Practice question · Sort into groups
Sort each investment-menu situation by its linear-algebra diagnosis.
Groups: Adds a new dimension · Redundant (dependent)
- Real estate exposure your portfolio cannot replicate
- A commodity fund uncorrelated with your stock/bond mix
- An "aggressive" fund = 80% fund A + 20% fund B
- A leveraged fund that is 2× an index you already hold
- Fund C is always exactly 50% A plus 50% B
Hints
- Diversification requires a genuinely new direction.
- A relabelled or rescaled version of what you already hold adds nothing.
Show the answer
Adds a new dimension: A commodity fund uncorrelated with your stock/bond mix, Real estate exposure your portfolio cannot replicate
Redundant (dependent): Fund C is always exactly 50% A plus 50% B, A leveraged fund that is 2× an index you already hold, An "aggressive" fund = 80% fund A + 20% fund B
Why
A product diversifies only if it is linearly independent of what you hold. Leverage and remixes are old vectors with new labels, span unchanged.
Practise Vector Spaces
The app has 6 more questions on this lesson, and keeps your place in the course. Business I is free to start.
More questions on Vector Spaces
- Order the reasoning to find the dimension of the space spanned by a set of vectors.
- Match each concept to its definition.
- Why must every basis of ℝ³ have exactly three vectors, never two, never four?
- An analyst tracks 12 macroeconomic series and finds they are all built from 3 underlying factors. What is…
- Which statements about span and independence are true?
- (2,2) and (3,3) together span only the line y = x, while (1,0) and (0,1) span the whole plane. What does that…
- Four vectors in ℝ³ can be linearly independent.