Topic 1 · In-Class Case
Riverside Memorial
A 3-asset portfolio optimization case for a hospital endowment. Apply Mean-Variance Efficiency theory with real constraints to find the optimal allocation.
Asset Classes
3
Risk-Free Rate
3.0%
Policy Portfolio SR
—
Case Background
The Riverside Memorial Endowment
Riverside Memorial Hospital has an endowment fund that needs to be invested across three asset classes: Stocks, Bonds, and Real Estate. The current Policy Portfolio allocates 40% to stocks, 30% to bonds, and 30% to real estate. The case asks whether this allocation is efficient — and if not, what the optimal allocation should be.
Stocks
Expected Return: 10.0%
Std Deviation: 16.0%
Bonds
Expected Return: 5.5%
Std Deviation: 7.0%
Real Estate
Expected Return: 9.0%
Std Deviation: 14.0%
Correlation Structure
0.35
0.20
0.20
Optimal Portfolios
Policy vs. MVE vs. GMV
Using the Excel Solver (replicated below), three key portfolios emerge. The MVE (Tangency) Portfolio maximizes the Sharpe ratio. The GMV Portfolio minimizes risk. The Policy Portfoliois the current allocation — which may or may not lie on the efficient frontier.
| Portfolio | Stocks | Bonds | Real Estate | E[r] | σ | SR |
|---|---|---|---|---|---|---|
| MVE (Tangency) | 27.8% | 38.0% | 34.2% | 7.95% | 8.47% | 0.584 |
| GMV Portfolio | 2.2% | 83.9% | 13.9% | 6.08% | 6.69% | 0.461 |
| Policy Portfolio | 40.0% | 30.0% | 30.0% | 8.35% | 10.88% | 0.491 |
- Policy Portfolio
- MVE Portfolio
- GMV Portfolio
Constraint Scenarios
Effect of Weight Constraints
The Excel workbook models two constraint scenarios. Real-world endowments cannot short-sell assets or take extreme positions, so constraints always push the efficient frontier inward — reducing the achievable Sharpe ratio.
No Shorting
Weights ≥ 0 for all assets
Most conservative. Prevents negative allocations.
E[r]
7.95%
σ
8.47%
SR
0.584
Near Policy Portfolio
Stocks: 20–60%, Bonds: 10–50%, RE: 10–50%
Constrained around the current policy portfolio.
E[r]
7.60%
σ
8.20%
SR
0.561
Interactive Tool
Efficient Frontier Calculator
The calculator below is pre-loaded with the Riverside Memorial data. Adjust the sliders to see how changes in expected returns, risk, or correlations shift the efficient frontier. Switch to "Conservative Mix" or "Aggressive Growth" presets to compare different endowment philosophies.
Efficient Frontier Calculator
Adjust inputs to see the efficient frontier update in real time
Risk-Free Rate
Expected Returns
Standard Deviations (Risk)
Correlations
Risk–Return Space
- Efficient Frontier
MVE Portfolio
E[r]: 7.95%
σ: 8.47%
Stocks: 27.8%
Bonds: 38.0%
Real Estate: 34.2%
GMV Portfolio
E[r]: 6.08%
σ: 6.68%
Stocks: 2.2%
Bonds: 83.9%
Real Estate: 13.9%
Policy Portfolio
E[r]: 8.35%
σ: 9.31%
Stocks: 40.0%
Bonds: 30.0%
Real Estate: 30.0%
MVE Sharpe Ratio
0.585
In-Class Discussion
Key Questions to Prepare
Original Excel Workbook
Run the Solver yourself to explore all constraint scenarios