Interactive Tool
Building the actual portfolio
Once you understand diversification, you have to build something. Mix assets and watch the efficient frontier emerge; dial the single biggest decision you'll make: how much rides in stocks versus bonds; and learn why the "safe" bond half carries its own risk when interest rates move.
Method: the efficient frontier and capital market line are traced by Monte-Carlo sampling (thousands of random portfolios) from these inputs: nominal historical return, volatility, and correlation estimates from Damodaran (1928–2025), locked. Switch to Custom to edit.
Historical correlation (US Stocks ↔ US Treasuries (10yr)): 0.02, the real, measured co-movement. Switch to Custom to drag it yourself.
Simulation
A simulated path over 20 years: each thin line is an asset's price, the bold line is your rebalanced portfolio. Notice how the portfolio rides steadier than its riskiest holdings. That steadiness is diversification. Single plays one draw and holds; Live cycles fresh scenarios continuously.
Efficient frontier
Each dot is a possible mix. The curve is the efficient frontier: the best return for each level of risk. Add cash at the risk-free rate and the straight capital market line beats the curve: every investor should hold the tangency portfolio and dial risk with cash. Its slope is the Sharpe ratio.
This portfolio
- Expected return
- 8.3%
- Volatility (risk)
- 10.5%
- Sharpe ratio
- 0.51
Where risk went
Diversification removed 3.1% of risk, for free, without lowering expected return.
Range of outcomes
400 simulated 20-year runs- Typical (median)
- 4.9×
- Unlucky → lucky (5–95%)
- 2.2× – 10.3×
- Chance of a loss
- 0%
- Worst dip (typical / bad run)
- −21% / −32%
The single path above is just one draw. Across 400 runs, outcomes fan out enormously, and even good portfolios suffer deep temporary drops along the way. That spread is the risk you're paid for.
A simplified model for learning, not a forecast or advice. It assumes returns are normally distributed and inputs are stable and known. Real markets have fatter tails, and these estimates are uncertain. See the notes below on what mean-variance theory leaves out.
From frontier to allocation to bonds — and keeping it there
- Mix assets. Combine holdings with different correlations and the efficient frontier appears: the set of best-possible risk/return trade-offs, and the free-lunch benefit of not putting everything in one place.
- How much in stocks? The stock/bond dial is the decision that matters most. More stocks lifts long-run return but deepens the worst drop you must survive, set by your ability, willingness, and need to take risk.
- Bonds & rates. Bonds anchor a portfolio, but when rates rise their prices fall, and longer bonds fall harder (duration). Matching bond maturity to when you need the money is the quiet art of the "safe" sleeve.
- Rebalancing. Left alone, a portfolio drifts: stocks out-grow bonds and a tidy 60/40 quietly becomes a risky 80/20. Rebalancing on a schedule or a threshold pulls it back — controlling the risk you hold rather than chasing extra return.
Educational only, not financial advice.
Sources & further reading
How this tool was made
The frontier and allocation math runs live in your browser. Asset risk, return, and correlation inputs are estimated from long-run historical series (Damodaran, Fama–French, Shiller); the stock/bond and rebalancing tabs replay real annual US returns since 1928; and the bond tab uses Treasury yield data from FRED.
Research
- Markowitz, H. (1952). “Portfolio Selection.” The Journal of Finance 7(1): 77–91. The founding paper of modern portfolio theory.
- Tobin, J. (1958). “Liquidity Preference as Behavior Towards Risk.” The Review of Economic Studies 25(2): 65–86. Introduces the separation theorem.
- Sharpe, W. F. (1966). “Mutual Fund Performance.” The Journal of Business 39(1): 119–138. Introduces the reward-to-variability (Sharpe) ratio.
- Perold, A. F., & Sharpe, W. F. (1988). “Dynamic Strategies for Asset Allocation.” Financial Analysts Journal 44(1): 16–27. The classic taxonomy of buy-and-hold, constant-mix (rebalancing) and portfolio-insurance strategies. Rebalancing is concave: it does best in volatile but trendless markets and lags in trending ones — and because it buys more as prices fall, it offers less downside protection than buy-and-hold, not more.
Data
- Historical Returns on Stocks, Bonds, Bills & Real Estate — United States, Aswath Damodaran, NYU Stern School of Business. Annual series from 1928 (histretSP.xls), published by the author without stated usage terms; used with attribution.
- Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis. Series retrieved from FRED and cited to their originators per FRED's terms of use: Treasury yields (Board of Governors), CPI (BLS), 30-year mortgage rates (Freddie Mac PMMS), consumer credit rates (Board of Governors). The S&P Cotality Case-Shiller home-price index (© S&P Dow Jones Indices) is marked 'pre-approval required' on FRED, so only three headline statistics computed from it (long-run appreciation, worst drawdown, rolling-return range) appear here; the index levels are not republished.
Educational use only, not financial advice. Every figure traces back to the sources above or to the inputs you set — the full method and the source code are public.