Merton fraction

Quantitative Finance Glossary

Constant optimal proportion of wealth in the risky asset under CRRA utility with risk-aversion γ: π^* = dfracμ - rγ,σ^2 — solution of the Merton portfolio problem via HJB. Striking property: under constant investment opportunity set, π^* is constant in wealth and time (constant-mix rebalancing). Generalises to stochastic-opportunity-set settings via the addition of a hedging-demand term (Merton 1971); empirical 'horizon effects' come from this hedging demand.

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