GF570 Unit 4 Foundation Asset Allocation Model Example

Three Mixes, None Enough: A Unit 4 Asset Allocation Model That Tests Candidates Against the Policy

[Student Name]

Purdue University Global

GF570: Portfolio Management

Unit 4 Asset Allocation Model

[Instructor Name]

[Date]

The foundation and every capital market assumption are composite and illustrative; the articles cited are real.

Exhibit 1: Capital Market Assumptions

Expected annual returns and volatilities for the seven asset classes in the policy:

1. U.S. equity: 8.0 percent return, 16.0 percent volatility.

2. Non-U.S. equity: 8.6 percent, 18.0 percent.

3. Core bonds: 4.6 percent, 5.5 percent.

4. Inflation-linked bonds: 4.3 percent, 6.0 percent.

5. Real assets: 7.0 percent, 15.0 percent.

6. Private equity: 11.0 percent, 24.0 percent.

7. Cash: 3.5 percent, 1.0 percent.

These are arithmetic expectations over ten years, drawn from published long-term surveys and adjusted for current bond yields.

Exhibit 2: Correlations

U.S. and non-U.S. equity: 0.80. Equities with core bonds: 0.05 to 0.10. Equities with real assets: 0.60 to 0.65. Equities with private equity: 0.70 to 0.75. Core bonds with inflation-linked bonds: 0.75. Real assets with private equity: 0.55. Cash is assumed uncorrelated with everything.

Exhibit 3: The Three Candidates

Mix A, 60 percent growth assets. U.S. equity 30, non-U.S. 18, core bonds 28, inflation-linked 8, real assets 6, private equity 6, cash 4. Expected return 6.80 percent; volatility 9.82 percent.

Mix B, 73 percent growth assets. U.S. equity 32, non-U.S. 23, core bonds 16, inflation-linked 6, real assets 6, private equity 12, cash 5. Expected return 7.45 percent; volatility 11.95 percent.

Mix C, 85 percent growth assets. U.S. equity 36, non-U.S. 26, core bonds 9, inflation-linked 3, real assets 8, private equity 15, cash 3. Expected return 7.97 percent; volatility 13.79 percent, above the policy ceiling.

Step 1: Converting to Compound Returns

The return objective is a compound rate, so arithmetic expectations must be reduced by roughly half the variance. Mix A compounds at about 6.32 percent, Mix B at about 6.73 percent and Mix C at about 7.02 percent. None reaches 7.95 percent.

Step 2: Checking the Loss Limit

The fifth-percentile one-year result, expected return less 1.645 times volatility, is about negative 9.4 percent for A, negative 12.2 percent for B and negative 14.7 percent for C. All three pass the 15 percent loss limit, though C only narrowly.

Step 3: Where Correlation Does the Work

If Mix B's assets moved together perfectly, its volatility would equal the weighted average of their volatilities, about 14.3 percent. Its actual expected volatility is 11.95 percent. Imperfect correlations, chiefly between stocks and bonds, remove more than two points of risk. That gap is the reason Mix B fits inside the ceiling at all (Markowitz, 1952).

Even the most aggressive mix the policy allows compounds about a point short of 7.95 percent, so the trustees face a choice the model cannot make for them: accept a likely slow erosion of real value, raise the risk ceiling, or find a way to spend less.

Step 4: Probability of Meeting the Objective

Treating ten-year compound returns as roughly normal, with volatility shrinking by the square root of ten, the chance of earning at least 7.95 percent a year over the decade is about 30 percent for A, 37 percent for B and 42 percent for C. Mix C buys five percentage points of probability by breaching the volatility ceiling.

Why Allocation Matters Most

A classic study of pension plans found that the policy mix, not manager picks or market timing, accounted for the bulk of how their quarterly returns moved (Brinson et al., 1986). A later study drew a sharper line: the mix governs a fund's own swings over time but explains less of why one fund beats another (Ibbotson & Kaplan, 2000). Either way, the choice among these three mixes will shape the foundation's results more than any later decision.

Testing the Assumptions

The result depends on the capital market assumptions, so the model was rerun with two changes. If expected equity returns were one point higher, Mix B would compound at about 7.5 percent, still short. If bond returns were one point lower, Mix B would compound at about 6.5 percent and Mix A would fall further behind. No reasonable change in assumptions brings any compliant mix to 7.95 percent. The gap is structural rather than an artifact of conservative inputs.

What the Trustees Should Hear

The plain message is that the policy as written asks for more than the markets are likely to provide at the risk the trustees accept. That is not a failure of the model; it is information the trustees need before they approve a mix.

Recommendation

Adopt Mix B, the highest-returning mix within the volatility ceiling. Report to the trustees that, under current assumptions, it has roughly a 37 percent chance of meeting the 7.95 percent objective over ten years, and that the foundation's real value is more likely to erode slowly than to grow. Ask the trustees whether they prefer to accept that outcome, raise the ceiling toward 14 percent, or reduce costs and spending toward the legal minimum.

References

Brinson, G. P., Hood, L. R., & Beebower, G. L. (1986). Determinants of portfolio performance. Financial Analysts Journal, 42(4), 39-44. https://doi.org/10.2469/faj.v42.n4.39

Ibbotson, R. G., & Kaplan, P. D. (2000). Does asset allocation policy explain 40, 90, or 100 percent of performance? Financial Analysts Journal, 56(1), 26-33. https://doi.org/10.2469/faj.v56.n1.2327

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x