Why are twenty tech stocks barely a portfolio?

Twenty holdings sounds diversified. Twenty holdings that all sell software to the same customers, in the same currency, funded by the same interest-rate environment, valued on the same multiples and moved by the same news cycle is one idea bought twenty times. Here is the arithmetic that proves it.

Effective bets, not holdings

There is a simple way to translate a holding count into what it is actually worth. For N equally weighted holdings with average pairwise correlation ρ, the number of effectively independent bets is roughly:

N ÷ ( 1 + (N − 1) × ρ )

Run it for twenty holdings:

• ρ = 0.7 (a tight sector cluster): 20 ÷ (1 + 19 × 0.7) = 20 ÷ 14.3 ≈ 1.4 independent bets.
• ρ = 0.2 (holdings spread across genuinely different exposures): 20 ÷ (1 + 19 × 0.2) = 20 ÷ 4.8 ≈ 4.2 independent bets.

Twenty rows on the screen. In one case, roughly one and a half real decisions; in the other, about four. Same count, triple the actual diversification.

What it costs in risk terms

Using Unit 1's volatility formula — twenty holdings, each at 35% annual volatility:

• At ρ = 0.7: portfolio volatility ≈ 29.6%.
• At ρ = 0.2: portfolio volatility ≈ 17.1%.

And the punchline: at ρ = 0.7, adding infinitely many more same-sector names only gets you to 29.3%. The twenty-name sector basket has already collected essentially all the diversification that kind of basket can ever offer, and it is not much. The remaining 29.3% is the sector's shared fate, and no amount of counting removes it.

Why sector clusters correlate so tightly

The cause is shared plumbing. Companies in one industry usually share:

• the same customers and the same demand cycle,
• the same input costs and supply chains,
• the same regulatory exposure,
• the same valuation lens — long-duration growth stories reprice together when interest rates move, as 2022 demonstrated across whole sectors at once,
• the same news. One earnings miss from a bellwether re-rates the neighbours by lunchtime.

Those channels are exactly what correlation measures. A high ρ inside a sector is not a statistical quirk to diversify around; it is a description of a real, shared economic engine.

The general form of the trap

Technology is only the most visible version. The same structure hides in ten banks (one interest-rate bet), a set of commodity producers (one commodity-cycle bet), five funds that each hold the same mega-caps (one large-cap bet in five wrappers), or an employer's shares held alongside a salary from that employer (one company, two ways).

In the data

A company's sector label comes from a classification scheme, and more than one scheme is in use. Vodafone's record carries two:

Read the last two lines: Telecom Services in one scheme, Wireless Telecommunication Services in the other. Across a whole portfolio the schemes disagree often enough that a concentration count computed on one is not the same count as on the other, and neither knows which companies share a demand cycle.

Try it now

1. The two charts below are a concentrated growth fund and one of the largest companies inside it, over the same year. Count the distinct shapes: two, or one drawn twice? A wrapper and its own biggest constituent are not two exposures.

2. Take your holding count, estimate ρ by eye (tight cluster ≈ 0.7, mixed ≈ 0.3), and run N ÷ (1 + (N − 1) × ρ). What is the real number of bets?
3. Describe the result neutrally. "This is concentrated in one exposure" is an observation about structure, not a recommendation to change anything.