Simulating Returns with Lump-Sum and Periodic Contributions

Summary

The document gives a recursive method for simulating portfolio value when an initial lump sum is combined with periodic investments. At each step, add the contribution arriving during that period to the previous portfolio value, then apply the next period’s return. The initial lump sum is the starting value; with a constant contribution beginning after the first step, the initial contribution is zero and later contributions equal the periodic payment.

The method applies regardless of how the returns are generated. The question describes using a normal inverse function with random probabilities and historical mean and volatility, but the answer focuses on how to incorporate cash flows into the portfolio path. It does not assess whether normally distributed returns or five-year historical estimates are suitable, and it does not specify contribution timing beyond its stated convention. Those assumptions should be set consistently with the simulation’s time steps.

Key ideas

• Add each period’s cash contribution to the previous portfolio value before applying that period’s return.
• Treat the lump sum as the initial portfolio value.
• Set the first contribution to zero when periodic investing begins after the initial step.
• Contribution timing must align with the return interval used in the simulation.

Tags

# How do you simulate returns for a portfolio when you have Lumpsum + Monthly investments (SIP) in place?


# How do you simulate returns for a portfolio when you have Lumpsum + Monthly investments (SIP) in place?












I'm trying to simulate portfolio returns using Norm.inv function in excel. Inputs to the formula: Prob= Rand, Std dev= Historical, Mean= 5 year historical average.

Its easy to do this when you're assuming all your investments will receive at least some weight of your monthly installment. See below:

Or when you're just simulating growth of your lumpsum portfolio. See below:

The solution I'm seeking is what do I do for a portfolio where I have x wt as lumpsum and y wt as SIP?

## Answer by Pontus Hultkrantz (score 1)

https://quant.stackexchange.com/a/59616

Your formula in the first example is on the right track.

Standing at time step $i$, your value at next time step $i+1$ is $V_{i+1} = (V_{i} + c_i)(1+r_{i+1})$, i.e. your previous portfolio value plus an influx of $c_i$ in cash (SIP) are yielding a one step return of $r_{i+1}$. Explicitly you have

\begin{align} V_0 &= V_0 \\ V_1 &= (V_0 + c_0)(1+r_1) \\ V_2 &= (V_1 + c_1)(1+r_2) \\ V_{i+1} &= (V_{i} + c_i)(1+r_{i+1}) \\ \end{align}

So if your starting value (lump sum) is $V_0$, and there is a constant SIP payment starting from time step $1$ of $c$ then $c_0=0$ and $c_i=c$ for $i>0$.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.