Abstract. This note decomposes the risk of the Trading Floor, a disclosed paper book (simulated, not run with real money), into standalone desk risk and the risk that survives combining ten desks into one platform.

1. The book

Ten desks: three systematic sub-strategies (equity beta, low volatility/betting against beta (BAB), and trend/time-series momentum (TSMOM)) and seven long/short desks run inside sectors. Risk parity on inverse volatility gives riskier desks proportionally smaller weights, and the whole is scaled to the volatility target in Table 1. The construction is disclosed and unlevered.

2. What diversification buys

A platform earns its structure from imperfect correlation among many desks, not from conviction in one. The fundamental law of active management is explicit: value added rises with the breadth of independent bets (Grinold and Kahn, 2000). The diversification ratio, the weighted average of standalone desk volatilities divided by the volatility of the combined portfolio (Choueifaty and Coignard, 2008), prices that breadth here, before any leverage is applied to reach the target.

Table 1. Risk decomposition of the combined book.
QuantityValue
Weighted average of standalone desk volatility20.9%
Combined unlevered book volatility7.7%
Diversification ratio2.72x
Risk reduction from diversification~63%
Volatility target10.0%

3. Correlation structure

Average pairwise absolute correlation is low enough that the desks offset one another rather than reinforce. The low-volatility/BAB desk is negatively correlated to equity beta, a hedge that fires precisely when beta hurts. The trend/TSMOM desk is positively correlated to beta, adding directional exposure in persistent regimes. The sector desks cluster because they share one momentum factor, so the allocator budgets them as a single group rather than ten independent positions. Left alone, a correlated cluster rebuilds the concentration that risk parity exists to remove.

Table 2. Selected pairwise correlations among desks.
RelationshipCorrelation
Average pairwise absolute (all ten desks)0.29
Low-volatility/BAB vs. equity beta−0.66
Trend/TSMOM vs. equity beta+0.60
Sector desks, within cluster+0.3 to +0.5

4. Limitations

The universe is current S&P constituents, which is survivorship biased (it contains only companies that survived to the present), so any return or Sharpe ratio (return per unit of risk) behind the book is an upper bound and is not the subject here. Correlations are historical and vary with regime. The hedge and the sector cluster can both migrate in stress, and budgeting the sector desks as one group guards against that migration rather than promising it will not occur.

This is a record of construction, not of alpha (excess return). It is kept because the discipline it records (uncorrelated sub-strategies, a correlated cluster budgeted as one, an honest survivorship caveat) is what separates a diversified book from a levered, concentrated book that merely calls itself diversified.

References

  1. Choueifaty, Y., and Coignard, Y. (2008). Toward Maximum Diversification. Journal of Portfolio Management, 35(1), 40–51.
  2. Grinold, R. C., and Kahn, R. N. (2000). Active Portfolio Management (2nd ed.). McGraw-Hill.