# Merton v2.2 scenario comparison

Frozen October 6 public model. These are scenario utility diagnostics, not out-of-sample investment returns. Utilities are multiplied by 100 for readability.

| Method | SPY | IEF | VTIP | Gold | PDBC | BTC | Cash | Central CAGR | Volatility | Central U | Mean U | P10 U | P5 U | Worst sampled U | Distance |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Central | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% | 14.18 | 18.52 | 6.08 | 5.84 | 1.67 | 0.45 | -3.85 | 0.00 |
| Box benchmark | 0.0% | 52.9% | 0.0% | 0.0% | 17.2% | 20.2% | 9.7% | 11.44 | 13.06 | 5.38 | 5.30 | 2.31 | 1.46 | -1.61 | 27.27 |
| Expected utility | 0.0% | 40.8% | 0.0% | 12.3% | 18.7% | 28.2% | 0.0% | 14.00 | 18.16 | 6.06 | 5.87 | 1.74 | 0.52 | -3.61 | 6.99 |
| Mean utility minus 0.5 SD | 0.0% | 44.6% | 0.0% | 11.7% | 20.0% | 23.7% | 0.0% | 12.91 | 15.69 | 5.93 | 5.76 | 2.24 | 1.21 | -2.49 | 12.06 |
| Mean utility minus 1 SD | 0.0% | 48.6% | 0.0% | 10.8% | 21.1% | 19.5% | 0.0% | 11.80 | 13.41 | 5.61 | 5.45 | 2.51 | 1.67 | -1.64 | 17.20 |
| Mean utility minus 2 SD | 3.4% | 50.3% | 5.5% | 8.3% | 20.4% | 12.1% | 0.0% | 9.64 | 9.60 | 4.53 | 4.42 | 2.46 | 1.92 | -0.74 | 27.11 |

## Commodity geometric excess-growth sensitivity

| Input | Asset CAGR | Merton drift | SPY | IEF | VTIP | Gold | PDBC | BTC | Cash |
|---|---|---|---|---|---|---|---|---|---|
| 0% premium | 3.65% | 5.20% | 0.0% | 47.0% | 0.0% | 24.4% | 0.0% | 28.7% | 0.0% |
| 1% premium | 4.69% | 6.20% | 0.0% | 41.4% | 0.0% | 21.9% | 8.3% | 28.4% | 0.0% |
| 2% premium | 5.74% | 7.20% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 3% premium | 6.80% | 8.20% | 0.0% | 29.3% | 0.0% | 16.6% | 26.1% | 28.0% | 0.0% |

## Commodity arithmetic excess-drift sensitivity

| Input | Asset CAGR | Merton drift | SPY | IEF | VTIP | Gold | PDBC | BTC | Cash |
|---|---|---|---|---|---|---|---|---|---|
| 0% premium | 1.98% | 3.58% | 0.0% | 47.0% | 0.0% | 24.4% | 0.0% | 28.7% | 0.0% |
| 1% premium | 3.00% | 4.58% | 0.0% | 47.0% | 0.0% | 24.4% | 0.0% | 28.7% | 0.0% |
| 2% premium | 4.04% | 5.58% | 0.0% | 45.1% | 0.0% | 23.5% | 2.7% | 28.6% | 0.0% |
| 3% premium | 5.09% | 6.58% | 0.0% | 39.1% | 0.0% | 20.9% | 11.7% | 28.3% | 0.0% |

## SPY EPS / terminal valuation sensitivity

| Input | Asset CAGR | Merton drift | SPY | IEF | VTIP | Gold | PDBC | BTC | Cash |
|---|---|---|---|---|---|---|---|---|---|
| 4% EPS / 16× | 2.36% | 3.95% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 4% EPS / 18× | 3.57% | 5.13% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 4% EPS / 20× | 4.67% | 6.18% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 5% EPS / 16× | 3.34% | 4.91% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 5% EPS / 18× | 4.57% | 6.09% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 5% EPS / 20× | 5.68% | 7.14% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 6% EPS / 16× | 4.33% | 5.86% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 6% EPS / 18× | 5.56% | 7.04% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 6% EPS / 20× | 6.68% | 8.09% | 5.9% | 31.8% | 0.0% | 18.9% | 15.7% | 27.7% | 0.0% |
| 7% EPS / 16× | 5.31% | 6.80% | 0.0% | 35.4% | 0.0% | 19.3% | 17.2% | 28.2% | 0.0% |
| 7% EPS / 18× | 6.56% | 7.97% | 4.7% | 32.5% | 0.0% | 19.0% | 16.0% | 27.8% | 0.0% |
| 7% EPS / 20× | 7.69% | 9.03% | 15.8% | 25.8% | 0.0% | 18.3% | 13.2% | 26.9% | 0.0% |