How to Read This Graph (Risk vs. Return)

Each dot is one random portfolio (a set of weights across the 8 stocks). The x-axis is risk (standard deviation). The y-axis is expected return.

What “Efficient Frontier” Means

The efficient frontier is the “top edge” of all those dots. For a given level of risk, portfolios on the frontier have the highest return. Equivalently: for a given return, frontier portfolios have the lowest risk.

Dominated vs. Efficient (the key idea)

• Efficient: no other portfolio has higher return with the same or lower risk.
• Dominated: you can find another portfolio that is better in both ways (more return and less risk).

Where Correlation Shows Up (Diversification)

Correlation controls how much risk you can “mix away”:

• Lower correlation → dots spread more to the left → you can reach lower risk.
• Higher correlation → dots bunch up → diversification is weaker → risk stays high.
• Negative correlation → strongest diversification → sometimes produces the lowest-risk portfolios.