Portfolio concepts / conceptos de cartera
Diversification, correlation and concentration: a worked crypto example
Use fictional weights and returns to separate concentration, sample correlation and shared crypto dependencies without implying protection or future performance.
You will learn
- Distinguish diversification, correlation and concentration without treating any one measure as a risk score.
- Compute a simple concentration proxy from fictional weights and explain why token count is not an effective number of independent exposures.
- Reproduce the Pearson correlation for two four-period fictional return series and interpret it as a sample, not a forecast.
- Identify shared market, issuer, network, stablecoin, bridge or custody dependencies and explain why diversification cannot promise protection.
Before you begin
No portfolio, market feed, account or token contract was accessed. All weights and returns below are fictional arithmetic examples, not recommendations or forecasts.
Three questions, three different measures
Diversification describes how exposures are spread across different sources of risk. Correlation describes how two measured series moved together over a specified sample. Concentration describes how much weight sits in a small number of positions or common exposures. A portfolio can hold many tickers and still depend on one issuer, one chain, one stablecoin, one bridge or one custodian.
Investor.gov explains diversification as spreading investments and warns that it does not fit every goal or remove investment risk. That is general U.S. investor education for traditional portfolios, not crypto-specific evidence or a prescribed allocation. The calculations here are a way to inspect fictional weights and observations; they do not establish that a real portfolio is diversified or suitable.
Evidence: SEC/Investor.gov guide to diversification and its limits
General U.S. investor education about asset allocation, diversification and rebalancing. Its examples concern traditional investment portfolios; it does not establish cryptoasset correlations, a suitable allocation or a guarantee against loss.
Solved fictional example: count the weights, not the labels
Fictional arithmetic only. Let each wᵢ be one position’s share of total portfolio value, written as a fraction, with all weights adding to 1. The Herfindahl-style concentration proxy is HHI = Σwᵢ²; its reciprocal 1/HHI is sometimes read as an “effective count” under this simple weighting convention. It is not a risk score, a measure of correlation, or a standard that proves diversification.
In the first made-up mix, ten positions each weigh 10%: HHI = 10 × 0.10² = 0.10 and 1/HHI = 10. In the second, three positions each weigh 1/3: HHI = 3 × (1/3)² = 1/3 ≈ 0.3333 and 1/HHI = 3. These figures summarize weights only. Different assets can share the same underlying risk even when their names differ.
| Fictional mix | Weights | Largest three total | HHI = Σw² | 1 / HHI |
|---|---|---|---|---|
| A | 10 × 10% | 30% | 0.10 | 10 |
| B | 3 × 33⅓% | 100% | 0.3333… | 3 |
Evidence: SEC/Investor.gov guide to diversification and its limits
General U.S. investor education about asset allocation, diversification and rebalancing. Its examples concern traditional investment portfolios; it does not establish cryptoasset correlations, a suitable allocation or a guarantee against loss.
Solved fictional example: correlation is tied to the chosen sample
For paired observations xᵢ and yᵢ, Pearson’s sample correlation is r = Σ[(xᵢ−x̄)(yᵢ−ȳ)] / √(Σ(xᵢ−x̄)² × Σ(yᵢ−ȳ)²). It ranges from −1 to +1 when both series vary. The result describes linear co-movement in these observations; it does not identify a cause or tell you what comes next.
Use four fictional period returns for A: −10%, 0%, +10%, +20%. If B repeats A exactly, r = +1; an equal-weight A/B mix has the same four returns as A. If B is the exact inverse (+10%, 0%, −10%, −20%), r = −1 and the equal-weight return is 0% in each of these four rows. Perfect inverse movement is a constructed edge case, not a real-world expectation. Small samples, selected dates, missing data and changing market conditions can make a historical estimate misleading.
| Fictional period | A return | B = A | Equal-weight A/B | B = −A | Equal-weight A/(−A) |
|---|---|---|---|---|---|
| 1 | −10% | −10% | −10% | +10% | 0% |
| 2 | 0% | 0% | 0% | 0% | 0% |
| 3 | +10% | +10% | +10% | −10% | 0% |
| 4 | +20% | +20% | +20% | −20% | 0% |
| Sample r | — | +1.00 | — | −1.00 | — |
A safe paper check: label the sample and shared risks
Normalize the fictional weights
Write the denominator and measurement time, then divide each position value by the total. Confirm the fractions sum to 1; do not infer a weight from a ticker count.
Group common dependencies
On paper, tag the issuer or claim, underlying asset, chain, bridge or wrapper, stablecoin, custodian and platform. Mark unknowns explicitly; a shared tag is a dependency to investigate, not a forecast of loss.
Use comparable observations
If practicing correlation, use the same return interval, time zone, denomination and four-or-more matched timestamps. Record the selected period and formula. Do not mix a BNB quote from one venue with another asset’s unmatched daily close.
Try a joint-stress row
Ask whether the example still works if all holdings fall together or an access route is unavailable. This is a scenario, not a probability estimate. If weights, timestamps or sources are missing, report “not enough information” instead of a score.
Evidence: SEC/Investor.gov guide to diversification and its limits · BSC native BNB gas role
General U.S. investor education about asset allocation, diversification and rebalancing. Its examples concern traditional investment portfolios; it does not establish cryptoasset correlations, a suitable allocation or a guarantee against loss.
Used only for the documented role of native BNB as BSC gas. The same page contains dated validator details; those counts and performance claims are not reused as current facts.
Check your understanding
In the fictional three-label mix of 60%, 20% and 20%, what is HHI, and does its reciprocal prove three independent risks?
Show explanation
HHI = 0.60² + 0.20² + 0.20² = 0.44, so 1/HHI ≈ 2.27 under this simple weight proxy. No: the reciprocal is not a count of independent exposures and does not prove that prices, network access, custody or counterparties are diversified.
Primary sources
- Beginners’ Guide to Asset Allocation, Diversification, and RebalancingInvestor.gov / U.S. Securities and Exchange Commission · 2026-10-26
General U.S. investor education about asset allocation, diversification and rebalancing. Its examples concern traditional investment portfolios; it does not establish cryptoasset correlations, a suitable allocation or a guarantee against loss.
- Introduction - BNB Smart ChainBNB Chain · 2026-10-26
Used only for the documented role of native BNB as BSC gas. The same page contains dated validator details; those counts and performance claims are not reused as current facts.