# Is the stock market a better choice?

I'm only 18 but I'm starting to save money for the future. I have some money in savings, but I'm putting a lot into stocks and am starting to look at mutual funds. I wasn't sure if that pays the best down the road or if I should put it all in savings, or a CD, or savings bonds. Which would be best?

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• John W
Lv 7
9 years ago

If you define the best as long term growth of your portfolio then the answer is according to the probabilities and the return keeping in mind that there are limits to reasonable risk. For example, using a pure 50/50 coin toss as the epitome of risk, if you had a chance to wager on as many coin tosses as you'd like one at a time at 2 to 1 payout where if you win you won twice your wager and your wager would be returned to you while if you lost you would lose your wager, how much would you wager with each coin toss. The payout is favourable, in the long run for every \$1 lost you should be making \$1.50 so the more you wager, the more you stand to win. If you wager nothing then you win nothing and you lose nothing but if you wager everything you have with each coin toss, you are only guaranteeing that you will lose everything eventually so what is the optimal wager to maximize the growth of your portfolio? John L. Kelly when applying Claude Shannon's (the father of the information age) information theory realized that the optimum in a binary situation could be calculated by the equation:

f = (bp - q ) / b

where f is the fraction of your portfolio to wager, b is the payout, p is the probability of a win and q is the probability of a loss which in this example gives you:

f = ( 2 * 0.5 - 0.5 ) / 2 = 0.25

This is known as the Kelly Criterion. Unbeknowst to Kelly, Daniel Bernoulli had proposed the geometric mean of outcome as the appropriate measure for investment in 1738, hence the appropriate wager f for the aforementioned coin toss would be such that the following would be at a maximum:

e^( q * ln( 1 - f ) + p * ln( 1 + b * f ) )

which is at a maximum at f = 0.25

The Bernoulli approach requires iterative methods to solve (trial and error) but allows for multiple outcomes, outcomes that do not include a total lose and concurrent events (concurrent events are just more outcomes).

The equations actually show that if you wager more than 50% of your portfolio, you will actually be losing money even though it's a money making opportunity.

If you could wager on two such coin tosses at a time, again as often as you'd like, the optimal wager becomes 23% on each coin toss thereby risking 46% of your capital instead of the mere 25% and you start losing money when you wager more than 40% on each coin toss instead of the 50%, so you can risk up to 80% of your portfolio before losing money instead of the 50% with the single coin toss at a time scenario. So with more investment opportunities, you can invest a greater portion of your portfolio.

What this exemplifies is that there are limits to risk and you should never be fully invested so long as there is a risk of total loss. It also shows that diversification allows you to have more of your portfolio invested while still achieving the optimum for growth.

Our natural inclination is towards excessive risk, this is because we've evolved to be risk takers. To evolution, it doesn't matter if most of us fail so long as a few are obscenely successful. Hence your natural tendency will be to over bet and though that increases the chance of someone becoming very wealthy, it virtually guarantees that you will not. If you want to be personally rich, you will have to fight your own innate judgement of risk. You will often hear the advice to be aggressive when young but the opportunity value of what you risk when you're young is much greater then that of the same dollar amount when you are older, you should start off conservative because you have less and you will be holding your investments longer which means they will surely have to face a market downturn. You will hear the advice to invest in an aggressive 100% stock fund, mathematically such a portfolio guarantees a dibilitating loss as an eventuality, the optimum for growth can and has been proven by Claude Shannon at MIT to be 50/50. Ben Graham has written that the optimum is likely to be 45% invested in stocks and 55% in bonds. There is significant opportunity value in what you don't invest, it's what allows you to take advantage of a market downturn by simply rebalancing. The cash in your portfolio acts as a ratchet or one way valve so that you can benefit from both price increases and price drops. A 100% portfolio can do nothing in a downturn except lose money, to a 50/50 portfolio, a market downturn is a wonderful buying opportunity.

The best will not be all in stocks or all in savings or bonds, the best will be a portfolio of several investments according to the risk and the returns.

• 4 years ago

• Anonymous
5 years ago

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• Anonymous
5 years ago

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• 5 years ago