🎓 Prepared by students from Boğaziçi University

What is Diversification?

Diversification is the principle of spreading your investments across different asset classes, sectors, and geographies to reduce risk. By not putting all your money in one place, you protect your portfolio against losses in any single investment.

Short answer

Diversification spreads investments across multiple assets to lower overall portfolio risk without reducing expected return. More assets = less volatility; fewer assets = more risk.

Portfolio Risk vs Number of Assets
1814950
x: Number of Assets · y: Portfolio Risk (%)Unsystematic riskSystematic risk (irreducible)
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Try it: interactive calculator

Portfolio Risk
1,178.47%
= sqrt(60^2*20^2 + 40^2*8^2 + 2*60*40*-0.2*20*8)
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Step-by-step worked examples

You have $10,000. Put $6,000 in stocks (volatility 20%) and $4,000 in bonds (volatility 8%). Stocks and bonds have −0.3 correlation. Find portfolio risk.

Portfolio Risk = √(0.6²×0.2² + 0.4²×0.08² + 2×0.6×0.4×(−0.3)×0.2×0.08)
= √(0.0144 + 0.001024 − 0.002304)
= √0.01312 = 11.45%

Compare 1 stock (20% risk) vs portfolio of 10 uncorrelated stocks. Roughly how much does risk drop?

1 stock: 20% risk
10 uncorrelated stocks (equal weight 10% each): portfolio risk ≈ 20%/√10 ≈ 6.3%
Risk reduced by ~68%

Your portfolio: 50% US stocks, 30% international, 20% bonds. If US market drops 15% but others rise 5%, net portfolio change?

Change = 0.5×(−15%) + 0.3×(+5%) + 0.2×0% = −7.5% + 1.5% = −6%
Diversification cushions the blow
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Flashcards

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Quick quiz

Q1.Diversification reduces which type of risk?

Correct answer: B. Diversification eliminates company/sector-specific (unsystematic) risk, not market-wide (systematic) risk.

Q2.60% stocks (20% volatility) + 40% bonds (8% volatility), −0.3 correlation. Approximate portfolio risk?

Correct answer: B. √(0.36×0.04 + 0.16×0.0064 − 2×0.24×0.16) ≈ 11.4%

Q3.Two highly correlated investments (ρ=0.95)?

Correct answer: B. High correlation means they move together — diversification benefit is minimal.

Q4.Why add international stocks to a US portfolio?

Correct answer: B. International and US stocks often move independently, reducing portfolio volatility.
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Common mistakes

Diversification guarantees no losses.Correct: It reduces volatility and unsystematic risk, but market downturns still hurt.

Owning 50 similar stocks is diversified.Correct: Correlation matters. 50 tech stocks move together. Mix sectors, geographies, and asset types.

Once diversified, never rebalance.Correct: Rebalance annually to maintain target weights as prices shift.

Bonds always offset stock losses.Correct: Only if they're negatively correlated — in rare market crises, both can fall.

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FAQ

What is the diversification principle?

Spread investments across assets, sectors, and geographies to reduce risk without sacrificing expected return.

How do you measure diversification?

By correlation (−1 to +1) and portfolio risk formula. Lower correlation and more assets = better diversification.

Can you diversify away all risk?

No. Systematic (market) risk remains. Diversification removes unsystematic (company-specific) risk only.

Diversification benefits in a recession?

Yes, if assets have low/negative correlation. Bonds often hold steady when stocks fall.

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