Why Risk – Return Frontiers Are Curved – Even When Risk Can Be Cancelled

Following a thought experiment on multi-manager diversification

How Many Managers Are Too Many?

In the previous article, we explored a simple but useful idea:

In the limit, portfolio volatility approaches zero while expected return remains unchanged.

This naturally raises a deeper set of questions:

1. If risk can be fully cancelled, doesn’t the portfolio become risk-free?

2. If many different returns can all be made risk-free through diversification, why does the efficient frontier still slope upward?

3. What does this imply for how investors should think about risk when constructing portfolios?

This article addresses these questions directly.

When Risk Is Fully Cancelled, Is the Return Risk-Free?

Yes.

If a return stream becomes deterministic through diversification – meaning all stochastic fluctuations are eliminated – then from an investor’s perspective, that return is risk-free.

It does not matter whether the underlying strategies are individually risky. What matters is the portfolio-level outcome.

From the standpoint of an allocator choosing among combinations of managers:

• If diversification eliminates all uncertainty,

• then the resulting return sits at risk = 0 on the efficient frontier.

In other words, if such a construction exists, it should be treated exactly like a risk-free return – regardless of how it was produced.

If Many Returns Can Be Made Risk-Free, Why Isn’t the Frontier Flat?

Now suppose the following:

• There exist many groups of managers,

• each group delivers a different expected return,

• and within each group, risk can be fully cancelled through diversification.

In that case, each group collapses to a single point on the risk = 0 axis, each with a different return.

At risk = 0, the investor would simply choose the highest available return.

All lower-return risk-free points would be dominated and discarded.

So far, the efficient frontier is not a curve at all – just a single point at risk = 0.

Now consider what happens next.

Suppose there exists another asset (or team, or strategy) with a higher return – but whose risk cannot be fully cancelled.

This creates a new trade-off:

• Higher return,

• but with unavoidable residual risk.

At this moment, a second point appears on the efficient frontier:

• higher return,

• higher risk.

If no such asset exists, the frontier does not expand.

This logic repeats. At each level of risk:

• If part of the risk can be cancelled without sacrificing return, the frontier shifts left.

• A new point only appears when achieving a higher return requires accepting additional, non-cancellable risk.

This is why the efficient frontier always slopes upward:

Higher return corresponds to a higher share of irreducible risk.

What This Means for Investors

From an investor’s perspective, portfolio construction can be understood in two steps.

First, cancel what can be cancelled:

• Diversify across managers, strategies, instruments, and time horizons.

• Eliminate idiosyncratic noise and redundant exposures.

• Compress risk without giving up return.

Second, choose which risks to keep:

• The remaining risk is not a failure of diversification.

• It is the price paid for return.

These residual risks are unavoidable at the portfolio level. They are precisely the risks that define where you sit on the efficient frontier.

In this sense, investing is not about seeking risk, but about selecting which irreducible risks you are willing to bear in exchange for return.

Closing Thought

Efficient frontiers are not curved because diversification is imperfect.

They are curved because diversification has a boundary.

Once everything that can be cancelled is cancelled, the only way to earn more is to accept risk that cannot be eliminated.

And that – not volatility, not variance, not noise – is what risk truly means in portfolio construction.

Why Risk – Return Frontiers Are Curved – Even When Risk Can Be Cancelled was originally published in Coinmonks on Medium, where people are continuing the conversation by highlighting and responding to this story.