In a rising market, the riskiest portfolios climb the leaderboard almost automatically. So is the leader skilled, or just carrying more market risk? This week you get the number that tells them apart.
Learning objectives. After this week you can (1) explain what beta measures; (2) compute an expected return with the CAPM; and (3) compute your portfolio's beta and alpha.
Remember this: the market pays you only for risk you can't diversify away, and beta measures that risk.
1) Beta
Anyone can erase firm-specific risk for free by diversifying (Week 7), so the market pays nothing extra for it. Beta (β) measures the rest: how strongly a holding moves with the whole market, which here means SPY. SPY has β = 1 by definition; cash has β = 0.
- β = 1: tends to move 1% when SPY moves 1%.
- β = 2: tends to move 2% when SPY moves 1%, in both directions.
- β = 0.5: tends to move 0.5%, a defensive holding (utilities and consumer staples often sit here).
You don't have to estimate it yourself: Yahoo Finance lists each stock's beta on its quote summary page.
2) The CAPM
E(r) = rf + β × (E(rm) − rf)
The Capital Asset Pricing Model reads: expected return = the risk-free rate (rf, what a Treasury pays for no risk) plus beta times the market risk premium (E(rm) − rf, the extra the market is expected to earn over Treasuries). With rf = 4% and E(rm) = 10%, the premium is 6%:
| Holding | β | CAPM expected return |
|---|---|---|
| Aggressive tech name | 1.2 | 4% + 1.2 × 6% = 11.2% |
| Defensive utility | 0.5 | 4% + 0.5 × 6% = 7.0% |
3) Your portfolio's beta and alpha
βp = Σ (Weight × β), cash at 0 · α ≈ Your Return − βp × SPY's Return
$50,000 in a β = 1.3 stock, $30,000 in a β = 0.9 stock and $20,000 in cash gives βp = 0.50 × 1.3 + 0.30 × 0.9 + 0.20 × 0 = 0.92. Alpha (α) is the return beyond what your beta predicted. Over a few weeks the risk-free part is tiny, so the shortcut above works. If SPY rose 1.0% and this portfolio rose 1.5%, beta predicted 0.92%, so α ≈ +0.58%. A β = 2 portfolio that gained 2.1% in the same stretch has α of only about +0.1%: nearly all of its gain was market risk, not skill.
Quick self-check
(a) rf = 4%, E(rm) = 10%, β = 1.5. CAPM expected return? (b) 40% in β = 1.2, 40% in β = 0.8, 20% cash. Portfolio beta? (Answers: 4 + 1.5 × 6 = 13%; 0.48 + 0.32 + 0 = 0.80.)
Common mistakes
- Treating beta as total risk. It measures only the market-wide part.
- Crowning high-beta luck. In an up market, high beta wins without any skill.
- Forgetting cash. Cash counts at β = 0 and pulls your beta down.
This week in the arena
Look up the Yahoo Finance beta of each stock you hold. Multiply each by that holding's weight (Value ÷ Total value), count cash at zero, and add: that is your βp. Multiply it by SPY's return since Week 1 (you found it in Week 5) and compare the result with your own Total return. The gap is your alpha.