The source files can be found in examples/.
Cross-sectional factor model through a Pipeline
The deep dive built a cross-sectional factor model, fitted two orthogonal uncertainty sets from it and solved a constrained book, by wiring the estimators into a JuMPOptimiser by hand. This page reaches the same weights through a Pipeline, and it is short because almost nothing has to change.
The reason it is short is the answer to the question this page exists to settle: the point-in-time Asset Panel needs no Pipeline Data Slot of its own. The panel rides rd.pnl on the returns carrier, and :returns is a slot the Pipeline already has. So:
- No new slot, and no declaration. A step that needs the panel reads the carrier it was already handed.
- Every step that slices the carrier slices the panel with it, because both go through the same view contract.
- A fold slices the panel before the Pipeline sees the data, through that same contract.
What the Pipeline does add is that the three pieces become three named steps, and the middle one — the uncertainty set — reads the :prior slot the first step wrote. That is the route the hand-wired version hides inside the optimiser.
using PortfolioOptimisers, StableRNGs, Statistics, LinearAlgebra, Dates, PrettyTables, DataFrames, Clarabelnumfmt = (v, i, j) -> begin return isa(v, AbstractFloat) ? round(v; sigdigits = 4) : vend;1. The same panel, and the same specification
The generator and the estimator below are the deep dive's, unchanged and at the same seed, so the book this page solves is the book that page solved. Read §1 and §2 there for what each piece is; here they are just the input.
function synthetic_panel(; T = 500, N = 80, seed = 661_001) rng = StableRNG(seed) industries = ["Energy", "Financials", "Health Care", "Technology"] Kind = length(industries) ind = rand(rng, 1:Kind, N) beta = 1.0 .+ 0.35 .* randn(rng, N) Ltrue = randn(rng, N, 4) alpha = 0.0004 .* randn(rng, N) onehot = Float64[ind[i] == k for i in 1:N, k in 1:Kind] Btrue = hcat(beta, onehot, Ltrue) ftrue = hcat(0.009 .* randn(rng, T), 0.005 .* randn(rng, T, Kind), 0.004 .* randn(rng, T, 4)) ivol = 0.008 .+ 0.012 .* rand(rng, N) X = ftrue * transpose(Btrue) + randn(rng, T, N) .* transpose(ivol) .+ transpose(alpha) logcap = 20.0 .+ 1.4 .* transpose(view(Ltrue, :, 1)) .+ 0.3 .* cumsum(randn(rng, T, N); dims = 1) ./ sqrt(T) mcap = exp.(logcap) shares = mcap ./ 50.0 fields = ["market_cap" => mcap, "book_equity" => mcap .* exp.(-0.7 .+ 0.5 .* transpose(view(Ltrue, :, 2)) .+ 0.05 .* randn(rng, T, N)), "net_income_ttm" => mcap .* (0.05 .+ 0.02 .* transpose(view(Ltrue, :, 3)) .+ 0.004 .* randn(rng, T, N)), "adj_shares_outstanding" => shares, "adj_volume" => shares .* exp.(-4.5 .+ 0.6 .* transpose(view(Ltrue, :, 4)) .+ 0.15 .* randn(rng, T, N)), "signal" => transpose(alpha) .+ 0.0002 .* randn(rng, T, N)] listed = [i <= N ÷ 5 ? rand(rng, 20:120) : 1 for i in 1:N] amsk = [t >= listed[i] for t in 1:T, i in 1:N] for (_, a) in fields a[.!amsk] .= NaN end inputs = [[NumericPanelInput(; name = n, vals = a, alg = ForwardPanelFill(; val = 0.0)) for (n, a) in fields] CategoricalPanelInput(; name = "industry", vals = repeat(reshape(industries[ind], 1, N), T, 1), levels = industries)] days = filter(d -> Dates.dayofweek(d) <= 5, Date(2015, 1, 1):Day(1):(Date(2015, 1, 1) + Day(2 * T + 10)))[1:T] return ReturnsResult(; nx = ["A" * lpad(i, 3, '0') for i in 1:N], X = ifelse.(amsk, X, NaN), ts = days, pnl = asset_panel(inputs; amsk = amsk, emsk = amsk))endrd = synthetic_panel()style(d) = CompositeExposure(; descriptors = [d], family = "style")factors = ["market" => CompositeExposure(; descriptors = [EWMarketBeta()], outlier = nothing, scoring = nothing, family = "market"), "industry" => OneHotExposure(; field = "industry", family = "industry"), "size" => style(LogMarketCap()), "value" => style(BookToPrice()), "earnings_yield" => style(EarningsToPrice()), "liquidity" => style(EWShareTurnover())]pe = CrossSectionalFactorPrior(; factors = factors, families = ["industry" => nothing], neutralise = ["style" => "industry"], wa = BlendedInverseVarianceWeights(; lambda = 0.5), rfe = FixedWeightedReturnForecast(; scores = DescriptorScores(; descriptors = [Passthrough(; field = "signal")], outlier = nothing, scoring = nothing), scale = 1.0), lambda = 1.0, c = 1.0)CrossSectionalFactorPrior
factors ┼ Vector{Pair{String}}: Pair{String}["market" => CompositeExposure
descriptors ┼ 1-element Vector{EWBeta}
│ EWBeta ⋯
weights ┼ nothing
min_coverage ┼ Float64: 0.0
outlier ┼ nothing
scoring ┼ nothing
group ┼ nothing
bw ┼ String: "benchmark_weights"
family ┴ String: "market"
, "industry" => OneHotExposure
field ┼ String: "industry"
family ┴ String: "industry"
, "size" => CompositeExposure
descriptors ┼ 1-element Vector{PanelFieldLog}
│ PanelFieldLog ⋯
weights ┼ nothing
min_coverage ┼ Float64: 0.0
outlier ┼ CrossSectionalWinsoriser
│ low ┼ Float64: 0.01
│ high ┴ Float64: 0.99
scoring ┼ CrossSectionalStandardiser
│ min_group_size ┼ Int64: 8
│ atol ┴ Float64: 1.0e-12
group ┼ nothing
bw ┼ String: "benchmark_weights"
family ┴ String: "style"
, "value" => CompositeExposure
descriptors ┼ 1-element Vector{PanelFieldRatio}
│ PanelFieldRatio ⋯
weights ┼ nothing
min_coverage ┼ Float64: 0.0
outlier ┼ CrossSectionalWinsoriser
│ low ┼ Float64: 0.01
│ high ┴ Float64: 0.99
scoring ┼ CrossSectionalStandardiser
│ min_group_size ┼ Int64: 8
│ atol ┴ Float64: 1.0e-12
group ┼ nothing
bw ┼ String: "benchmark_weights"
family ┴ String: "style"
, "earnings_yield" => CompositeExposure
descriptors ┼ 1-element Vector{PanelFieldRatio}
│ PanelFieldRatio ⋯
weights ┼ nothing
min_coverage ┼ Float64: 0.0
outlier ┼ CrossSectionalWinsoriser
│ low ┼ Float64: 0.01
│ high ┴ Float64: 0.99
scoring ┼ CrossSectionalStandardiser
│ min_group_size ┼ Int64: 8
│ atol ┴ Float64: 1.0e-12
group ┼ nothing
bw ┼ String: "benchmark_weights"
family ┴ String: "style"
, "liquidity" => CompositeExposure
descriptors ┼ 1-element Vector{EWVolumeRatio}
│ EWVolumeRatio ⋯
weights ┼ nothing
min_coverage ┼ Float64: 0.0
outlier ┼ CrossSectionalWinsoriser
│ low ┼ Float64: 0.01
│ high ┴ Float64: 0.99
scoring ┼ CrossSectionalStandardiser
│ min_group_size ┼ Int64: 8
│ atol ┴ Float64: 1.0e-12
group ┼ nothing
bw ┼ String: "benchmark_weights"
family ┴ String: "style"
]
neutralise ┼ Vector{Pair{String, String}}: ["style" => "industry"]
families ┼ Vector{Pair{String, Nothing}}: ["industry" => nothing]
cre ┼ CrossSectionalLinearRegression
│ alg ┼ PseudoInverseFallback()
│ intercept ┴ Bool: false
wa ┼ BlendedInverseVarianceWeights
│ p ┼ Float64: 0.5
│ lambda ┼ Float64: 0.5
│ ratio ┼ Float64: 20.0
│ wins ┴ Tuple{Float64, Float64}: (0.025, 0.975)
pe ┼ EmpiricalPrior
│ ce ┼ PortfolioOptimisersCovariance
│ │ ce ┼ Covariance
│ │ │ me ┼ SimpleExpectedReturns
│ │ │ │ w ┴ nothing
│ │ │ ce ┼ GeneralCovariance
│ │ │ │ ce ┼ SimpleCovariance: SimpleCovariance(true)
│ │ │ │ w ┴ nothing
│ │ │ alg ┼ FullMoment()
│ │ │ w ┴ nothing
│ │ mp ┼ MatrixProcessing
│ │ │ pdm ┼ Posdef
│ │ │ │ alg ┼ UnionAll: NearestCorrelationMatrix.Newton
│ │ │ │ kwargs ┴ @NamedTuple{}: NamedTuple()
│ │ │ dn ┼ nothing
│ │ │ dt ┼ nothing
│ │ │ alg ┼ nothing
│ │ │ order ┴ NTuple{4, Symbol}: (:pdm, :dn, :dt, :alg)
│ me ┼ SimpleExpectedReturns
│ │ w ┴ nothing
│ horizon ┼ nothing
│ fill_limit ┴ nothing
ve ┼ RegimeAdjustedExpWeightedVariance
│ decay ┼ Float64: 0.9828205985452511
│ min_obs ┼ Int64: 40
│ hac_lags ┼ nothing
│ regime_method ┼ FirstMomentRegimeAdjusted
│ │ x ┴ Float64: 0.7978845608028654
│ regime_decay ┼ Float64: 0.9659363289248457
│ regime_min_obs ┼ Int64: 20
│ regime_lohi_mult ┼ nothing
│ min_val ┼ Float64: 1.4901161193847656e-8
│ centred ┼ Bool: false
│ cache ┴ nothing
ce ┼ ExpWeightedCovariance
│ decay ┼ Float64: 0.9828205985452511
│ min_obs ┼ Int64: 40
│ centred ┼ Bool: true
│ cache ┴ nothing
f_mp ┼ MatrixProcessing
│ pdm ┼ Posdef
│ │ alg ┼ UnionAll: NearestCorrelationMatrix.Newton
│ │ kwargs ┴ @NamedTuple{}: NamedTuple()
│ dn ┼ nothing
│ dt ┼ nothing
│ alg ┼ nothing
│ order ┴ NTuple{4, Symbol}: (:pdm, :dn, :dt, :alg)
mp ┼ MatrixProcessing
│ pdm ┼ Posdef
│ │ alg ┼ UnionAll: NearestCorrelationMatrix.Newton
│ │ kwargs ┴ @NamedTuple{}: NamedTuple()
│ dn ┼ nothing
│ dt ┼ nothing
│ alg ┼ nothing
│ order ┴ NTuple{4, Symbol}: (:pdm, :dn, :dt, :alg)
th ┼ Float64: 0.0
bp ┼ Float64: 1.0
mcap ┼ String: "market_cap"
bw ┼ String: "benchmark_weights"
lag ┼ Int64: 1
minra ┼ nothing
rfe ┼ FixedWeightedReturnForecast
│ scores ┼ DescriptorScores
│ │ descriptors ┼ 1-element Vector{Passthrough}
│ │ │ Passthrough ⋯
│ │ neutralise ┼ nothing
│ │ cre ┼ CrossSectionalLinearRegression
│ │ │ alg ┼ PseudoInverseFallback()
│ │ │ intercept ┴ Bool: false
│ │ outlier ┼ nothing
│ │ scoring ┼ nothing
│ │ group ┴ nothing
│ scale ┼ Float64: 1.0
│ weights ┼ nothing
│ min_coverage ┼ Float64: 0.0
│ unit ┴ IdiosyncraticReturnUnit()
lambda ┼ Float64: 1.0
c ┴ Float64: 1.0
The panel is already on the carrier, so it is already in the :returns slot. Nothing below mentions it again.
pretty_table(DataFrame("Carrier" => string(nameof(typeof(rd))), "Panel Fields on rd.pnl" => length(rd.pnl.pf), "Slot it rides" => ":returns"))┌───────────────┬────────────────────────┬───────────────┐
│ Carrier │ Panel Fields on rd.pnl │ Slot it rides │
│ String │ Int64 │ String │
├───────────────┼────────────────────────┼───────────────┤
│ ReturnsResult │ 7 │ :returns │
└───────────────┴────────────────────────┴───────────────┘2. The hand-wired route
This is the deep dive's §5 book: a minimum-risk portfolio under both orthogonal sets and a factor mandate written in a factor name. Everything is a field of one JuMPOptimiser.
The universe the mandate is written against is read off the estimator with cross_sectional_factor_sets, before any fit: it declares the factor axis the fit will produce, one-hot industry levels included, under the ncf key, and one plain group per Factor Family. The one-hot levels are read off the panel, so nothing here hand-types a list that a change of the panel's industry levels would leave stale.
solver = Solver(; name = :clarabel, solver = Clarabel.Optimizer, check_sol = (; allow_local = true, allow_almost = true), settings = Dict("verbose" => false))universe = cross_sectional_factor_sets(pe, rd)mandate = ExposureConstraintEstimator(; lce = LinearConstraintEstimator(; val = "size >= 0.10"), space = FactorSpace())ucs = OrthogonalUncertaintySet(; kappa = 100.0)direct = optimise(MeanRisk(; r = UncertaintySetVariance(; ucs = ucs), obj = MinimumRisk(), opt = JuMPOptimiser(; pe = pe, slv = solver, bgt = 1.0, wb = WeightBounds(; lb = 0.0, ub = 0.1), sets = universe, lcse = mandate, ret = ArithmeticReturn(; ucs = ucs))), rd)MeanRiskResult
jr ┼ JuMPOptimisationResult
│ pa ┼ ProcessedJuMPOptimiserAttributes
│ │ pr ┼ LowOrderPrior
│ │ │ X ┼ 440×80 Matrix{Float64}
│ │ │ o_X ┼ 440×80 Matrix{Float64}
│ │ │ mu ┼ 80-element Vector{Float64}
│ │ │ sigma ┼ 80×80 Matrix{Float64}
│ │ │ chol ┼ 88×80 Matrix{Float64}
│ │ │ w ┼ nothing
│ │ │ ens ┼ nothing
│ │ │ kld ┼ nothing
│ │ │ ow ┼ nothing
│ │ │ rr ┼ CrossSectionalFactorModel
│ │ │ │ M ┼ 80×9 Matrix{Float64}
│ │ │ │ L ┼ 80×8 Matrix{Float64}
│ │ │ │ b ┼ 80-element Vector{Float64}
│ │ │ │ csr ┼ CrossSectionalRegression
│ │ │ │ │ f ┼ 440×8 Matrix{Float64}
│ │ │ │ │ eps ┼ 440×80 Matrix{Float64}
│ │ │ │ │ n ┼ 440-element Vector{Int64}
│ │ │ │ │ b ┴ nothing
│ │ │ │ Ms ┼ Array{Float64, 3}: [NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 0.19740699332896053 0.1115018326159599 0.3736307145742192 0.7436144200359093 -0.040241495525491736 0.4507800925388562 0.4421147786542468 0.6494279598008927 0.8457465397413958 -0.07612269801705311 0.7947219701104539 1.1620083684657474 0.41292432636648396 0.3522605323814725 1.5055399247022372 0.28850692322394583 0.9273672102218911 0.9910469828040471 0.31730763370019244 0.8299525331688494 0.9973911577074821 0.56705489895269 1.1780599563877892 0.05182193332504167 0.6464056809844674 0.3508483621647657 0.025897797049496334 0.5153043419882041 0.6434947752482921 0.9377045394466362 0.9513765317125116 0.13862127390754872 0.570880167967133 -0.054408929787290956 0.26977838241075686 1.0001647933102351 0.196142926256858 0.8512386974173369 0.29787582306121346 1.0572193977758173 0.4530553315713796 0.6715342926465973 0.2877358402838596 0.5124767322367568 1.1370437173886572 0.5189768759222804 0.30823616429051537 -0.0521676135587547 0.3531168050796139 0.5678021838458018 0.677723022162935 0.7267402200593833 1.0019809717769927 0.659145975260893 1.461829011514879 0.9645587902140421 1.834054554142853 0.38199094701719033 0.3730177136891476 1.1603482701496224 0.4851147125806229 0.3827615784288209 0.7667812295925532 0.6636082503015472; 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│ │ │ │ vs ┼ 440×80 Matrix{Float64}
│ │ │ │ esigma ┼ 80-element Vector{Float64}
│ │ │ │ rw ┼ 440×80 Matrix{Float64}
│ │ │ │ bw ┼ 440×80 Matrix{Float64}
│ │ │ │ nf ┼ 9-element Vector{String}
│ │ │ │ fam ┼ 9-element Vector{String}
│ │ │ │ fcb ┼ FactorFamilyBasis
│ │ │ │ │ fnm ┼ Vector{String}: ["industry"]
│ │ │ │ │ fi ┼ 1-element Vector{Vector{Int64}}
│ │ │ │ │ di ┼ Vector{Int64}: [1]
│ │ │ │ │ ratios ┼ 440×3 Matrix{Float64}
│ │ │ │ │ K ┴ Int64: 9
│ │ │ │ lag ┼ Int64: 1
│ │ │ │ rf ┼ FixedWeightedReturnForecastResult
│ │ │ │ │ mu ┼ 80-element Vector{Float64}
│ │ │ │ │ hist ┼ 440×80 Matrix{Float64}
│ │ │ │ │ weights ┴ Vector{Float64}: [1.0]
│ │ │ fpr ┼ LowOrderPrior
│ │ │ │ X ┼ 440×9 Matrix{Float64}
│ │ │ │ o_X ┼ nothing
│ │ │ │ mu ┼ 9-element Vector{Float64}
│ │ │ │ sigma ┼ 9×9 Matrix{Float64}
│ │ │ │ chol ┼ nothing
│ │ │ │ w ┼ nothing
│ │ │ │ ens ┼ nothing
│ │ │ │ kld ┼ nothing
│ │ │ │ ow ┼ nothing
│ │ │ │ rr ┼ nothing
│ │ │ │ fpr ┴ nothing
│ │ wb ┼ WeightBounds
│ │ │ lb ┼ 80-element StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}
│ │ │ ub ┴ 80-element StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}
│ │ lt ┼ nothing
│ │ st ┼ nothing
│ │ lcsr ┼ LinearConstraint
│ │ │ ineq ┼ PartialLinearConstraint
│ │ │ │ A ┼ 1×80 LinearAlgebra.Transpose{Float64, Matrix{Float64}}
│ │ │ │ B ┴ Vector{Float64}: [-0.1]
│ │ │ eq ┴ nothing
│ │ ctr ┼ nothing
│ │ gcardr ┼ nothing
│ │ sgcardr ┼ nothing
│ │ smtx ┼ nothing
│ │ sgmtx ┼ nothing
│ │ slt ┼ nothing
│ │ sst ┼ nothing
│ │ sglt ┼ nothing
│ │ sgst ┼ nothing
│ │ tn ┼ nothing
│ │ fees ┼ nothing
│ │ plr ┼ nothing
│ │ ret ┼ ArithmeticReturn
│ │ │ settings ┼ JuMPReturnsSettings
│ │ │ │ scale ┼ Float64: 1.0
│ │ │ │ lb ┼ nothing
│ │ │ │ rte ┼ Bool: true
│ │ │ │ fee ┼ Bool: true
│ │ │ │ mic ┴ Bool: true
│ │ │ ucs ┼ OrthogonalUncertaintySet
│ │ │ │ q ┼ Float64: 0.05
│ │ │ │ method ┼ ChiSqKUncertaintyAlgorithm()
│ │ │ │ scaling ┼ IdentityScaling()
│ │ │ │ kappa ┼ Float64: 100.0
│ │ │ │ metric ┴ InverseIdiosyncraticVarianceMetric()
│ │ │ mu ┴ 80-element Vector{Float64}
│ │ sca ┼ SumScalariser()
│ │ imsk ┴ nothing
│ retcode ┼ OptimisationSuccess
│ │ res ┴ Dict{Any, Any}: Dict{Any, Any}()
│ sol ┼ JuMPOptimisationSolution
│ │ w ┴ 80-element Vector{Float64}
│ model ┼ A JuMP Model
│ │ ├ solver: Clarabel
│ │ ├ objective_sense: MIN_SENSE
│ │ │ └ objective_function_type: QuadExpr
│ │ ├ num_variables: 91
│ │ ├ num_constraints: 7
│ │ │ ├ AffExpr in MOI.EqualTo{Float64}: 1
│ │ │ ├ Vector{AffExpr} in MOI.Nonnegatives: 1
│ │ │ ├ Vector{AffExpr} in MOI.Nonpositives: 2
│ │ │ └ Vector{AffExpr} in MOI.SecondOrderCone: 3
│ │ └ Names registered in the model
│ │ └ :T, :bgt, :cdev_cucs_soc1, :cucs_variance_risk_1, :dev_cucs1, :gc_soc1, :k, :lcs_ineq_1, :lw, :nbucs_cone_1, :obj_expr, :ret, :ret_1, :ret_vec, :risk, :risk_vec, :sc, :so, :t_cucs1, :t_nbucs_1, :variance_flag, :w, :w_lb, :w_ub, :x_cucs1, :x_nbucs_w_1, :z_cucs1
r ┼ UncertaintySetVariance
│ settings ┼ RiskMeasureSettings
│ │ scale ┼ Float64: 1.0
│ │ ub ┼ nothing
│ │ rke ┴ Bool: true
│ ucs ┼ OrthogonalUncertaintySet
│ │ q ┼ Float64: 0.05
│ │ method ┼ ChiSqKUncertaintyAlgorithm()
│ │ scaling ┼ IdentityScaling()
│ │ kappa ┼ Float64: 100.0
│ │ metric ┴ InverseIdiosyncraticVarianceMetric()
│ sigma ┴ 80×80 Matrix{Float64}
fb ┴ nothing
3. The Pipeline route
Three steps, and each one is a piece the hand-wired optimiser held in a field:
- The prior step is the estimator itself. It writes the
:priorslot. - The uncertainty step is the same
OrthogonalUncertaintySet, wrapped in aPipelineStepbecause a computed uncertainty-set result cannot say on its own which parameter it bounds.target = :bothderives the mean set and the covariance set from a singleucscall — and, crucially, it reads the:priorslot the first step wrote, which is what makes the sets orthogonal to this optimisation's own factor model. - The optimisation step carries no
peand noucsof its own. The Pipeline injects the two slots into it.
pipe = Pipeline(; steps = ("prior" => pe, "uncertainty" => PipelineStep(; est = ucs, writes = :uncertainty, target = :both), "opt" => MeanRisk(; r = UncertaintySetVariance(), obj = MinimumRisk(), opt = JuMPOptimiser(; slv = solver, bgt = 1.0, wb = WeightBounds(; lb = 0.0, ub = 0.1), sets = universe, lcse = mandate, ret = ArithmeticReturn()))))piped = fit(pipe, rd)pretty_table(DataFrame("Step" => collect(piped.names), "Wrote" => ["prior", "uncertainty (mu and sigma)", "opt"], "Result" => [string(nameof(typeof(piped.ctx.prior))), string(nameof(typeof(piped.ctx.uncertainty.mu))) * " / " * string(nameof(typeof(piped.ctx.uncertainty.sigma))), string(nameof(typeof(piped.results[3])))]); title = "What each step put in which slot") What each step put in which slot
┌─────────────┬────────────────────────────┬──────────────────────────────────────────────────────────┐
│ Step │ Wrote │ Result │
│ String │ String │ String │
├─────────────┼────────────────────────────┼──────────────────────────────────────────────────────────┤
│ prior │ prior │ LowOrderPrior │
│ uncertainty │ uncertainty (mu and sigma) │ NormBallUncertaintySet / CompactCovarianceUncertaintySet │
│ opt │ opt │ MeanRiskResult │
└─────────────┴────────────────────────────┴──────────────────────────────────────────────────────────┘4. The two routes agree
Not approximately — the Pipeline runs the same estimators on the same data in the same order, so the weights are identical to the last bit.
pretty_table(DataFrame("max |w_pipeline - w_direct|" => maximum(abs, piped.w - direct.w), "sum(w)" => sum(piped.w), "Names held" => count(>(1e-6), piped.w), "Size exposure" => (transpose(direct.pa.pr.rr.M) * piped.w)[6]); formatters = [numfmt], title = "The Pipeline reaches the deep dive's book") The Pipeline reaches the deep dive's book
┌─────────────────────────────┬─────────┬────────────┬───────────────┐
│ max |w_pipeline - w_direct| │ sum(w) │ Names held │ Size exposure │
│ Float64 │ Float64 │ Int64 │ Float64 │
├─────────────────────────────┼─────────┼────────────┼───────────────┤
│ 0.0 │ 1.0 │ 36 │ 0.1 │
└─────────────────────────────┴─────────┴────────────┴───────────────┘5. And they agree fold by fold
The same holds under cross-validation, which is the claim that matters: a fold slices the carrier — and the panel on it — before either route sees the data, so both refit the prior, both refit the two uncertainty sets against that fold's own factor model, and both re-base the mandate through the loadings the fold actually fitted.
walk = IndexWalkForward(252, 63)folds_direct = cross_val_predict(MeanRisk(; r = UncertaintySetVariance(; ucs = ucs), obj = MinimumRisk(), opt = JuMPOptimiser(; pe = pe, slv = solver, bgt = 1.0, wb = WeightBounds(; lb = 0.0, ub = 0.1), sets = universe, lcse = mandate, ret = ArithmeticReturn(; ucs = ucs))), rd, walk)folds_pipe = cross_val_predict(pipe, rd, walk)pretty_table(DataFrame("Fold" => eachindex(folds_pipe.pred), "max |w_pipeline - w_direct|" => [maximum(abs, folds_pipe.pred[i].res.w - folds_direct.pred[i].res.w) for i in eachindex(folds_pipe.pred)], "Names held" => [count(>(1e-6), p.res.w) for p in folds_pipe.pred]); formatters = [numfmt], title = "Fold by fold, the two routes are the same book")pretty_table(DataFrame("max |predicted returns difference|" => maximum(abs, folds_pipe.mrd.X - folds_direct.mrd.X)); formatters = [numfmt], title = "And so are the returns they predict") Fold by fold, the two routes are the same book
┌───────┬─────────────────────────────┬────────────┐
│ Fold │ max |w_pipeline - w_direct| │ Names held │
│ Int64 │ Float64 │ Int64 │
├───────┼─────────────────────────────┼────────────┤
│ 1 │ 0.0 │ 36 │
│ 2 │ 0.0 │ 37 │
│ 3 │ 0.0 │ 36 │
└───────┴─────────────────────────────┴────────────┘
And so are the returns they predict
┌────────────────────────────────────┐
│ max |predicted returns difference| │
│ Float64 │
├────────────────────────────────────┤
│ 0.0 │
└────────────────────────────────────┘Where to go next
- Cross-sectional factor model, end to end is the long version of every estimator on this page.
- Pipelines covers the slots, the routing and the hyper-parameter search this page only touches.
- Reading a Return Forecast before an optimiser sees it scores the Return Forecast this page's prior carries, before any optimiser acts on it.
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