6 Setting the tactical allocation
By default the game copies the strategic allocation into the tactical allocation. Disabling the automatic tactical allocation on the Investment strategy page opens the tactical grid. There you use your views to tilt the tactical allocation away from the strategic one. The tactical allocation is the one the round is run on; the strategic allocation stays the benchmark. The page estimates the tracking error of your tactical allocation against the benchmark and the projected information ratio from the forecast returns.
6.1 What the model does
The tactical step is a Black–Litterman model. It takes the strategic allocation as the starting point, blends in the views you entered in station 3, and produces a posterior set of expected returns. Station 4 then optimises the tactical allocation on those posterior returns, within the band and the tracking-error budget. The point of the model is that the tilt is driven by your views and not by the optimiser chasing noise in the expected-return estimates.
6.1.1 The prior: the strategic allocation, reverse-optimised
The model starts from the strategic allocation. Rather than asking “what returns do I expect?”, it asks the reverse question: what expected returns would make the strategic allocation optimal? That is the prior, and it is the same one introduced in the previous chapter:
\[ \Pi = \gamma \Sigma w \]
where \(w\) is the strategic allocation, \(\Sigma\) is the covariance matrix, and \(\gamma\) is the client’s risk aversion. The prior encodes both the capital market assumptions and the client’s risk tolerance. If you have no views, the posterior equals the prior, and the tactical allocation equals the strategic one.
6.1.2 The views
A view is a statement about expected returns, expressed in one of two forms:
- Absolute: “US equities earn 12 % over cash”. In the model this is a row of the view matrix \(P\) that picks out US equities, with the view’s expected return in the corresponding row of \(Q\).
- Relative: “euro-area equities beat Swiss equities by 2 points”. This is a row of \(P\) with \(+1\) on euro-area equities and \(-1\) on Swiss equities, and the 2 points in \(Q\). A relative view does not move both positions the same way: it moves the long side up and the short side down, in proportion to how precise the view is.
Each view has a confidence, which enters the model through the matrix \(\Omega\). A high-confidence view has a small entry in \(\Omega\) (low uncertainty); a low-confidence view has a large entry. In station 3 the views are treated as independent, so \(\Omega\) is diagonal and each view’s confidence affects only that view’s pull on the posterior.
6.1.3 The posterior
The posterior expected returns are the precision-weighted average of the prior and the views:
\[ E(R) = \underbrace{\left[(\tau\Sigma)^{-1} + P^T\Omega^{-1}P\right]^{-1}}_{\text{combined precision}} \underbrace{\left[(\tau\Sigma)^{-1}\Pi + P^T\Omega^{-1}Q\right]}_{\text{precision-weighted sum}} \]
Every symbol is one of four things: an input you supply, a parameter you set, a matrix the station builds from your views, or a quantity the model computes. The table lists them all.
| Symbol | What it is | In the station |
|---|---|---|
| \(E(R)\) | The posterior expected excess returns, one per position. | The output. These are the returns station 4 optimises on. |
| \(\Pi\) | The prior expected excess returns, one per position. | Computed from the fixed SAA: \(\Pi = \gamma\Sigma w\). |
| \(\Sigma\) | The covariance matrix of the positions. | From station 2’s sample covariance. |
| \(\tau\) | A scalar that scales the uncertainty in the prior. | An input. Default 0.05. |
| \(P\) | The view matrix. Each row is one view: \(+1\) on the position the view is “for”, \(-1\) on the position it is “against” (or a single \(+1\) for an absolute view). | Built by the station from the views you entered. |
| \(Q\) | The view returns, one per view: the expected return the view asserts, in annual terms. | Built by the station from the views you entered. |
| \(\Omega\) | The view covariance matrix, diagonal when views are independent. Each diagonal entry is the variance of the corresponding view. | Built by the station from the confidence you set on each view. |
| \((\tau\Sigma)^{-1}\) | The precision of the prior: how strongly the model believes the strategic allocation. | Computed. |
| \(P^T\Omega^{-1}P\) | The precision of the views: how strongly the model believes your views, in the directions they point. | Computed. |
With the symbols in hand, the formula says one thing: the posterior is a weighted average of the prior \(\Pi\) and the views \(Q\), with the weights set by their relative precision. If the views are very precise relative to the prior, the posterior is pulled close to \(Q\). If the prior is very precise, the posterior stays close to \(\Pi\). If there are no views, \(P\) and \(Q\) are empty, \(P^T\Omega^{-1}P = 0\), and the posterior equals the prior.
What \(\tau\) and \(\Omega\) do. \(\tau\) scales the uncertainty in the prior. A larger \(\tau\) means the model is less confident in the strategic allocation, so the views receive relatively more weight; a smaller \(\tau\) anchors the posterior more firmly to the strategic allocation. The conventional choice, and the default in station 3, is \(\tau = 0.05\). Changing \(\tau\) changes every view’s influence at once; it is not a per-view setting. \(\Omega\) encodes the confidence in each view. A smaller entry means the model treats the view as more precise, so the posterior moves further; a larger entry means the view is treated as noisy, so the posterior moves less. Together, \(\tau\) and \(\Omega\) determine how far the tactical allocation tilts away from the strategic one.
6.1.4 Why the tactical step differs from the strategic one
The Black–Litterman posterior is used in station 4 with three modifications relative to station 2:
- No home rule. The home rule defines the benchmark, so keeping it in the tactical step would force the equity book to grow or shrink in fixed regional proportions, and a view on one market could not act. The client’s other limits stay, the commodity floor included.
- The sample covariance. Risk is measured with the covariance of station 2, not the posterior covariance. Using the posterior covariance would raise measured risk as soon as any view is entered, and push every fund from equities into bonds regardless of what the view said.
- Band and tracking-error budget. The maximum deviation per position (default ± 5 points) and the tracking-error budget (default 2 % a year) limit how far the tactical allocation can stray from the benchmark. If the optimum exceeds the budget, the deviation is scaled down to it.
With these in place, every deviation from the strategic allocation is traceable to a view. A view that agrees with the prior leaves the tactical allocation at the strategic one; a view that disagrees produces a tilt, and the size of the tilt is set by the confidence and by the band and budget.
6.2 Station 4 of the app
Inputs:
- Strategic allocation to work on: one of the SAAs fixed in station 2.
- Maximum deviation per position: a band of ± this share around each strategic weight; default 0.05, five points. The long-only floor stays in force.
- Tracking-error budget, percent a year; default 2, and 0 means none. If the optimum exceeds the budget, the deviation is scaled down to it.
Press Optimise the tactical allocation of every fund. For each fixed SAA the station maximises the utility of station 2, with the client’s γ and limits, on the posterior expected returns of station 3, within the band.
Without views the tactical allocation equals the SAA. A view that agrees with the prior leaves it there too. So every deviation comes from a view. Output: the strategic matrix, the tactical matrix, their difference in points, the tracking error, the expected active return under the posterior and under the prior, and the in-sample comparison. A negative expected active return under the posterior is flagged.
The summary table applies your views to every fixed SAA and shows the tilt per asset class: the same view produces a different tilt per client.
6.3 Worked example
View: US equities earn 12 % over cash, confidence 50 % (Chapter 5). Band ± 5 points and tracking-error budget 2 %, the defaults; the budget does not bind.
The Hartleys (γ = 8, home UK), deviation of the tactical from the strategic allocation in points:
| USD | GBP | EUR | CHF | JPY | Total | |
|---|---|---|---|---|---|---|
| Government bonds | −5.0 | 0 | 0 | 0 | 0 | −5.0 |
| Corporate bonds | −4.0 | +1.0 | 0 | 0 | 0 | −3.0 |
| Equities | +5.0 | +2.0 | +0.5 | +0.5 | 0 | +8.0 |
| Commodities | 0 | 0 | 0 | 0 | 0 | 0 |
Tracking error 1.3 % a year, expected active return +0.7 % under the posterior. US equities rise by the full band of 5 points: the band, not the view, decides how much. The rest of the view goes to the markets that move with US equities, whose posterior rose too (Chapter 5): the UK gains 2 points, the euro area and Switzerland half a point each. The tilt is funded from US government bonds, again the full band, and US corporate bonds.
The equity book no longer keeps the benchmark’s home share: the UK falls from 49 to 46 % of it. That is intended. The home rule defines the benchmark, not the bet.
The Keller trust (γ = 5, home euro area), same view: equities +10 points (US +5, euro area +2.5, UK +2, Switzerland +0.5), government bonds −5 and corporate bonds −5, both in dollars; tracking error 1.5 %, expected active return +1.0 %. Same view, a larger tilt: with a lower γ the Kellers accept more risk for a point of expected return.
With a tracking-error budget of 1 % both tilts are scaled down: the Hartleys to +6.4 points of equity, the Kellers to +6.5 (the summary table, before rounding).
6.4 Two cautions
An absolute view on a foreign-currency position is also a currency view. The game’s data are in dollars, unhedged, and all positions in one currency share that currency. Take the view “euro-area government bonds earn 4 % over cash”, confidence 50 %. For the Hartleys the station moves 5 points into euro-area government bonds and 5 more into euro-area corporate bonds, on which you had no view, funded from US bonds. That is 10 points of euro against the dollar; tracking error 1.0 %. For a view on foreign rates, state it relative to US government bonds: “euro-area government bonds beat US government bonds by 3.5 points” (the prior spread is 1.8). That says what the bet is. It does not remove the euro: here the station builds the same 10-point euro position. Read the currency totals of the deviation matrix before you enter it.
The client’s commodity floor stays a floor. A negative view cannot take commodities below it. Give the Hartleys the view “commodities earn 0 % over cash” (prior 2.6 %): commodities stay at 5 %, and the station rearranges the rest instead, government bonds +4 points, corporate bonds −3.5, equities −0.5. The expected active return is −0.1 %, and the app flags it: the tilt buys lower risk, not return. If the floor blocks your view, leave the fund at its SAA.
6.5 Entering it in the game
- Investment strategy → disable Automatic tactical allocation for the fund.
- Type the tactical matrix (currency × asset class) from station 4.
- Read the game’s tracking-error estimate and projected information ratio. The estimate will not equal the app’s exactly (the game uses its own forecast returns and a shorter history), but the order of magnitude must agree. A projected information ratio below zero means the game’s forecasts disagree with your views; decide which you believe.
- Repeat for every fund with the same views.
6.6 Rules of thumb
- Tracking error 1 to 3 % a year is a normal tactical budget for a fund with a fixed benchmark; conservative clients at the low end.
- A tilt into a foreign bond is a currency bet. The attribution will show it as a currency effect. Make it only if it is the bet you mean. Cash is outside the benchmark: parking part of the fund in money market is an under-investment against every class, and the information ratio will say so.
- A negative expected active return is a warning. Use fewer views, relative rather than absolute, or a narrower band, or leave the fund at its SAA.
- Stay close to what the card describes. The band in station 4 is your choice, not a client limit, and the tactical step does not impose the home rule. A tactical matrix far from the guidance bands costs clients.
- Re-enter every round. Between rounds the game moves holdings with returns and flows; the tactical grid you entered last round is not where the fund is now.
- No views, no tilt. If the outlook gives you nothing you believe, leave the automatic tactical allocation on. Zero tracking error is a decision, not a failure.
6.7 Deliverable of this step
The tactical matrix per fund in the game, the tracking error and projected information ratio noted beside the views in the team forum.