Incremental Value Over the Existing Book

A researcher presents a new strategy with a standalone Sharpe ratio of 1.1 and asks for capital. On its own that looks fundable. But the desk already runs a portfolio with a combined Sharpe of 1.5, and the new strategy is 70% correlated with strategies already in it. Added at any meaningful size, it drags the combined Sharpe ratio down rather than up — a standalone-attractive strategy that destroys value for the book as a whole. Incremental value is the correct test: not "is this good," but "does adding this, at the size proposed, improve the risk-adjusted return of the portfolio we already run."

Why standalone quality isn't enough

A portfolio's combined Sharpe ratio depends on each component's own Sharpe ratio and its correlation to everything else already in the book. A high-Sharpe strategy that is highly correlated with the existing book can lower the combined Sharpe ratio, while a mediocre standalone strategy that is nearly uncorrelated can raise it — diversification value can outweigh standalone quality. This is the same logic as a spanning test, but framed for a capital allocation decision rather than a yes/no statistical test: instead of asking whether the new strategy is span-able at all, incremental value asks by how much the specific proposed allocation moves the specific numbers that matter — combined Sharpe, combined drawdown, combined volatility — at the size actually being requested.

Worked example: adding capital to an existing book

Existing book: 12% return, 8% volatility, Sharpe $= 1.5$. New strategy standalone: 11% return, 10% volatility, Sharpe $= 1.1$, correlation to the existing book $\rho = 0.7$. Allocate 20% of capital to the new strategy, 80% remaining in the existing book. Combined return: $0.8(12\%) + 0.2(11\%) = 9.6 + 2.2 = 11.8\%$. Combined variance: $0.8^2(8\%)^2 + 0.2^2(10\%)^2 + 2(0.8)(0.2)(0.7)(8\%)(10\%) = 0.4096\% + 0.04\% + 0.1792\% = 0.6288\%$, so combined volatility $\approx \sqrt{0.6288} \approx 7.93\%$. Combined Sharpe: $11.8/7.93 \approx 1.49$ — essentially unchanged, slightly worse. Despite a respectable standalone Sharpe of 1.1, this specific allocation adds almost no incremental value because the correlation is too high relative to the standalone quality on offer. A second candidate with the same 1.1 Sharpe but $\rho = 0.1$ against the existing book would raise the combined Sharpe meaningfully at the same allocation size — same standalone number, opposite verdict.

What this means in practice

Every capital allocation committee should ask for the incremental-value calculation, not just the standalone backtest, before funding a new strategy — correlation to the existing book is as important an input as the strategy's own Sharpe ratio, and neither one alone determines the right answer. This also means the "best" strategy to add next changes as the book itself changes: a strategy rejected as redundant today can become valuable later if the composition of the existing book shifts, and vice versa.