Portfolio variance

easyMathsacceptance —~10 min

Implement portfolio_variance(w, cov) — wᵀ·Σ·w for a weight vector w and a covariance matrix cov given as a list of rows: the double sum over i, j of w[i]·w[j]·cov[i][j].

Diversification lives entirely in the off-diagonal terms; a risk model that only adds up variances has no idea two positions can hedge each other. Return the variance rounded to 6 decimal places.

example 1

input

w=[0.6, 0.4], cov=[[0.04, 0.0], [0.0, 0.09]]

output

0.0288

example 2

input

w=[0.6, 0.4], cov=[[0.04, 0.012], [0.012, 0.09]]

output

0.03456

note

Same weights and variances, now with a positive covariance — the answer must rise.

constraints

1 ≤ n ≤ 20
cov is symmetric

teacher · 2 hints · the first is free

●solution.py· utf-8 · spaces:4

def portfolio_variance(w: list, cov: list) -> float:
    """w^T Σ w, rounded to 6 dp."""
    total = 0.0
    for i in range(len(w)):
        # TODO: the cross terms w[i]·w[j]·cov[i][j] for j != i are missing
        total += w[i] * w[i] * cov[i][i]
    return round(total, 6)

ln 1, col 1tab indent · esc leave editor

python 3.13 · pyodide

+ 6 hidden on submit

input · keyword arguments to portfolio_variance()

w=[0.6, 0.4], cov=[[0.04, 0.0], [0.0, 0.09]]

expected

0.0288

the judge calls portfolio_variance() with exactly these inputs · outputs are compared to 6 decimal places

● standing bypython 3.13 in your browser · pyodide 0.28.3 · judged on the server to 6 dp⌘↵ run · ⌘⇧↵ submit

paper only · educational · not advice