Monte Carlo Simulation of a GP Promote.
A promoted interest (GP promote) gives the operating partner a share of the joint venture's
returns only after the preferred return (hurdle) has been achieved. If the venture's gross
return is ε, the preferred return is y, and the promote percentage is k, the promote paid is
p = k × max(ε − y, 0) and the investor nets h = ε − p
The simulation generates many possible joint venture returns based on the assumed expected
return (μ) and volatility (σ), with each simulated return representing one possible
future outcome. The histogram illustrates the distribution of these simulated returns, split at
the preferred return (the hurdle, which acts as the strike price of the option): below the
hurdle no promote is paid, above the hurdle the GP receives k × (Return − Preferred
Return). The summary statistics report the expected promote, its volatility, the probability
that a promote is paid, and the investor's expected net return after paying the promote.
This visualization demonstrates how uncertainty in investment returns translates into the GP's
expected compensation. Because the GP receives no payoff below the hurdle but shares in the
upside above it, the promoted interest has the same payoff structure as a call option, and its
expected value is driven by volatility rather than by expected return alone. The exact
closed-form value is shown alongside each simulated one, and a portfolio section below shows
how correlation across five ventures affects the distribution of promotes paid.
Assumptions
Expected gross return μ12.0%
Volatility σ15.0%
Preferred return y12.0%
Promote k20%
Number of draws
Expected promote E[p]
–
Std. dev. of promote
–
Investor's net return E[h]
–
Std. dev. of net return
–
Simulated gross return
–
SD of gross returns
–
A portfolio of five correlated ventures
Correlation ρ between ventures0.00
Five ventures share the assumptions above, with pairwise correlation ρ between their
gross returns. Correlation leaves each venture's expected promote unchanged, but it changes
the distribution of the promote bill across the portfolio: when ventures move
together, good years promote everything at once and bad years promote nothing, fattening
both tails. Drag the slider and watch the histogram spread.
The exact values shown under the simulated statistics come from the closed-form solution:
since the promote is k times a call on a normally distributed return,
E[p] = k[σφ(d) + (μ−y)Φ(d)] with d = (μ−y)/σ, where
φ and Φ are the standard normal density and distribution functions. The simulation
converges to this value as the number of draws grows; run at 250 draws a few times to see how
noisy a small sample can be. The methodology follows the accompanying Excel workbook, which
replicates the same procedure with 250 draws and an editable correlation matrix.