Push from two stocks to n. With equal weights across n stocks, the variance formula generalizes to something worth reading slowly:
σp² = (1/n) × (average variance of the stocks) + (1 − 1/n) × (average covariance between them)As n grows, the first term, the stocks' own variance or private turbulence, is divided away toward zero. But the second term isn't, because its weight (1 − 1/n) rises toward one. In a large portfolio, what remains is nothing but the average covariance. A diversified portfolio's risk is co-movement, full stop.
Numbers make it visceral. Suppose the average stock has σ = 30% (variance 900) and the average pairwise correlation is 0.25, so the average covariance is 225:
| Number of stocks n | Portfolio σ |
|---|---|
| 1 | 30.0% |
| 2 | 23.7% |
| 5 | 19.0% |
| 10 | 17.1% |
| 30 | 15.7% |
| 100 | 15.2% |
| ∞ | 15.0%, the floor |
Half the single-stock's risk gone by n = 30, and then the curve goes flat. No n reaches zero. The floor, √225 = 15%, is the co-movement that every additional stock brings with it.
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Systematic vs idiosyncratic risk, and why only one is priced
Name the two layers, because the names carry the pricing logic:
- Idiosyncratic (firm-specific, diversifiable) risk. The part that washes out: a plant fire, a failed drug trial, a USFDA warning letter on one facility, a promoter scandal, a lost anchor client, a fraud. One company's disaster is noise to a 40-stock portfolio.
- Systematic (market, non-diversifiable) risk. The floor: recessions, rate cycles, inflation shocks, wars, pandemics, tax regimes. These hit everything at once. No number of additional stocks dilutes them, because each new stock arrives already carrying them.
Now the pricing punchline, and it's the most important argument of the week. The bootcamp planted the flag: if you can cancel a risk cheaply, the market will not pay you for carrying it. Here's the full argument. Suppose a stock offered extra expected return purely as compensation for its idiosyncratic risk. Diversified investors can buy it, fold it into a portfolio where that idiosyncratic risk washes out, and pocket the extra return while bearing no extra portfolio risk. Think of mutual funds, index funds, FPIs, insurers, the people setting prices at the margin in any liquid large-cap. They'll do it, and in size. Their buying raises the price until the free extra return is gone. What survives competition is compensation only for the risk the marginal, diversified investor actually has to carry. That risk is covariance with the common factors, which is systematic risk. Bearing avoidable risk isn't virtuous, and nobody pays you for it. It's just avoidable.
Practical corollaries: how many stocks, and what about India?
Three practical corollaries:
- How many stocks? The arithmetic says 20–30 reasonably spread names capture most of the washout, and classic studies put "most" at 85–95% of the achievable reduction. Beyond ~30 the gains are small. Whether you should want maximum diversification, versus Buffett's punch-card concentration, is a philosophy question with good arguments both ways, and Phase 9 stages that debate properly. The pricing argument here needs only one fact. The marginal price-setter is diversified, so prices embed no reward for firm-specific risk, whatever you personally choose to hold.
- India-specific: thirty NIFTY names across sectors kill most firm-specific risk but leave you fully exposed to India-systematic risk: RBI cycles, oil (India imports ~85% of its crude), monsoons, FPI flow reversals, INR episodes. Adding global assets diversifies away some of that, and adds currency wrinkles that the macro phase covers. The world's common cycle still keeps the global floor above zero.
- A flag for later: the owner of an unlisted family business, or a promoter with 60% of wealth in one company, isn't diversified. For them the firm's total σ is the lived risk. Damodaran's "total beta" adjustment for such owners is built when you assemble the full cost of capital.