The Kelly Criterion, derived from information theory, gives the theoretically optimal fraction of capital to allocate to a bet with known positive expected value. For a stock with expected return μ and variance σ², the Kelly fraction is approximately f* = μ/σ². In practice, implementation is far messier.
Why Full Kelly is Dangerous
The Kelly fraction maximises long-run geometric mean wealth — but at the cost of extreme volatility in the short run. A portfolio running full Kelly typically has drawdowns of 50%+ at some point during its lifetime, even when the underlying edge is real. For most investors, the psychological cost of watching half their portfolio evaporate — even temporarily — makes full Kelly untenable.
Fractional Kelly in Indian Equity Context
Practitioners overwhelmingly use half-Kelly or quarter-Kelly in practice. Half-Kelly has 75% of the expected geometric growth rate of full Kelly while reducing variance by 50% — an attractive tradeoff. For a concentrated 10-stock Indian equity portfolio:
- Full Kelly with typical return/risk estimates produces position sizes of 20–40% in "best ideas" — highly concentrated and fragile
- Half-Kelly produces 10–20% positions — concentrated but manageable
- Quarter-Kelly converges toward equal weight for diversified portfolios (5–10% positions)
Equal Weight and Risk Parity as Alternatives
Equal weight avoids the estimation error problem entirely — you don't need to forecast returns. Research suggests that estimation error in expected returns overwhelms any benefit from optimal weighting for portfolios of 15+ stocks. For Indian retail investors without persistent proprietary alpha, equal weight or risk-parity (equal volatility contribution) often outperforms Kelly-based sizing simply because it avoids the damage from overconfident bets.
Spectrum's Portfolio Optimisation module lets you compare efficient frontier portfolios (which implicitly use a form of mean-variance optimisation) against your current equal-weight allocation, showing where reweighting adds genuine risk-adjusted value versus where estimation error makes it noise.