Walk me through the Fundamental Law (IC × √B)

The Fundamental Law of Active Management

$$IR \approx IC \cdot \sqrt{B}$$

Three variables. Let's build each one from the ground up.

The three terms

The IC is formally: $IC = \text{Corr}(\hat{r}{i,t},\ r)$ — how well do your forecasts predict what actually happens? ^[2]

What the law says in plain English

Two paths to a high IR:

1. Be very accurate — high IC per bet, or
2. Bet often and independently — high B

The $\sqrt{B}$ term is the crucial insight: skill compounds with breadth the same way a casino compounds a house edge across thousands of hands. A tiny, consistent edge across many independent bets beats a large, sporadic edge across a few. ^[4]

Worked example: large-cap vs. mid-cap

Large-cap fund (Nifty 100 universe): ^[1]

• $IC = 0.04$ (crowded, heavily-analysed stocks)
• Effective breadth $B = 60$ (many positions move together)

$$IR \approx 0.04 \times \sqrt{60} = 0.04 \times 7.75 \approx 0.31$$

Mid-cap fund (less-covered universe):

• $IC = 0.07$ (more information asymmetry)
• Effective breadth $B = 100$

$$IR \approx 0.07 \times \sqrt{100} = 0.07 \times 10 = 0.70$$

This is not an accident. Large-cap stocks are covered by 30–60 analysts each — any edge gets competed away fast. Mid-cap stocks have fewer analysts, higher residual Volatility — definition">volatility, and more room for skill to matter. ^[6]

Three things that quietly destroy B

Breadth counts independent forecasts, not just total positions. Watch for:

1. Correlated holdings — 100 stocks all moving with Nifty = effective B of maybe 15–20
2. Long-only constraint — can't act on negative views, so you lose half your potential bets
3. benchmark" title="Benchmark — definition">Benchmark hugging — Tracking Error — definition">tracking error budgets force managers to stay close to the index, reducing active bets ^[1]

The full form (with Transfer Coefficient)

When constraints prevent a manager from building their optimal portfolio:

$$IR \approx TC \cdot IC \cdot \sqrt{B}$$

$TC$ = correlation between what the manager wants to hold and what they actually hold. A long-only constraint typically drags $TC$ down to 0.6–0.7. A hedge fund that can short stocks has $TC$ closer to 1.0 — which is why hedge funds with genuine skill can structurally outperform equivalent long-only funds. ^[1]

The practical question this unlocks

Once you know a fund's IR, you can test whether it clears the fee hurdle:

$$IR \times TE > \text{fee differential vs. passive index}$$

If a large-cap fund has $IR = 0.2$ and tracking error $TE = 4\%$, expected alpha = $0.2 \times 4 = 0.8\%$. If the fee premium over a Nifty index fund is 1.1%, the fund destroys value on pure economics — even before accounting for tax drag on turnover. ^[5]

Apply this → Use Explore Funds to look up the 5-year IR of any fund you hold. Multiply by its tracking error. Compare that number to the fee differential vs. the cheapest passive alternative in the same category.