Market timing is the attempt to switch a significant portion of your assets between different types of investments in an effort to maximize profits. If this is your investment strategy, good luck, because you’ll need it.

Academics such as Burton Malkiel, author of “A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing,” believe it is impossible to time the market. But, active traders and the get-rich-quick disagree. They claim to have seen it work in practice.

Mathematics and game theory can help us determine if market timing is a good strategy. Too many investment decisions are made as a result of emotional considerations. Usually those emotions are greed, fear, or pride. Emotions can dim the vision of even seasoned investors, fooling them into thinking their personal experience represents the set of all possible outcomes. We can illustrate the problems of market timing by looking at a simple game.

Consider the following game. You start with $1,000 and play for ten turns. Each turn you can invest your money in Investment A or Investment B. There are only two possible outcomes each turn. The first possible outcome is that Investment A appreciates 30% and with Investment B you just get your money back. The other possible outcome is the exact opposite: Investment B appreciates 30% and Investment A just returns your money.

If you invest half of your money in Investment A and half in Investment B, you are guaranteed to earn 15% each turn. After ten turns your $1,000 will have appreciated to $4,046. I’m going to call this the 50-50 asset allocation model.

Now, imagine that you decide to take a chance and each turn try to pick the investment that will earn 30%. I’ll call this the lottery method. Since you can’t lose money, and your average return is still 15%, you think on average you won’t do much worse than the 50-50 asset allocation. You couldn’t be more wrong.

Assuming that your choice is just a coin toss – and you don’t have foreknowledge of which investment is going to do well – the odds are you will do worse.

Let’s just take a look at the first two turns. With the 50-50 asset allocation model, your $1,000 grows to $1,150 and then to $1,322.50. The 15% gain on the first turn is compounded with another 15% gain on the second turn for a total compounded return of over 32%.

If, on the other hand, you try to guess the best category there are only four possibilities, and three of them are worse than the 50-50 asset allocation model. If you are wrong twice, you will end up with your original $1,000. If you are right and then wrong, or wrong and then right, you will earn 30% and end up with $1,300, falling $22.50 below the returns of the 50-50 asset allocation model!

Strategy	First Turn	Second Turn	Total Return
Asset Allocation	15.00%	15.00%	32.25%
Investment A	30.00%	0.00%	30.00%
Investment B	0.00%	30.00%	30.00%

Only if you are right on each of your two tries will you beat the returns of asset allocation. Your $1,000 from the first correct guess will appreciate to $1,300 and on the second guess to $1,690. Only in this case would your 30% compounding return beat the average return of the 50-50 asset allocation model.

For those of you trying desperately to remember your high school math, this is a case where the mean (average) return is higher than the median (middle or typical) return. On average you earn the same, but typically you fall below the consistent asset allocation model’s return.

Now imagine expanding this difference between mean and median for ten turns. In our 50-50 asset allocation model with consistent 15% returns, your $1,000 will grow to $4,046. If, instead, you use the lottery method, you will do better than the 50-50 asset allocation model less than 38% of the time.

While your average return with the lottery method is still $4,046, it is buoyed up by the extremely rare case when you guess right ten times in a row and end up with $13,786. If you are that rare individual, you will likely consider yourself brilliant and mistakenly believe that market timing works. You may even start an investment newsletter called “The Lucky Penny” and try to teach others your selection method.

The median or typical return of the lottery method, however, is only $3,713 representing only a 14.02% compounded return. Over half the returns of the lottery method fall within the standard deviation in the range of $2,856 to $4,827 (11.06% to 17.05%).

Remember, in our game the diversified 50-50 asset allocation model offers a safe 15% return. With those returns, is it really wise to press for the 17.05% return with the lottery method? It seems counter-productive to risk an extra 2.05% gain against a 3.94% loss, but that is what trying to time the market does on average in this case. Asset allocation produces not only more consistent returns, but better returns.

You have to pick the winning investment consistently in order for the lottery method to do better than the asset allocation model. Our game did not include the very real possibility of losing money. If the parameters of the game are changed to include the possibility of losing money, the 50-50 asset allocation does even better.

Losses are harder to recover from. In fact, losses hurt you more than wins help you. If you lose 50% of your capital one turn you must gain more than 100% to make up for what you could have had due to the power of compound interest.

In the real world, 50-50 asset allocation isn’t the same thing as a risk-free return, but it does offer a smoother ride than trying to pick this month’s winning category. Math can explain a lot; a few gray hairs help too.