How this instrument works
Portfolio expected return is a weighted average, not a plain one. Each holding contributes to the total in proportion to the share of money sitting in it, so a small position with a spectacular forecast barely moves the number, while a large position with a modest forecast dominates it. The arithmetic is linear on purpose: expected value adds up cleanly across holdings, which is why the formula is a straight sum of weight times return with no interaction term between the two positions.
The two-asset version here is the building block behind every larger allocation decision. A retail investor splitting savings between a stock fund and a bond fund uses it to see what the blend is projected to earn before committing money. A financial planner sizing a client's stock-to-bond ratio runs the same sum to compare an 80/20 split against a 60/40 one. Typical inputs pair a stock-like return in the high single digits with a bond-like return in the low single digits, and the output lands somewhere between the two, exactly where the weights place it.
The output says nothing about how bumpy the ride is. Two mixes can share an identical blended figure while one swings far more than the other, because expected return ignores how the two holdings move together — that is the job of a variance or covariance calculation, not this one. A frequent misreading is treating the two weight fields as independent, when they describe one pie: if they don't sum to 1, the missing or extra share is effectively sitting in unmodeled cash or leverage, and the output quietly stops describing a fully invested portfolio.
- Set Weight of asset 1 (0-1) to the fraction of the portfolio held in the first position — 0.6 for 60%.
- Set Expected return of asset 1, % to the return you project that holding will earn.
- Repeat for the second holding with Weight of asset 2 (0-1) and Expected return of asset 2, %.
- Check that the two weights add to 1 — anything else means part of the portfolio isn't accounted for.
- Read Portfolio expected return, % — the single weighted figure the two holdings produce together.
Worked example — 60% stocks, 40% bonds
Put 60% of a portfolio into a holding expected to return 10% and the remaining 40% into one expected to return 4%. Weight of asset 1 (0-1) is 0.6, Expected return of asset 1, % is 10, Weight of asset 2 (0-1) is 0.4, and Expected return of asset 2, % is 4. The blend is (0.6 × 10) + (0.4 × 4) = 6 + 1.6 = 7.6, so Portfolio expected return, % reads 7.6.
Notice the result sits closer to 10% than the midpoint of 10% and 4% would suggest, because the larger position carries more weight in the sum. Nudge the split toward 50/50 with the same two return figures and the blended number drops to 7.0 — a reminder that shifting money between two holdings moves the projected return even when neither holding's own forecast changes at all.
Questions
What does the portfolio expected return figure actually represent?
It is the weighted average of the return you project for each holding, weighted by how much money sits in each one. It is a projection built from the numbers you supplied, not a guarantee — real returns in any single period can land well above or below it, and the figure only describes the center of a range of outcomes.
What happens if the two weights don't add up to 1?
The sum still computes, but it stops describing a fully invested two-asset portfolio. Weights under 1 imply the rest sits in unmodeled cash earning nothing in this formula; weights over 1 imply borrowed money added to the position. Keep them summing to 1 unless you're deliberately modeling cash drag or leverage.
Does a higher blended number mean the better mix?
Not on its own. This figure ignores how bumpy the path to that average return is — two mixes can share the same expected return while one swings far more than the other, because expected return says nothing about volatility or how the two holdings move relative to each other. Comparing mixes on return alone skips half the decision.
Where do the individual expected-return inputs come from?
Common sources are a trailing historical average, an analyst or fund forecast, or a model like CAPM that derives a return from an asset's beta and the market risk premium. This instrument takes those figures as given and blends them; it doesn't estimate r1 or r2 for you.
Can this be extended to more than two holdings?
Yes — the same weighted-sum logic keeps adding one weight-times-return term per holding, so a five-fund portfolio uses the identical arithmetic with five terms instead of two. This two-asset version keeps every term visible, which is useful for checking the math by hand before scaling it up.
Why is there no term for how the two assets move together?
Because expected value is linear — the average of a sum equals the sum of the averages, regardless of whether the two holdings rise and fall together or move independently. That correlation matters enormously for the portfolio's risk, but it drops out entirely of the expected-return arithmetic, which is exactly why return and risk are always evaluated as a pair.
References
- U.S. SEC Investor.gov — investing basics, asset allocation, and glossary
- Kenneth French Data Library, Tuck School of Business — historical asset return data
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.