Portfolio Value Optimization: Allocate Budget Across Assets with Risk Constraints. LeakCode

Question Details

Problem

You have a budget B (integer units) to allocate across n assets. Asset i has a function value[i][k] representing the value gained by investing k units in it (non-decreasing, not necessarily linear). You also have a risk score risk[i][k] for each investment level, and a total risk cap R. Maximize total portfolio value without exceeding B or R.

python
def max_portfolio_value(
    value: list[list[int]],   # value[i][k]: value of investing k units in asset i
    risk: list[list[int]],    # risk[i][k]: risk of investing k units in asset i
    B: int,
    R: int
) -> int:
    pass

Example


**Input**:
value = [[0,3,5,6], [0,4,6,7], [0,2,4,8]]
risk  = [[0,1,2,4], [0,2,3,5], [0,1,3,6]]
B = 4, R = 6

**Output**: 11
# Allocate 1 to asset 0 (v=3,r=1), 1 to asset 1 (v=4,r=2), 2 to asset 2 (v=4,r=3)
# total value=11, total risk=6, total budget=4

Follow-ups

What is the time complexity of your DP solution? Can you improve space usage?
How would you handle fractional allocations (continuous version)?
What changes if risk is a covariance matrix rather than per-asset scalars?

Full Details

Problem

You have a budget B (integer units) to allocate across n assets. Asset i has a function value[i][k] representing the value gained by investing k units in it (non-decreasing, not necessarily linear). You also have a risk score risk[i][k] for each investment level, and a total risk cap R. Maximize total portfolio value without exceeding B or R.

python
def max_portfolio_value(
    value: list[list[int]],   # value[i][k]: value of investing k units in asset i
    risk: list[list[int]],    # risk[i][k]: risk of investing k units in asset i
    B: int,
    R: int
) -> int:
    pass

Example


**Input**:
value = [[0,3,5,6], [0,4,6,7], [0,2,4,8]]
risk  = [[0,1,2,4], [0,2,3,5], [0,1,3,6]]
B = 4, R = 6

**Output**: 11
# Allocate 1 to asset 0 (v=3,r=1), 1 to asset 1 (v=4,r=2), 2 to asset 2 (v=4,r=3)
# total value=11, total risk=6, total budget=4

Follow-ups

What is the time complexity of your DP solution? Can you improve space usage?
How would you handle fractional allocations (continuous version)?
What changes if risk is a covariance matrix rather than per-asset scalars?

Free preview. Unlock all questions →

Topics

Coding Onsite Phone

More from Robinhood

Reddit Robinhood SWE Interview Reddit Robinhood mobile SWE interview experience 1p3a Robinhood Frontend Engineering Onsite Interview Experience and Challenges 1p3a Robinhood Fulltime SDE Technical Phone Screen Interview Experience 1p3a Robinhood software engineer coding interview on fractional shares inventory