R solve.QP 跟踪误差最小化约束不一致

Question

我正在努力 Solve.QP 以获得最小化跟踪错误的解决方案。我有一个由 6 个资产组成的基准（asset_a 到 asset_f）。对于我的投资组合，我有上限和下限（我不能在 asset_f 中拥有头寸）。还给出了 cov 矩阵。我想获得 6 种资产的投资组合权重，以最小化跟踪误差与基准（asset_f 中的位置等于零）。

基准：

asset_a: 0.3
asset_b: 0.3
asset_c: 0.1
asset_d: 0.1
asset_e: 0.1
asset_f: 0.1

下界：

asset_a: 0.166
asset_b: 0.133
asset_c: 0.037
asset_d: 0.035
asset_e: 0.039
asset_f: 0

上限：

asset_a: 1
asset_b: 1
asset_c: 1
asset_d: 1
asset_e: 1
asset_f: 0

基准权重和界限：

test.benchmark_weights = c(0.3, 0.3, 0.1, 0.1, 0.1, 0.1)
test.lowerbound = c(0.166, 0.133, 0.037, 0.035, 0.039,0)
test.upperbound = c(1, 1, 1, 1, 1, 0)

cov 矩阵 (test.Dmat):

test.dmat = matrix(c(0.0119127162,  0.010862842,    0.010266683,    0.0009550136,   0.008242322,    0.00964462, 0.0108628421,   0.010603072,    0.009872992,    0.0011019412,   0.007422522,    0.0092528873,   0.0102666826,   0.009872992,    0.010487808,    0.0012107665,   0.006489204,    0.0096216627,   0.0009550136,   0.001101941,    0.001210766,    0.0115527788,   0.001181745,    0.0008387247,   0.0082423222,   0.007422522,    0.006489204,    0.0011817453,   0.012920482,    0.005973886,    0.00964462, 0.009252887,    0.009621663,    0.0008387247,   0.005973886,    0.0089904809), nrow=6, ncol=6)

dvec (test.dvec):

test.dvec = matrix(c(0, 0,  0,  0,  0,  0), nrow=6, ncol=1)

Amat 约束矩阵 (test.Amat):

test.amat = matrix(c(1,1,1,1,1,1, 1,1,1,1,1,0, -1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-1,0,0,0, 0,0,0,-1,0,0, 0,0,0,0,-1,0, 0,0,0,0,0,-1, 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,1,0,0,0, 0,0,0,1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,0, -1,0,0,0,0,0, 0,-1,0,0,0,0, 0,0,-1,0,0,0, 0,0,0,-1,0,0, 0,0,0,0,-1,0, 0,0,0,0,0,0), nrow=6, ncol=20)

bvec (test.bvec)

test.bvec =cbind(0, 1, t(test.benchmark_weights), t(test.lowerbound), -t(test.upperbound)) %>% as.matrix()

然后运行求解器

solve.QP(as.matrix(test.Dmat), test.dvec, test.Amat, test.bvec)

给我

约束不一致，无解！

Answer 1

您的 Amat 和 bvec 似乎有问题，即您不必传入等于 1 的前 5 个资产的权重总和等于 1 的 6 个资产的权重总和1 和基准权重不是约束，但边界是：

library(quadprog)
N = 6L
test.dvec = rep(0, N)
test.amat = cbind(
    rep(1, N),
    diag(1, N),
    diag(-1, N))
test.bvec = c(1, test.lowerbound, -test.upperbound) 

res = solve.QP(test.dmat, test.dvec, test.amat, test.bvec, meq=1L)
round(res$solution, 2)
#[1] 0.17 0.13 0.10 0.44 0.17 0.00

R solve.QP 跟踪误差最小化约束不一致

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