Log vs simple returns

easyMathsacceptance —~10 min

Implement returns(prices, kind) — the per-period returns of a price series: kind = "simple" gives p_t / p_{t-1} - 1, kind = "log" gives ln(p_t / p_{t-1}). The list is one shorter than the prices.

Log returns add across time; simple returns add across a portfolio. Confusing the two is how a backtest gains a percent a year out of thin air. Return the values rounded to 4 decimal places.

example 1

input

prices=[100.0, 101.0, 99.0, 102.0], kind="simple"

output

[0.01, -0.0198, 0.0303]

example 2

input

prices=[100.0, 101.0, 99.0, 102.0], kind="log"

output

[0.01, -0.02, 0.0299]

constraints

2 ≤ len(prices) ≤ 10_000
every price > 0
kind ∈ {simple, log}

teacher · 2 hints · the first is free

●solution.py· utf-8 · spaces:4

from math import log


def returns(prices: list, kind: str) -> list:
    """Simple or log returns, one per step, rounded to 4 dp."""
    out = []
    for a, b in zip(prices[:-1], prices[1:]):
        ratio = b / a
        # TODO: kind == "log" is not handled — every call returns simple returns
        out.append(round(ratio - 1, 4))
    return out

ln 1, col 1tab indent · esc leave editor

python 3.13 · pyodide

+ 6 hidden on submit

input · keyword arguments to returns()

prices=[100.0, 101.0, 99.0, 102.0], kind="simple"

expected

[0.01, -0.0198, 0.0303]

the judge calls returns() 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