Spanning Tests for New Strategies

A researcher pitches a new strategy with an attractive standalone Sharpe ratio of 1.4. Should the desk add it? Standalone performance is the wrong question if the desk already runs ten correlated strategies — a new strategy that behaves like a blend of the existing ones adds nothing, however good it looks alone. A spanning test asks the right question directly: can the existing set of strategies, combined in some weighting, already replicate the new strategy's risk and return? If yes, the new strategy is "spanned" by the old ones and adds no diversification value regardless of its solo Sharpe ratio.

The idea, without the linear algebra

Think of each strategy as a point in risk-return space, and the full set of possible combinations of existing strategies as tracing out an efficient frontier — the best return achievable for each level of risk. A new strategy is spanned if its own risk-return point already lies on or inside that frontier: some mix of the strategies you already have could have produced the same or better outcome. A new strategy is not spanned — genuinely valuable — only if it lies outside the existing frontier, meaning no combination of current strategies could have matched it. Formally this is tested by regressing the new strategy's returns on the existing strategies' returns and checking whether the regression intercept (its alpha relative to the existing book) is statistically distinguishable from zero; a zero alpha means the new strategy is just a repackaged combination of what's already there.

Drag the correlation slider toward 1 and watch the frontier flatten toward the two individual assets — that's the geometric picture of spanning: when a candidate strategy is highly correlated with (spanned by) the existing book, combining them barely extends the achievable frontier at all. Push correlation down and the frontier bulges outward — that bulge is the diversification value a genuinely unspanned strategy provides.

Worked example: two candidate strategies

The desk already runs a value-momentum blend. Candidate A has a standalone Sharpe of 1.4 but 0.85 correlation with the existing blend; regressing A on the existing book gives an intercept statistically indistinguishable from zero — A is spanned, and adding it moves the frontier almost nowhere despite its attractive solo number. Candidate B has a lower standalone Sharpe of 0.9 but only 0.15 correlation with the existing blend; its regression intercept is significantly positive — B is not spanned, and even though it looks worse alone, it pushes the achievable frontier outward and is the one worth adding.

What this means in practice

Standalone Sharpe ratio is a screening tool, not a decision rule, for any desk running more than one strategy — the question that actually matters is incremental, not standalone. Spanning tests formalize "does this add anything the existing book can't already do" and prevent a portfolio from accumulating strategies that are superficially different (different signals, different researchers, different asset classes even) but statistically redundant once combined. This is also why correlation to the existing book, not just correlation to the market, belongs in every new-strategy writeup.