Keep the comparison consistent
The first question holds estimates and the objective fixed. The reallocation example specifies only sector weights. Read those conditions before making a claim about an optimum or a performance measure.
Explain the mechanism
For a set restriction, ask whether the new portfolios were already available before the rule. For mechanical reallocation, calculate the new exposures. Performance claims require more than an eligibility rule or weights that sum to one.
Try the questions
Expected returns, risk estimates and the objective are unchanged. What follows from adding an exclusion constraint to the optimizer?
- A.
The optimum cannot improve solely because previously available portfolios are excluded.
- B.
The exclusion guarantees a higher Sharpe ratio.
- C.
All retained sector weights must remain equal to their starting weights.
Answer and explanation
Answer: A
The new feasible set is a subset of the old one. Restricting it cannot improve the optimum of the same objective under unchanged inputs.
- A
Any newly allowed optimal portfolio was already available before the exclusion.
- B
A feasible-set restriction does not supply a performance guarantee.
- C
An exclusion can require reallocation; remaining weights need not be unchanged.
Weights are 20% Energy, 40% Industrials and 40% Financials. Energy is excluded and its weight is reallocated pro rata. What are the new retained weights?
- A.
40% and 40%.
- B.
50% and 50%.
- C.
60% and 40%.
Answer and explanation
Answer: B
Each retained weight is 40% divided by the retained total of 80%, or 50%.
- A
These weights would total only 80% after the exclusion.
- B
This preserves their relative proportions while restoring the total to 100%.
- C
This does not preserve the original equal proportions of the retained sectors.
Only the weights in the previous question are supplied. Which additional conclusion is justified?
- A.
The portfolio volatility must decrease.
- B.
Its Sharpe ratio must increase.
- C.
Its sector exposure changed relative to the original allocation.
Answer and explanation
Answer: C
The allocation changed, but numerical risk and performance conclusions require more information.
- A
Volatility also depends on volatilities and covariances, which are not supplied.
- B
Expected return, risk and the risk-free-rate convention are not supplied.
- C
The two retained weights rose from 40% to 50%, while Energy fell to zero.