CAPM
Expected return = risk-free return + beta × market risk premium.
CAPM estimates the return an investment should earn for its level of market risk. More risk (beta) ⇒ more required return.
Example: Rf = 2%, premium = 6%, β = 1.5 → E(R) = 2% + 1.5×6% = 11%.
| Asset | σ (annual) | Notes |
|---|---|---|
| S&P 500 Total Return (σm) | 15.00% | Large-cap U.S. equities ~12–18%. |
| S&P MidCap 400 Total Return | 18.00% | Mid-caps often 15–20%. |
| Russell 2000 Total Return | 22.00% | Small-caps ~18–25%. |
| Bloomberg U.S. Aggregate (Agg) | 4.00% | Investment-grade bonds ~3–6%. |
| Gold Spot (USD) | 18.00% | Can range from mid-teens to ~25%. |
| Bloomberg Galaxy Crypto (BGCI) | 60.00% | Crypto is highly volatile (50–100%+). |
| Asset | Corr(i,m) | σi | σm | βi = Corr × (σi/σm) |
|---|---|---|---|---|
| S&P 500 | 1.00000000 | 0.15000000 | 0.15000000 | 1.0000 |
| S&P MidCap 400 | 0.97015600 | 0.18000000 | 0.15000000 | 1.1642 |
| Russell 2000 | 0.95933300 | 0.22000000 | 0.15000000 | 1.4077 |
| Bond (Agg) | 0.50382100 | 0.04000000 | 0.15000000 | 0.1344 |
| Gold | 0.92681900 | 0.18000000 | 0.15000000 | 1.1122 |
| Crypto Index | 0.86671000 | 0.60000000 | 0.15000000 | 3.4668 |
| SOFR (risk-free) | 0.00000000 | 0.00000000 | 0.15000000 | 0.0000 |
CAPM: E(Ri) = Rf + βi × (Market Premium). Alpha = Projected − CAPM.
| Asset | βi | CAPM E(Ri)% | Projected% | Alpha% (Proj − CAPM) |
|---|---|---|---|---|
| S&P 500 Total Return | 1.0000 | 9.00% | 9.00% | 0.00% |
| SOFR Overnight Index Avg | 0.0000 | 3.50% | 3.50% | 0.00% |
| S&P MidCap 400 Total Return | 1.1642 | 9.80% | 11.00% | 1.20% |
| Russell 2000 Total Return | 1.4077 | 11.24% | 13.00% | 1.76% |
| Bloomberg U.S. Aggregate Bond (Agg) | 0.1344 | 4.24% | 5.00% | 0.76% |
| Gold Spot (USD) | 1.1122 | 9.62% | 8.50% | -1.12% |
| Bloomberg Galaxy Crypto Index (BGCI) | 3.4668 | 22.57% | 22.00% | -0.57% |