Having dabbled in stocks (and lost quite spectacularly in the Internet bust), I really find today's 3 hour System Optimization class on optimizing stock portfolio by Professor David Simchi-Levi insightful. We covered how we can use the principles of System Optimization to maximize returns and/or minimize risk.
I particularly enjoyed the part of the lecture on how we relate diversification to correlation and demonstrated that a diverse stock portfolio is a optimal portfolio that minimizes risk. It makes more sense to me after the professor had explained diversification with correlation.
All other factors being equal, let us consider a simple case of a portfolio that consists of only 2 stocks. If a their share prices are positively correlated, then if the share price of stock A goes up, stock B is likely to go up as well. In this scenario, it doesn't make sense to diversify since you can always invest all your money in either stock. If you are looking for low risk, invest in the stock with the lowest standard deviation. For high return, you invest in the stock with the highest return. For uncorrelated stocks, they tend to be unpredictable and hence uninteresting. With negatively correlated stocks, when 1 stock goes up, the other goes down which effectively mitigates the risk. Hence, when determining a stock portfolio where the objective function is minimal risk, the optimal solution is almost always a diverse portfolio of stock.