I am voting you up because this is a legitimate question with a correct possible answer. Yes, you shouldn't buy penny stocks, yes you shouldn't speculate, yes people will be jealous that you have money to burn.

Your question: how to maximize expected return. There are several definitions of return and the correct one will determine the correct answer.

• Expected value: this is the arithmetic average of possible outcomes weighted by their likelihood. It is the correct choice when evaluating a specific decision/project where you will end the venture after the decision instead of completing it continuously.
• Maximize geometric return: this is the geometric weighted average of outcomes. It is the correct choice when you will be repeating a decision/algorithm over and over. It is optimized by The Kelly Criterion and it deathly afraid of going bust (since in the long run one bust makes everything else irrelevant).
• Risk-adjusted return: is the valuation of a portfolio performance when compared versus a comparable asset class, see Sharpe Ratio. This is the correct choice for choosing the best portfolio manager when different levels of risk are available. (A great bond fund is better than a shitty equity fund, even though it is expected to return less.)

For your situation, $1,000 sounds like disposable income and that you have the human capital to make more income in the future with your productive years. So we will not assume you want to take this money and reinvest the remains until you are dead. This rules out #2.

It sounds like you are the sole beneficiary of this fund and that your value proposition is regardless of asset class and competition to other investment opportunities. In other words, you are committed to blowing this $1,000 and would not consider instead putting the money towards paying down credit card debt or other valuable uses. This rules out #3.

You are left with #1, expected value.

Now there is already evidence that penny stocks are a losing proposition. In fact, some people have been successful in setting up honeypot email accounts and waiting for penny stock spam... then shorting those stocks. So to maximize expected return, invest 0% of your bankroll. But that's boring, let's ignore it.

As you have correctly identified, the transaction costs are significant, $14 in tolls on crossing the bridge both ways on a $1,000 investment already exceeds the 5-year US bond rate. Diversification will affect the correlation and overall risk (Kelly Criterion) of your portfolio -- but it has no effect on your expected return.

In summary, diversification has zero effect on your expected return and is not justified by the cost.

I am voting you up because this is a legitimate question with a correct possible answer. Yes, you shouldn't buy penny stocks, yes you shouldn't speculate, yes people will be jealous that you have money to burn.

Your question: how to maximize expected return. There are several definitions of return and the correct one will determine the correct answer.

1. Expected value: this is the arithmetic average of possible outcomes weighted by their likelihood. It is the correct choice when evaluating a specific decision/project where you will end the venture after the decision instead of completing it continuously.
2. Maximize geometric return: this is the geometric weighted average of outcomes. It is the correct choice when you will be repeating a decision/algorithm over and over. It is optimized by The Kelly Criterion and it deathly afraid of going bust (since in the long run one bust makes everything else irrelevant).
3. Risk-adjusted return: is the valuation of a portfolio performance when compared versus a comparable asset class, see Sharpe Ratio. This is the correct choice for choosing the best portfolio manager when different levels of risk are available. (A great bond fund is better than a shitty equity fund, even though it is expected to return less.)

For your situation, $1,000 sounds like disposable income and that you have the human capital to make more income in the future with your productive years. So we will not assume you want to take this money and reinvest the remains until you are dead. This rules out #2.

It sounds like you are the sole beneficiary of this fund and that your value proposition is regardless of asset class and competition to other investment opportunities. In other words, you are committed to blowing this $1,000 and would not consider instead putting the money towards paying down credit card debt or other valuable uses. This rules out #3.

You are left with #1, expected value.

Now there is already evidence that penny stocks are a losing proposition. In fact, some people have been successful in setting up honeypot email accounts and waiting for penny stock spam... then shorting those stocks. So to maximize expected return, invest 0% of your bankroll. But that's boring, let's ignore it.

As you have correctly identified, the transaction costs are significant, $14 in tolls on crossing the bridge both ways on a $1,000 investment already exceeds the 5-year US bond rate. Diversification will affect the correlation and overall risk (Kelly Criterion) of your portfolio -- but it has no effect on your expected return.

In summary, diversification has zero effect on your expected return and is not justified by the cost.