🎓 Prepared by students from Boğaziçi University

What Is Modern Portfolio Theory?

Modern Portfolio Theory (MPT) is a mathematical framework that shows how to build an optimal investment portfolio by balancing risk and return. Developed by Harry Markowitz, MPT proves that diversification reduces overall risk without sacrificing expected returns.

Short answer

Modern Portfolio Theory states that an investor can optimize returns by diversifying across assets—the combination matters more than individual asset performance.

Efficient Frontier — Risk vs. Return

x: Risk (%) · y: Expected Return (%)Efficient FrontierIndividual Assets

Try it: interactive calculator

Portfolio Risk σₚ

1,371.86%

= sqrt(60*60*15*15 + 40*40*20*20 + 2*60*40*0.3*15*20)

Weight of Asset 160 %Risk (σ) of Asset 115 %Weight of Asset 240 %Risk (σ) of Asset 220 %Correlation (−1 to +1)0.3

Step-by-step worked examples

You hold Stock A (σ=15%, E(R)=10%) and Stock B (σ=25%, E(R)=14%), correlation = 0.3. Calculate portfolio risk with 60% A and 40% B.

σₚ = √[(0.6)²(15)² + (0.4)²(25)² + 2(0.6)(0.4)(0.3)(15)(25)]
= √[81 + 100 + 54]
= √235 = 15.33%
Notice: 15.33% is less than the weighted average of 18% — diversification benefit!

Two assets have correlation = −1 (perfect negative). Weight 50/50. σ₁=10%, σ₂=15%. What is portfolio risk?

σₚ = √[(0.5)²(10)² + (0.5)²(15)² + 2(0.5)(0.5)(−1)(10)(15)]
= √[25 + 56.25 − 75]
= √6.25 = 2.5%
Perfect negative correlation nearly eliminates portfolio risk.

Compare two portfolios: (A) 100% Stock, σ=20%; (B) 70% Stock + 30% Bonds, σ=12%. Which follows MPT better?

Portfolio B has lower risk (12% vs 20%).
If bonds have similar or better expected return, B is on the Efficient Frontier.
Portfolio A is suboptimal — same or lower return with higher risk.

Flashcards

Quick quiz

Q1.Modern Portfolio Theory was developed by…

Correct answer: B. Markowitz won the Nobel Prize in Economics (1990) for this framework.

Q2.The Efficient Frontier is…

Correct answer: C. It shows the best return for each level of risk.

Q3.Correlation = −1 means…

Correct answer: B. Perfect negative correlation means assets offset each other — maximum diversification benefit.

Q4.Which reduces non-systematic risk?

Correct answer: B. Diversification spreads risk across unrelated assets; systematic risk remains.

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Common mistakes

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Thinking diversification eliminates all risk. — Correct: Diversification reduces non-systematic risk but not market (systematic) risk.

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Confusing correlation values (high vs. low). — Correct: Low or negative correlation is better for diversification.

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Believing the Efficient Frontier is static. — Correct: It shifts as expected returns, volatilities, and correlations change.

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Ignoring transaction costs and taxes in portfolio optimization. — Correct: Real portfolios must account for costs and tax efficiency.

FAQ

What is Modern Portfolio Theory?

MPT is a mathematical approach to building portfolios that maximize return for a given risk level by carefully diversifying across assets.

Why is correlation important in MPT?

Lower correlation between assets means they move independently, reducing overall portfolio risk through natural hedging.

What is the Efficient Frontier?

The set of optimal portfolios that offer the highest expected return for each level of risk.

Can I use MPT for my personal investments?

Yes — the principle (diversify across uncorrelated assets) applies to any investor. Simple index fund portfolios follow MPT.