Tuesday, December 7, 2010

Law of LARGE numbers and investing

In probability theory, the Law of Large Numbers (LLN) - Gerolamo Cardano (1501–1576) - is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. Conversely, a small number of trials might be skewed.


Think of flipping a coin. With a coin, there are two sides, so you have a 50% chance of flipping heads as you do tails. Where the law of LARGE numbers takes hold is, if you flip the coin 4 times, there is a greater likely hood of having a disproportion number of heads than if you flipped the same coin 400 times.

Another great example is rolling a die. If you roll a dice 6 times, logically, you should get each different number once 1, 2, 3, 4, 5, then 6. This is what logic tells you, but it is highly unlikely you will actually roll these numbers. You have a 16% chance of getting that number on each roll. Now, if you roll the same die 6000 times, you are more likely to get that more even distribution.

So, you ask, how does this apply to real estate? Simply, it applies to vacancy. When buying cash flow real estate, one of the biggest problems a client can face is vacancy. Vacancy is when your unit is empty. Empty units produce no rental income.

If you have one unit, and it is vacant you are out 100% of the income. If you have 10 units and one is vacant, you are only out 10% of the income. Extrapolate that to 100 units, you would need 10 vacant units to equal the % loss of having one unit empty in 10.

Professional investors, who retire on portfolios of real estate, tend to view more units as better than less units. The other factors they look at are more mortgage reduction and more value increase across 100 than 10 or 1.

The Law of Large Numbers is a valid consideration when looking at investments, as it proves that more units are better than less units when looking at cash flow. Just imagine, there are people who take this to the extreme levels, for instance a fellow in Smiths Falls owns over 200 units and a fellow in Cornwall owns over 700 units. These people have definitely taken the Law of Large Numbers very seriously!

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