A finished FIN-451 Topic 2 mean-variance allocation memo example, optimizing three asset classes at a 10 percent volatility ceiling, showing the weights swing on one input and adopting sturdier policy weights. Searches like "fin 451 topic 2 assignment example", "fin451 topic 2 sample" and "fin-451 topic 2 example" land here.
What a finished FIN-451 Topic 2 mean-variance allocation memo looks like
Illustrative inputs open the finished memo: domestic stocks expected at 7.0 percent with 16 percent volatility, international stocks at 7.5 and 18, bonds at 3.5 and 5, a correlation of 0.8 between the two equity classes and 0.1 between either one and bonds. Maximizing expected return at 10 percent volatility with no short positions, the optimizer returns 27 percent domestic, 32 international and 41 bonds, for an expected 5.73 percent. Lowering the international estimate to 7.0 moves the answer to 41.5, 19 and 39.5. Lowering it to 6.5 removes international entirely, at 60 and 40. The memo then tests fixed policy weights of 35, 25 and 40. They match the optimizer at the base inputs and trail it by about an eighth of a point in the worst case, while never changing.
How a FIN-451 Topic 2 example is structured
Four parts carry the memo: inputs, the optimization, a stress test of the inputs and the policy adopted. The inputs table gives each asset class its expected return, volatility and correlations, with a line on where each estimate comes from and how wide its error is likely to be. The optimization section states the objective, highest expected return at the 10 percent ceiling the investor's policy statement sets, along with the no-shorting constraint. The stress section reruns the optimizer with the international estimate moved down in half-point steps and tables the weights beside each run. A passage explains the mechanism: two highly correlated equity classes are near substitutes, so a small edge in one estimate tips the optimizer toward it. The policy section compares fixed weights with each optimized set on return and risk. The memo closes by stating the range within which each weight may drift.
Inputs labeled with their uncertainty
Every expected return carries a note on its source and its likely error, since the memo's argument turns on how little a half-point difference can be trusted.
An optimizer run at one ceiling
Highest expected return at 10 percent volatility, with no short positions allowed, gives 27 percent domestic stocks, 32 international and 41 bonds.
A half-point input, a thirteen-point swing
Cutting the international estimate from 7.5 to 7.0 percent drops its weight from 32 to 19, a change far larger than the change in the input.
Near substitutes explain the swing
With a correlation of 0.8 the two equity classes do almost the same job, so the optimizer treats a tiny edge in either estimate as decisive.
Policy weights that hold across inputs
Fixed weights of 35, 25 and 40 percent match the optimizer at base inputs and give up about an eighth of a point when the estimates move.
Allocation credited for the right reason
The memo cites the Brinson, Hood and Beebower study as evidence about the variation of returns over time, not as a claim about their level.
Where marks go in FIN-451 Topic 2
Memos that print the optimizer's weights and adopt them lose the most, since those weights are the least reliable feature of the analysis rather than a finding. A paper that runs one set of estimates cannot show whether the recommended mix survives a plausible error in any of them. Presenting expected returns to two decimals, with no word on where they came from, claims a precision the forecasts do not have. Citing the well-known allocation study as proof that allocation decides most of a portfolio's return misreads it, because its finding concerned the variation of returns over time. Corner solutions with an asset class at zero, left unremarked, usually signal an input problem rather than a preference. Papers that reject optimization outright, rather than constraining it, discard the discipline Markowitz supplied along with the fragility.
Get a FIN-451 Topic 2 example written to your instructions
Send the FIN-451 Topic 2 instructions and your classroom rubric, with the capital market assumptions or data your section supplies. We write a custom example to them, with the optimization run and stated, its inputs stressed one at a time, the weight swings tabled and a policy mix defended against the optimizer's output, in 24 to 48 hours. The first one is free.
FIN-451 Topic 2 questions, answered
What did Markowitz contribute to asset allocation?
The idea that a portfolio should be judged as a whole, by its expected return and its variance, with each holding valued for how it moves with the others rather than for its own risk alone. Mean-variance optimization follows from that: for a chosen level of risk, find the mix with the highest expected return. The framework remains the starting point for allocation work, even where its outputs are constrained.
Why do optimized weights change so much?
Because the optimizer treats its inputs as exact. When two assets are close substitutes, a small difference in expected return is enough to shift a large weight from one to the other, and expected returns are the hardest inputs to estimate. Richard Michaud's critique describes optimizers as error maximizers for this reason, overweighting whatever estimate happens to be too high. Constraints, ranges and blended estimates are the usual responses.
Is the 35, 25, 40 mix a recommendation for my portfolio?
No. The asset classes, returns, volatilities and the 10 percent ceiling are illustrative inputs, picked to expose how much an optimizer's answer depends on estimates. A real allocation depends on the investor's own objectives, constraints, accounts and costs, and on assumptions a professional would source and date. The memo demonstrates FIN-451 reasoning about optimization and its limits, and it gives no investment advice to anyone.