Why does splitting the money cut the risk?
Two assets with identical prospects and a correlation of minus 0.5. The half-and-half portfolio and the all-in position run on the same simulated draws, so the comparison is exact.
School Starter Monte Carlo Pro engine
After you install, this is the model to open.
Why Diversification Works
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
This one runs on a Pro engine, and every free install includes five full-quality runs on your own numbers, shared across all five Pro engines rather than five for each. After that, Pro is $199/year.
The answer
Twenty thousand simulated years, side by side:
- Expected return, both
- 7%
- Std dev, all-in
- 15 points
- Std dev, portfolio
- 7.37 points
- Bad year (P5)
- -5.1% vs -17.7%
The portfolio's spread is just under half, a measured 7.37 points against 15, with the same expected return: the only free lunch in finance, visible in one run. Set the correlation to 0 and rerun, then +0.5, and watch the benefit shrink; diversification is a correlation story, and now the story has numbers.
The model
Both assets Normal(7%, 15). One correlation pair at -0.5. Two output cells: the 50/50 portfolio and the all-in position, simulated together.
| Asset A and B | Normal(7%, 15) each |
| Correlation | -0.5 |
| Portfolio vs all-in | simulated |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
Next question
- Drill blind or pay to learn the odds first?Is the Test Worth Paying For?
- Why is the textbook schedule too optimistic?The Classic Project Network, Simulated
- Does discounting to fill the room ever work?What Does the Course Have to Charge?
- Is an equal share of the work actually fair?Share the Marking Fairly
- Did the course work or do the students just differ?Did the Course Move the Scores?
- Would more places actually fix the shortfall?Will the Programme Cover Its Costs?
Every model like this one, and the method behind them: Monte Carlo simulation.