Finance FAQ

Variance drain is the gap between an investment's arithmetic mean return and its compound (geometric) growth rate. It equals approximately ½σ², where σ is the volatility of returns. Higher volatility …

Leverage L scales arithmetic return linearly (Lμ) but scales variance drain quadratically (½L²σ²). Doubling leverage quadruples the drag. This is why leveraged ETFs can underperform their target …

The Kelly criterion gives the leverage ratio that maximizes compound growth: L* = (μ − r) / σ². It falls directly out of the variance drain formula — it is the point where the marginal return from …

Full Kelly assumes perfect knowledge of expected return (μ) and volatility (σ). In practice, both are estimated with error. Half-Kelly — sizing at L*/2 — sacrifices about 25% of theoretical growth but …

It is a mathematical relationship, not a physical force — the geometric mean is always less than or equal to the arithmetic mean (AM-GM inequality). But the P&L consequences are entirely real: two …

The answer depends on which metrics you prioritize. a16z points to 80% GPU utilization and $40.6 billion in annual revenue from top AI companies as evidence of real demand. AQR counters that the U.S. …

The CAPE ratio measures price relative to 10-year average inflation-adjusted earnings. At current levels around 40x, it suggests U.S. large cap equities may return roughly 3.9% annually over the next …

Yes, this is one way to reconcile the bullish and bearish views. Individual AI winners generating real revenue and high utilization could deliver spectacular returns even as broad market indices …

Both sources have financial incentives influencing their perspectives. a16z manages billions in venture capital and growth equity, so bullish AI narratives support their portfolio valuations. AQR runs …

Tech P/E multiples currently sit around 30-35x, elevated but nowhere near the 70-80x of 2000. More importantly, GPU utilization runs at 80% compared to just 7% for fiber optic cables during the dotcom …

AQR's 2026 capital market assumptions show U.S. buyouts returning 4.2% versus 3.9% for public equities. That's a 30 basis point premium for accepting years of lockup, unpredictable capital calls, and …

According to AQR's 2026 capital market assumptions, expected real returns for U.S. buyouts are 4.2% over the next 5-10 years. Private credit is even lower at 2.6%, down 0.5 percentage points …

Manager selection is critical. In venture capital, top decile managers generate 31.7% IRR while bottom decile managers return negative 7%. The spread between winners and losers is enormous. But this …

Too much capital chased the same opportunities. When every pension fund, endowment, and sovereign wealth fund allocates 20-30% to alternatives, the returns that made them attractive get arbitraged …

Access to companies you can't reach in public markets. 87% of U.S. companies with more than $100 million in revenue are now private. Value creation has shifted earlier: for 2020-2023 IPOs, 55% of …

Evidence suggests yes. Sara Hooker's research shows that compact models like Llama-3 8B now outperform massive predecessors like Falcon 180B. Scaling laws only reliably predict pre-training test loss, …

Yes. Llama-3 8B outperforms Falcon 180B, and Aya 23 8B beats BLOOM 176B despite having only 4.5% of the parameters. This is not an isolated fluke but a systematic trend visible in Open LLM Leaderboard …

Hedge fund short interest in utilities now sits at the 99th percentile relative to the past five years, according to Goldman Sachs data. The bet appears to be that AI data center demand may not …

As scaling hits diminishing returns, the skills that matter shift toward algorithmic cleverness, data quality, and architectural innovation rather than brute-force compute. Frontier labs are …

Yes, in the cryptographic sense. Statistical analysis of 20,000 rounds confirms the random number generator produces fair outcomes matching the stated 97% RTP. However, mathematical fairness doesn't …