FIN 401 · Risk & Mastery · Lesson 3 of 4
Portfolio Theory & Correlation Math
The math behind diversification — why 1+1 can equal less than 2 in risk.
In this lesson
Modern Portfolio Theory (MPT)
Harry Markowitz won a Nobel Prize for proving mathematically that diversification can reduce risk without reducing expected returns.
The key insight: a portfolio's risk is NOT the average of each stock's risk. Because stocks don't move perfectly together, their individual risks partially cancel out. A portfolio of 3 uncorrelated stocks has less total risk than any single stock alone.
This is the "free lunch" of finance — and it directly applies to StockPrince challenge strategy.
The efficient frontier
For any set of stocks, there's a curve of optimal portfolios called the efficient frontier. Each point on the curve represents the maximum expected return for a given level of risk.
Portfolios below the frontier are suboptimal — you could get more return for the same risk, or less risk for the same return.
In practice, this means: once you've picked your stocks, the allocation determines whether your portfolio is optimal or wasteful.
Efficient frontier (two assets)
InteractiveMin-var risk
9.7%
Its return
6.7%
Weight in A
89%
Lower correlation bends the curve left — that leftward bow is diversification turning two risky assets into a less risky blend.
Two portfolios with NVDA + JNJ: Portfolio A (50/50) might have 15% expected return with 20% volatility. Portfolio B (80/20) might have 18% expected return with 35% volatility. Which is "better" depends on the challenge format and your competition.
The correlation matrix
Correlation ranges from -1 to +1:
+1.0: Perfect correlation (stocks move identically). No diversification benefit.
0.0: Zero correlation (stocks move independently). Maximum diversification benefit.
-1.0: Perfect negative correlation (stocks move oppositely). Risk can theoretically be eliminated.
Key correlations for challenge building:
- NVDA ↔ AMD: ~0.80 (high, same sector)
- AAPL ↔ MSFT: ~0.75 (high, big tech)
- NVDA ↔ JNJ: ~0.15 (low, different sectors)
- Tech ↔ Utilities: ~0.20 (low, different drivers)
To maximize diversification, pick stocks with low correlation to each other.
Applying this to challenges
Hourly/Daily (fewer picks, short duration): Diversification has less time to work. Lean toward conviction + slight diversification. Correlation matters less.
Weekly/Monthly (more time, more variance): Diversification is your superpower. Pick 3 stocks with low pairwise correlation. Even if one stock tanks, the others are unlikely to tank simultaneously.
The optimal challenge portfolio: 1 high-conviction momentum pick (40-50%) + 1-2 uncorrelated secondary picks (25-30% each). This gives you upside exposure AND downside protection.
Scenario 1 of 3
+15 XPYou're building a weekly portfolio. Your candidates: NVDA (tech, bullish), AMD (tech, bullish), JPM (financials, neutral), UNH (healthcare, bullish), XOM (energy, neutral).
Which 3-stock combination gives the best risk-adjusted portfolio?
Scenario 2 of 3
+15 XPYou have the following correlation data for your candidates: NVDA↔AMD = 0.82, NVDA↔META = 0.65, NVDA↔UNH = 0.12, NVDA↔XOM = -0.05. You want NVDA as your lead pick (45%).
Which second stock gives you the best diversification benefit?
Scenario 3 of 3
+15 XPYou've run the numbers on two portfolio allocations for a weekly challenge. Portfolio A: Expected return 3.2%, volatility 2.8%. Portfolio B: Expected return 3.0%, volatility 1.4%. Both use the same 3 stocks but different weights.
Which portfolio sits on the efficient frontier?
Knowledge check
+50 XP1. What did Modern Portfolio Theory prove?
2. What correlation between two stocks gives the most diversification benefit?
3. For a weekly challenge, the optimal portfolio combines:
Apply what you learned
Build a correlation-diversified portfolio for your next challenge