Portfolio Optimization

Purpose

This calculator finds a set of investment weights across several stocks that achieves a specific target annualized return, using each stock's historical price movements. It is useful for deciding how to split an investment across a group of stocks so that the combined portfolio's expected return matches a goal you set, while only ever holding non-negative amounts of each stock.

Background

From historical prices to expected return

The calculator starts from a table of historical closing prices for each stock and converts them into daily returns (the day-to-day percentage change in price). Averaging those daily returns and scaling them up to a yearly basis gives each stock's expected annualized return. A portfolio's overall expected return is the weighted average of its stocks' expected returns, using the fraction of the portfolio invested in each one (the Weight). The calculator searches for the combination of weights — each between 0% and 100%, all summing to 100% — that makes this weighted-average return equal your Target Return.

Inputs

CSV File

A table of historical closing prices (uploaded, or given as a URL), with one column identifying the date of each observation and one additional column per stock, containing that stock's closing price on each date. Each column of prices is converted internally to daily returns before optimization. For example:

TranDate   StockA   StockB   StockC
1/1/2024   85.0     257.5    146.2
1/2/2024   85.0     257.5    146.2
1/3/2024   85.2     256.8    147.0
...

The first column's name and date format do not matter — it is never parsed as an actual date, only used as a row label. What matters is that the rows are already listed in chronological order, oldest first, since the day-to-day returns are calculated from row to row, not from the date values themselves. You can use a different date format entirely, or even use plain labels like Day1, Day2 — as long as the row order is correct, the result is unaffected.

Target Return

The annualized return you want the optimized portfolio to achieve, entered as a decimal fraction (for example, 0.3 for a 30% annual return). The calculator searches for portfolio weights that make the expected return equal to this value; a target far outside the range achievable by the stocks provided may not be reachable.

Show Input

When checked, the original uploaded price table is included in the results as Input Data, so you can review the source data alongside the optimization result. Leave unchecked to omit it.

Results

Success

Whether the optimizer found a set of weights that satisfies the constraints (weights between 0 and 1, summing to 1, and matching the Target Return). If this is not successful, the target may not be achievable with the stocks and historical data provided.

Expected Return

The annualized return actually achieved by the optimized weights. When Success is true, this should match your Target Return.

Optimized Portfolio

A table with one row per stock:

Stock — the stock's column name from the CSV File.
Weight — the fraction of the portfolio to invest in that stock, as found by the optimizer (between 0 and 1; all weights sum to 1). A weight of 0 (or a value effectively 0, shown in scientific notation) means that stock is excluded from the optimized portfolio.
Avg Annual Return — that stock's own annualized historical return, based on its average daily price change scaled up to a year. This is the per-stock return the optimizer weighs and combines to reach the portfolio's Expected Return; a negative value means the stock lost value on average over the historical period covered by the data.

Log

The raw output of the underlying numerical optimizer, useful mainly for troubleshooting if Success is false.

Input Data

The original uploaded price table, shown only when Show Input is checked; otherwise displays "Not Shown".

Understanding the Calculation

Each stock's price series is converted to day-to-day percentage returns, and the average daily return is scaled to an annual figure. The optimizer then searches for a Weight for every stock, subject to: every weight is between 0 and 1; all weights sum to 1; and the weighted-average annualized return of the portfolio equals the Target Return. Among the weight combinations that satisfy these conditions, the optimizer returns the first one it converges to — it is not necessarily minimizing risk or volatility, only matching the target return under the stated constraints.

Example

Using the sample historical price data for six stocks (ACMB, APOT, BPMO, SNGU, STQM, UNVC) with a Target Return of 0.3 (30% per year), the calculator finds a portfolio with:

Success: True, Expected Return: 0.30 (matching the target)
SNGU: weight ≈ 0.18
STQM: weight ≈ 0.47
UNVC: weight ≈ 0.35
ACMB, APOT, and BPMO: weight ≈ 0 (excluded)

This means investing roughly 18% in SNGU, 47% in STQM, and 35% in UNVC, with nothing in the other three stocks, is expected to achieve a 30% annualized return based on their historical price behavior. This makes sense given their individual Avg Annual Return values: SNGU is close to flat (about -5%), while STQM (about 47%) and UNVC (about 26%) are the strongest historical performers among the six, so the optimizer favors them to reach the 30% target; ACMB, APOT, and BPMO all show negative historical returns and are excluded entirely.

Important Assumptions and Interpretation

Expected returns and weights are derived purely from historical price movements in the CSV file; they are not a guarantee of future performance.
The optimizer only targets a specific return — it does not minimize risk, volatility, or correlation between stocks, so two different runs that both hit the target return may carry very different risk levels.
Weights are constrained to be non-negative (no short selling) and to sum to exactly 1 (the full portfolio is invested, with no cash held back).
If Success is false, or the Target Return is very high or low relative to what the historical data supports, the optimizer may not find a valid set of weights.