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Hoadley Portfolio Simulator

Overview

Portfolio optimizers, such as the Hoadley Portfolio Optimizer, and other asset allocation tools can be used to determine the combination of individual assets, mutual funds or asset classes in an investment portfolio which provides the maximum return per unit of risk. 

But this initial asset allocation is just the starting point for portfolio planning. 

The Need for Multi-Year Portfolio Simulation

Portfolio drift: An investment portfolio consists of multiple assets (individual assets, asset classes or  mutual funds), each with its own expected return, volatility and correlation with every other asset.  As a result, as soon as initial asset allocations are implemented the asset weightings in the portfolio will start to deviate from the intended allocations, usually significantly impacting long term portfolio returns and risks.   A portfolio might have an expected return of, say 10% pa and a volatility of 15% pa when it is first established, but after a few months this will no longer be the case. 

Rebalancing: An investment portfolio may be periodically rebalanced back to the initial optimal or strategic asset allocations.  But rebalancing may reduce returns and incur transaction costs which further impact long term portfolio performance. On the other hand, rebalancing less frequently, or only after the portfolio asset weights have drifted from the initial allocation by a specified amount, may reduce costs, but at the expense of increased risk.  What is the optimal rebalancing strategy?  Is it worth doing at all?

Uncertainty of returns: Portfolio planning must also recognize that there is no certainty about future portfolio returns. It is common to refer to expected investment returns as if these are the returns that will be realized over a five, ten or twenty year period, but in reality a wide range of returns is possible, each with a specific probability of occurring. The higher the portfolio volatility, the wider the range of returns and the lower the median compounded return will be.

Within a five year period, for example, there may be a 20% chance of the return for the period being negative even though the mean geometric return is 9% pa. It's important to understand what these risk are as well as just knowing the average expected return.

The Hoadley Portfolio Simulator

The Hoadley Portfolio Simulator uses Monte Carlo simulation to generate a large number of possible future portfolio outcomes over a multi-year time frame.  It then classifies the results into percentile groups, analyzes the frequency distribution of geometric (annually compounded) returns (as shown in the example below), and calculates rebalancing and other costs. 

Hoadley Portfolio Simulator Returns Distribution

The results can help the gain an understanding of such factors as the likelihood of achieving return targets, and the impact of different rebalancing strategies on future investment performance.

A key feature of the Hoadley Portfolio Monte Carlo Simulator is the generation of two scenarios for every simulation run: 

bullet Scenario 1: Rebalancing is based on the assumption that portfolios are periodically rebalanced back to the initial strategic or optimal asset allocation.  The rebalancing frequency, tolerance and rebalancing costs are controlled by the user.
 
bullet Scenario 2: No rebalancing is a "set and forget" scenario, based on the assumption that portfolios are never rebalanced. Scenario 2 provides a base-line against which the impact of various rebalancing strategies can be assessed.

Importantly, both scenarios produced from every simulation run are based on the same underlying simulation data -- they both use the same asset price data set generated by the simulator.  They therefore represent different portfolio management responses to the same underlying "market conditions" and provide an effective way of modelling the impact of rebalancing on future investment portfolio performance.

Inputs to the Portfolio Simulator

The portfolio inputs to the Monte Carlo simulator are expected returns, volatilities, the correlations for each asset (or fund or asset class) in the portfolio, and the initial portfolio asset weights.

Returns, volatilities and correlations are exactly the same inputs required by the Hoadley Portfolio Optimizer.  See estimating volatilities, correlations and returns.

Portfolio asset weights may reflect a strategic asset allocation, or they may represent the optimal portfolio from a portfolio optimizer, such as the Hoadley Portfolio Optimizer.
 

Simulator Outputs

Two sets of outputs are produced from each simulation run: one set for scenario 1 (with periodic rebalancing) and scenario 2 (with no rebalancing).  The outputs for each scenario are presented side by side for easy comparison, and include:

bullet Average asset weights in the portfolio at the end of the simulation period (eg after five years)
 
bullet Portfolio volatilities at the beginning of the period, at the end, and the mean.
 
bullet Portfolio expected returns, at the beginning of the period, and at the end of the period.
 
bullet The mean and median portfolio geometric (annually compounded) returns for the period and the standard deviation of the the returns.
 
bullet Geometric (annually compounded) returns and expected portfolio values by 13 percentile groupings to highlight the probability distributions of returns. The dollar difference between the end portfolio values for scenario 1 and 2 is also shown for each percentile grouping.
 
bullet Returns histograms showing the frequency distribution of geometric (annually compounded) returns.  Results are shown in table form and graphically for scenarios 1 and 2 separately, and combined on the one histogram, as shown in the above picture.
 
bullet Annual rebalancing costs (as a percentage of portfolio value) and the number of rebalancing events (ie the number of times the portfolio had to be rebalanced during the simulation period.

 
Software Environment

The Hoadley Portfolio Simulator requires Microsoft Excel (32-bit or 64-bit) running under Microsoft Windows.  For detailed systems requirements, including supported versions of Windows and Excel see systems requirements.

The Hoadley Finance Add-in for Excel version 10.1k or later must be installed before using the Simulator.
 

Download the Hoadley Portfolio Monte Carlo Simulator

The Hoadley Portfolio Monte Carlo Simulator is free to download to users who have purchased the Hoadley Finance Add-in for Excel and are still within their one year free download period..

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