Narcissus at the Pool

When Narcissus was born, his mother asked the blind prophet Tiresias whether her son would live to see old age. Yes, said the prophet, if he never comes to know himself.

He grew up so beautiful that everyone who saw him wanted him, and he wanted no one. He turned away the young men and the young women alike, and he turned away the nymph Echo, who could only repeat the last words spoken to her, until she wasted to nothing but a voice. At last one of those he had scorned lifted his hands to the sky and prayed: Let him love as we have loved, and let him never have what he loves. And Nemesis, the goddess who gives each thing its due, heard the prayer.

Deep in the woods there was a pool that no shepherd had ever found. No goats had drunk from it, no bird or beast had troubled it, no branch had ever fallen into it. The water was perfectly clear and perfectly still, like polished silver.

Narcissus, tired from the hunt, knelt to drink, and saw a face.

It was the most beautiful face he had ever seen. When he smiled, it smiled. When he reached toward it, it reached toward him. When he spoke, its lips moved in answer. It agreed with him in everything. He had found, at last, something that matched him perfectly.

He leaned down to kiss it, and it fled into ripples. He waited for the water to still, and it came back, as flawless as before. He could not leave it. He forgot to eat, forgot to sleep, forgot the hunt and the world beyond the trees. When at last he understood — it is me; I am the one I love — he still could not leave, because nothing out in the world had ever answered him so well.

He wasted away at the water’s edge, gazing. When the nymphs came to bury him, the body was gone. In its place was a flower with a yellow heart and white petals, bending over the pool.

The trading concept

Overfitting. A backtest is a pool that no one has ever disturbed: a record of the past, perfectly still, that holds no surprises because it has already happened. Tune a system against it long enough — adjust a rule here, add a filter there — and it begins to answer you perfectly. Every move you make, it makes. The curve rises smoothly, the drawdowns vanish, and what you are looking at is not the market but your own reflection.

The beauty is the danger. A model fitted closely enough to history can agree with that history in everything, and that is exactly what makes it useless for a future that has not read it. Reach toward the live market and the image breaks into ripples.

The discipline is to know the pool for what it is: test on data the model has never seen, prefer simple rules that survive to elaborate ones that shine, and be suspicious of any result that is too beautiful. For an automated system this is not a matter of taste. A machine will trade its reflection faithfully until the account is gone.

Further reading

• Ovid, Metamorphoses, Book 3 — Echo and Narcissus, the prophecy of Tiresias, and the prayer answered by Nemesis.
• David H. Bailey, Jonathan M. Borwein, Marcos López de Prado and Qiji Jim Zhu, “Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance,” Notices of the American Mathematical Society (2014).
• Marcos López de Prado, Advances in Financial Machine Learning (2018).