What you are actually watching
Diversification is the most repeated advice in investing and the least understood. Here is
the actual mechanism behind modern portfolio theory, why correlation is the only number
that really matters, and where the famous free lunch runs out.
Returns average, risks do not
Put half your money in something returning 10% and half in something returning 4%, and you
expect 7%. Nothing surprising. Returns are a straight weighted average, which is why the
expected return line on this page never does anything interesting.
Risk behaves differently. Portfolio variance carries a third term built from
correlation, and whenever
correlation is below a perfect 1, that term pulls your total risk below the
weighted average of the two risks. You get the average return and less than the average
risk. That gap is the free lunch.
Why two risky things can be safer than one
Load the stocks and bonds preset and press "jump to the lowest risk mix". That blend has a
proper name, the minimum variance portfolio, and here it lands at roughly
10% stocks. Its volatility comes out below that of holding 100% bonds,
while its expected return is higher.
Read that again, because it sounds like a mistake. Taking a slice of the riskier
asset made the whole portfolio safer. It works because on the days bonds have a
bad time, stocks are not reliably having a bad time too. Their wobbles partially cancel.
Nothing about either asset changed, only the fact that you now hold both.
Correlation sets the size of the benefit
Drag the correlation slider from left to right and watch the curve straighten out. At
−1 it collapses into a corner and you can build a portfolio with literally zero
volatility. At 0 you still get a healthy bulge. At +1 the curve becomes a straight line
and the benefit vanishes completely.
That is why professional investors obsess over correlation rather than over picking
winners. Twenty tech stocks are not a diversified portfolio, because they are one bet
wearing twenty hats. The "two similar stocks" preset shows exactly how little you gain at
a correlation of 0.85.
The uncomfortable part: correlations tend to rise in a crisis. Assets that
looked independent for a decade start falling together precisely when you needed them not
to. Diversification is real, but it is at its weakest on the worst days.
Half the curve is not worth holding
Notice the dashed grey section below the green minimum variance portfolio. Every mix on it
is a mistake, because for each one there is a point directly above with the same
risk and a higher return. Nobody should ever knowingly hold one.
The solid section above the green dot is the efficient frontier. Every
point on it is a legitimate choice, and picking between them is not a maths question but a
question about your own appetite for risk. This is the line where finance stops being able
to tell you what to do.
What this model assumes
Everything here rests on knowing expected returns, volatilities, and correlations in
advance. In reality you get estimates from history, and expected returns in particular are
notoriously difficult to forecast. Small errors in those inputs move the frontier a great
deal.
It also assumes volatility is a complete description of risk, which it is not. It treats
an upside surprise the same as a crash, and it assumes returns behave nicely when real
markets have fat tails. Use this to build intuition about how mixing works, not to
pick your actual allocation.
Things to try
Each one lands a point that the formula alone will not.
1Kill the free lunch
On any preset, drag correlation to +1. The curve snaps into a straight line and the
benefit box drops to zero. This is the case people implicitly assume, and it is the one
case where diversification does nothing at all.
2Build a riskless portfolio
Load the perfect hedge preset and press the lowest risk button. Volatility goes to
essentially zero while the return stays positive. Impossible in practice, but it shows
precisely what the correlation term does.
3Find the safer-than-safe mix
On stocks and bonds, compare the lowest risk portfolio against 100% bonds. Lower risk
and higher return at the same time. Then raise correlation to 0.8 and watch that
advantage disappear.
4Chase the best Sharpe ratio
Watch the orange dot as you change the risk-free rate. The mix that offers the best
return per unit of risk moves, which is why the "optimal" portfolio depends on what
cash pays.
Common questions about portfolio diversification
What is the efficient frontier?
The set of portfolios that give the highest expected return for each level of risk. On this chart it is the solid section above the lowest risk point. Anything below that point is inefficient, because you could hold the same risk and earn more. The frontier does not tell you which point to pick, only which ones to rule out.
How can adding a risky asset reduce my risk?
Because risk is not additive. Portfolio variance includes a correlation term, and when two assets do not move in lockstep, their fluctuations partly offset. As long as correlation is below 1, some mix of the two is less volatile than the weighted average, and often less volatile than the safer asset on its own.
What is a good Sharpe ratio?
It measures excess return per unit of volatility, so higher is better. Broad equity markets have historically sat somewhere around 0.4 over long periods. Treat any backtested strategy claiming a Sharpe above 2 with suspicion, since it usually means the risk has been hidden rather than removed.
Does diversification still work in a crash?
Less well, which is the most important caveat here. Correlations tend to rise sharply during crises, so assets that looked independent start falling together exactly when you most needed them not to. Diversification remains worth having, but a model calibrated on calm periods will overstate how much protection you get in a bad one.