Mean variance
Efficient frontier calculator return per unit of risk
Two or more close series. The engine estimates means and covariance, then lays out the mean-variance frontier: the mixes that take the least vol for each return.
BTC / ETH / SOL
8 frontier mixes
Long-only mean-variance mixes from the sample means and covariance. Left is calmer. Right reaches for the higher sample return.
- Mix 1
- 37.1%
- Mix 2
- 38.8%
- Mix 3
- 40.8%
Return 171.1%
Return 188.4%
Return 206.8%
- Frontier
| Vol (ann.) | Return (ann.) | BTC | ETH | SOL |
|---|---|---|---|---|
| 37.1% | 171.1% | 100.0% | 0.0% | 0.0% |
| 38.8% | 188.4% | 85.7% | 0.0% | 14.3% |
| 40.8% | 206.8% | 71.4% | 0.0% | 28.6% |
| 43.3% | 226.3% | 57.1% | 0.0% | 42.9% |
| 46.1% | 247.1% | 42.8% | 0.0% | 57.2% |
| 49.2% | 269.1% | 28.6% | 0.0% | 71.4% |
| 52.5% | 292.6% | 14.3% | 0.0% | 85.7% |
| 56.0% | 317.6% | 0.0% | 0.0% | 100.0% |
- Each row is daily, 365 periods a year. Annualized figures use 365 periods.
- 90 closes in the series. Computed by Thrive's portfolio engine. Rounded to the digit shown.
The curve is a constraint, not a promise
Each point is a long-only mix. Return is the weighted average of mean returns. Vol is the mix variance from the empirical covariance. Nothing on the curve is a forecast. It is the in-sample trade between the two.
The frontier is unstable when the window is short or the assets move as one. If Bitcoin, Ethereum, and Solana are all highly correlated, the curve collapses toward a single bet with different labels.
How this page runs it
Thrive's portfolio engine estimates arithmetic mean returns and the empirical covariance, then lays out the mean-variance frontier: weights, mean return, and volatility for each mix.
Weights are long only and sum to one. Means and vols are per period. The table also shows them annualized with the frequency you picked.
How to run it
- Paste one column of closes per asset, same number of rows.
- Run the frontier.
- Read the left side as the calmer mixes and the right side as the higher-return mixes.
- Open the correlation tool if the weights pile into one name.
FAQ
People also ask
It is the set of portfolios that deliver the highest mean return for a given variance, or the lowest variance for a given mean return, using the means and covariance you just estimated.
Mean-variance treats the sample means as known. A small edge in the window gets a large weight. That is the optimizer doing what you asked, and it is why the next page offers risk parity and a diversified minimum-variance mix.
No. Weights stay between 0 and 1 and sum to 1.
From 2 to 6 on this page, so the table stays readable and the run stays fast.
Related
Crypto portfolio optimizer
Max Sharpe, minimum variance, most diversified, and hierarchical risk parity. Same closes, four weight vectors, so you can see which method is just chasing the last winner.
Risk parity calculator
Equal risk contributions, inverse volatility, hierarchical risk parity, and minimum variance. Four ways to stop the riskiest name from owning the book.
Correlation matrix calculator
Empirical correlation from your closes. The heatmap is the number in each cell, not a color standing in for one.
Trading journal
The ratio on a pasted series is a lab result. The journal is the book you actually traded.
Bitcoin-Ethereum correlation
The live pair print behind a two-asset frontier.
Bitcoin volatility
The live 90-close vol print for the BTC sample.
Ethereum volatility
The live 90-close vol print for the ETH sample.
The frontier is the lab. The book is the job.
Thrive keeps the positions, the size, and the result in one journal so the mix you liked on paper can be checked against the mix you held.