A Modern Portfolio Theory exercise built from 72 months of AAPL and NVDA returns (Jan 2020–Dec 2025) — constructing the mean-variance efficient frontier, solving for the tangency (maximum Sharpe ratio) and minimum-variance portfolios via Solver, and estimating the resulting portfolio's CAPM alpha and beta against the market.
The two stocks are only moderately correlated (0.49), so combining them meaningfully reduces risk versus holding either alone. The tangency portfolio — 24.6% AAPL, 75.4% NVDA — earns the best risk-adjusted return of any combination on the frontier.
Individual asset statistics (2020–2025)
| Asset | Avg. Monthly Return | Annualized Return | Monthly SD | Annualized SD |
|---|---|---|---|---|
| AAPL | 2.20% | 26.35% | 8.04% | 27.84% |
| NVDA | 5.86% | 70.30% | 13.95% | 48.33% |
Each point on the curve is a different AAPL/NVDA weight combination (from -50% to +150% AAPL). The Capital Allocation Line runs from the risk-free rate through the tangency portfolio — the best available risk/return trade-off once a risk-free asset is available.
Mean-Variance Efficient Frontier
Frontier portfolios (AAPL weight -50% to 150%)
| AAPL Weight | NVDA Weight | SD | E(r) |
|---|---|---|---|
| -50% | 150% | 19.32% | 7.69% |
| -40% | 140% | 18.21% | 7.32% |
| -30% | 130% | 17.11% | 6.96% |
| -20% | 120% | 16.03% | 6.59% |
| -10% | 110% | 14.98% | 6.22% |
| 0% | 100% | 13.95% | 5.86% |
| 10% | 90% | 12.96% | 5.49% |
| 20% | 80% | 12.02% | 5.13% |
| 30% | 70% | 11.13% | 4.76% |
| 40% | 60% | 10.31% | 4.39% |
| 50% | 50% | 9.58% | 4.03% |
| 60% | 40% | 8.96% | 3.66% |
| 70% | 30% | 8.47% | 3.29% |
| 80% | 20% | 8.14% | 2.93% |
| 90% | 10% | 8.00% | 2.56% |
| 100% | 0% | 8.04% | 2.20% |
| 110% | -10% | 8.26% | 1.83% |
| 120% | -20% | 8.66% | 1.46% |
| 130% | -30% | 9.20% | 1.10% |
| 140% | -40% | 9.87% | 0.73% |
| 150% | -50% | 10.65% | 0.36% |
$1 invested in the tangency-weighted portfolio at the start of 2020 would have grown to $20.83 by the end of 2025 — behind NVDA alone (a generational run) but far ahead of AAPL alone, with meaningfully smoother volatility than holding NVDA outright.
Growth of $1 — AAPL vs. NVDA vs. Optimal Portfolio (2020–2025)
CAPM & performance measures — optimal portfolio
| Beta (vs. market) | 1.50 |
| Jensen's alpha (annualized) | +37.5% |
| Sharpe ratio (annualized) | 1.42 |
| Treynor ratio (monthly) | 3.17% |
Beta and Jensen's alpha estimated by regressing the portfolio's monthly excess returns on market excess returns (Mkt-RF), 72 months, Jan 2020–Dec 2025. A beta of 1.50 and a strongly positive alpha both reflect NVDA's outsized run over this specific window — not a claim of a repeatable market-beating strategy.