This sounded like a fun math problem, and there was so much bad math and rationale in

this thread that inspired this post, I figured I might as well work something out.

I pictured an investor, mid-20s, with enough for a rental down payment, who is wondering if they should buy a single rental property to hold for 30-50 years, or if they should invest that down payment in stocks.

Here's my baseline assumptions:

- You are 25 years old. You have saved up after college, and you have 22k to invest.
- You don't want to start a whole real estate business or empire, but are considering getting a single rental. You don't want to do any work on it yourself, so you will hire out all labor, property management, etc.
- You will pay market price for a 100k home, get 1% of the purchase price in monthly rent ($1000), and expenses will run 50% of your gross rents (500).
- Your interest rate is 4.5%, so your P&I payment on 80k for 30 years is 405.35 monthly.
- You will put down 20% (20k), and finance 80% (80k), and pay 2k closing costs. No PMI.
- Inflation runs 3%, and the house appreciates at the rate of inflation.
- Stocks return 7% real, so 10% including the 3% inflation.
- After getting the one house, you will reinvest all net rents received into the stock market for the same returns as the stock returns, because you just wanted this one home, so once per year you take your annual profits of $1,135.80 and invest them in the stock markets.
- I'm ignoring taxes for simplicity's sake, but the real estate should come out ahead, because depreciation on a 100k home is much more than the $1,135 annual profits.

We want to compare the returns of the two after 30 years, and after 50 years.

22k invested in stocks, at a 10% nominal return, is worth $383,886.85 after 30 years.

22k invested in stocks, at a 10% nominal return, is worth $2,582,598.76 after 50 years.

The 100k house at 3% return is worth $242,726.25 after 30 years.

The 100k house at 3% return is worth $438,390.60 after 50 years.

That's just a straightforward time value of money calculation. So just on appreciation, the stocks win. However, now we add in the rents:

$1,135.80 invested annually in stocks, at a 10% nominal return, is worth $186,832.31 after 30 years.

$1,135.80 invested annually in stocks, at a 10% nominal return, is worth $1,321,967.31 after 30 years.

**After 30 years**, RE total: $429,558.56 Stock total: $383,886.85

**Winner: Real Estate**.

**After 50 years**, RE total: $1,760,357.91 Stock total: $2,582,598.76

**Winner: Stocks**.

During the years you have leverage (those 30 years), real estate comes out ahead. Stocks start to pull ahead after that, because the bulk of your investment in RE is in an asset earning 3% (the inflation rate) versus stock's 10%.

Now, if we keep all other assumptions the same (cost of house, expenses, etc.) and just tweak how much rent we're getting (i.e. buy at a better price-to-rent ratio than the 1% rule),

**we find that real estate equals stocks after 50 years at a ratio of 1.12% monthly rent to purchase price** (in our example that would be monthly rent of $1120). At that price, you'd net $1,842.25 annually which, when invested for 50 years, along with the ~438k of real estate, would equal stock's 2.58MM. And it would be well ahead of stocks at the 30 year mark, it takes stocks til year 50 to catch up in that scenario.

If you can get a much better price to rent ratio, you'll do even better. For example a

**1.5% price-to-rent ratio** ($1500 monthly rent, in this example)

**leaves real estate with** over 5.25 million after 50 years,

**more than double stocks**.

Let me know if I missed anything, but I think all my assumptions were very reasonable. No big advantages to real estate that one can get (buying much better than the 1% rule, managing it yourself or doing any "sweat equity" to save on the expenses, buying a deal at below market, etc.). I included closing costs and used a reasonable interest rate. I did ignore taxes, but that should help the real estate case due to depreciation.

**tl;dr** The question was "What wins in the long run?" The answer is: it depends on how good the real estate investment is. At a 1% rule, it's pretty even between the two scenarios: Real estate wins over a 30 year timeframe, stocks win over a 50 year timeframe. At a much better ratio, like 1.5%, real estate wins hands down, with over double the money of stocks. At a worse ratio, naturally stocks would win.

Thoughts? Math I screwed up? Quibbles with assumptions?