proposing not having a mortgage in order to reduce risk, so I wanted to find out just how much risk there is. It ends up depending heavily on what your risk and return in the stock market are. At historical returns, you'd be an idiot to pay cash for the house. But a lot of people think (with some good reasons) that stock returns will be lower in the future - maybe as low as bond returns.