The idea (and the quiz) is stolen from Chris Kennedy at Bridge Alternatives. I kept it in the closet for almost a year now because I wanted to use it for a live episode of our podcast. I came to the realisation it will never happen.
Let’s play a game. No Excel, no Python, no calculator. Gut only.
You own a portfolio returning 5% with 15% volatility. You’re about to put 10% of it into one new asset, and you want the best possible risk/return ratio afterwards. In each pair below, pick one:
| New Asset | Return | Risk | Correlation |
|---|---|---|---|
| A1 | 4.00% | 7.96% | -0.2 |
| A2 | 4.00% | 46.04% | -0.2 |
| B1 | 10.54% | 20% | 0.8 |
| B2 | 3.57% | 20% | -0.2 |
| C1 | 9.33% | 27.5% | 0.4 |
| C2 | 6.50% | 12.5% | 0.4 |
| D1 | 6.43% | 10% | 0.5 |
| D2 | -2.64% | 40% | -0.6 |
Done?
My guess is that you chose A1, D1, probably C2, and I’m less certain about B. My slight preference would be for B1. What I’m most confident about is that you weighted each input in the same order as they were presented: return matters more than volatility, and volatility matters more than correlation.
The beauty of this game is that it pushes you to better understand how each input interacts with the others, often in a non‑intuitive way.
Everything is the same
Let’s run the numbers. A1 and A2 give you exactly the same portfolio risk, about 13.36%. Same return too, so the same result. So the other six. Every single one lifts your portfolio’s return/risk ratio by about 10%, from 0.333 to roughly 0.367. Whatever you picked, you picked a tie.
Yes, A2 has almost six times the risk of A1 and it’s still equivalent. How’s that possible?!?
The reason is that risk enters the portfolio in two places: the asset’s own volatility, which grows with the square of its size, and the correlation with your existing portfolio. With a negative correlation, that cross-term reduces risk, and for a while it wins. So you can pile on volatility and end up in the same spot.
The original post contains all the math and formulas if you’d like to review them. The beauty of this exercise is that it neatly illustrates a point this blog has been making since it began: you should look at your portfolio as a single, unified entity, not as a collection of separate lines in a spreadsheet. A key element here is that correlations matter too.
There is a range in which taking more risk with the new asset actually makes the overall portfolio better. The only way to identify that range is to consider the other two elements as well: return and correlation.
Plot the eight assets on a risk/return chart and they look like a random mess. Plot them with their correlation and the pattern appears: the lower the correlation, the less return you need to deliver the same improvement. The assets sit on lines, one per correlation level.
Go back and review all the characteristics of each potential new investment. The way the exercise is set up, you can explore all possible combinations: high return, high risk, and even negative return!
All the choices shown here lead you to the same result, but in real life your eye test can fail spectacularly. This is where personal finance should stop being purely personal…or at least where you should have a serious conversation with your gut.
Return and risk are easy to hold in your head. Correlation just isn’t. And that’s the problem with leaning on Sharpe ratios as a shortcut: they work if correlations are roughly similar across the candidates. They never are, and certainly not in the alternatives world (the real one, not the ‘private’ type of alternatives), where low correlation is the whole point.
Avoiding assets with a negative expected return, to pick one, based solely on that single factor can be a costly mistake, because the market prices all other assets in line with what they can deliver in combination with that asset as well.
A better shortcut
Here’s the part I really liked. What is the bare minimum an asset must offer to do no harm to my portfolio at some small weight?
RRR of the asset must be greater than correlation × RRR of the portfolio
That’s it. Three numbers: return/risk of the candidate (RRR), correlation to what you hold, and return/risk of what you hold.
Quick example from the original document. Your portfolio sits at 5/15, so RRR = 0.33. Someone pitches you something with a 0.2 return/risk and a 0.7 correlation to your portfolio. Sounds fine, not amazing, but additive, right? Hurdle: 0.7 × 0.33 = 0.23. You’re at 0.2. It fails. At any weight, it makes your portfolio worse.
The recurring problem in personal finance (think of the 4% rule) is that we look for shortcuts, quick answers that should allow us to make better decisions, and then we forget when those rules can actually be applied. All three inputs here are estimates, and you can rely on the past only up to a certain point. There is not even a firm consensus on which element is the easiest to estimate. “Correlation, at least compared to return and risk, is a relatively unstable measurement. Its measurement error is comparatively large” writes Chris. But if you ask Verdad, the ranking in terms of ease of estimation is correlation, volatility, and returns.
The problem doesn’t stop there. For many assets, correlation in the belly of the distribution is different from correlation in the tails. A reasonable approach would be to give priority to assets that exhibit a correlation of -1 in the tails. I would call it the David Dredge approach of using a lot of equity and a lot of long-vol/tail assets. But there’s also merit in the risk parity approach, which captures the zig-zag in normal times and (hopefully) also some crisis alpha when needed. First and second responders, four quadrants: the usual stuff discussed here on this blog.
Yes, you thought I had finally given you something easy, and we are back to a lot of confusion! Sorry.
Still, the quiz offers a few things worth keeping in mind:
- It’s a filter, not a ranking. Yes/no. You can’t use it to sort ideas from best to worst, and that’s the point. “Ranking by Sharpe is like ranking runners by finishing time without asking how far each one ran.” Do not make any decision by looking only at Sharpe… unless you don’t have a portfolio yet. In that case, yes, pick the highest Sharpe you can find (and then apply leverage, if needed).
- Correlation is a hurdle. Zero correlation means the asset just needs a positive expected return. At a correlation of 1, it needs to beat your portfolio outright. This is the most important part of the whole post. Pay close attention to correlation and its estimation. The moment you find a truly uncorrelated asset, you can almost stop caring about returns. Also remember that truly negative correlation is really hard to find. Think about an ETF like CRRY. It is relatively new and you do not know how much expected returns you can assign to it. On the other side, by construction, it is pretty uncorrelated to the equity risk premium. Definitely more than your factor ETF that has a ton of beta baked in.
- Sharpe still has a job. If an asset’s RRR beats your portfolio’s, it adds value whatever the correlation. Actually, you should ditch your portfolio and invest in that asset alone, and then repeat the exercise using that asset as the new reference. Imagine how many lads start their analysis with stocks simply because they offer the highest expected return. That isn’t even true, because the asset with the highest expected return is levered stocks… but who has the time to argue with those guys? If your portfolio is well diversified, those high-Sharpe assets will be rare. Most of the value will come from things that look worse on a standalone basis.
Caveats (because there are always caveats)
- This is a screening tool, not a weight optimizer. Please don’t size positions with it. Sizing is a different art 😉
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