Investment Planning and Capital Sufficiency Analysis

Capital sufficiency analysis (or capital needs analysis) is the process by which a wealth manager determines whether a client has, or will likely have, sufficient financial resources to meet his or her objectives.

Methods

Deterministic Forecasting

Deterministic forecasts are simply compounded portfolio returns, projected into the future. This could be done by hand on a piece of paper, or in a basic spreadsheet.

For example, if a client has a $1,000 portfolio, and the manager assumes a 7% compounded annual return is realistic, the following formula would forecast the portfolio value at the end of 10 years in a deterministic manner:

$$ \$1,000\times (1.07)^{10} = \$1,967 $$

There are a few issues with this analysis. The first is that it does not take into account taxes or fees. The second is that it does not account for volatility, which would be a drag on portfolio returns. This means deterministic forecasting is an acceptable place to start but is likely to overestimate final portfolio values. This is where Monte Carlo Simulation comes in.

Monte Carlo Simulation

Readers are likely already familiar with the basics of Monte Carlo simulation (MCS). as a refresher, Monte Carlo simulation is another method of forecasting final portfolio values but instead of using linear growth, MCS will use an arithmetic average for returns, and pair that with expected portfolio standard deviation. Each particular trial will use a random value for the inputs in the analysis, and then perform many thousand of these trails. The trials are then averaged, and a range of potential outcomes can be shown.

MCS cannot predict the future with perfect precision. What it can do is model portfolio returns in a more robust and realistic manner, as compared to deterministic forecasting. It can handle interim cash flows such as portfolio withdraws and taxes with ease, as well as handle a range of various input changes, like changing the inflation rate in the middle of the time horizon, for example.

Inputs and Interpretation of Monte Carlo Simulation Results

Inputs in the MCS analysis are likely to include, current portfolio statistics, expected return and volatility of portfolio, expected contributions, inflation, taxes, any major contributions or withdraws and expected time horizon. A (simplified) table of results may look something like the following:

$$ \begin{array}{c|c}
\textbf{Percentile} & \textbf{Year 10 Portfolio Value} \\ \hline
\bf{50th} & \$2,188 \\ \hline
\bf{75th} & \$1,921 \\ \hline
\bf{95th} & \$1,838 \\ \hline
\textit{Successful Trials} & \bf{98\%}
\end{array} $$

The table can be interpreted as stating, “the ending portfolio value was $2,188 at least 50% of the time”, or “the final portfolio value was at least $1,838 in 95 out of 100 trials”. The client and manager will deem a portfolio of ‘XXX’ amount of dollars as a success. The output will state in how many of the trials a success occurred.

When the outcomes do not satisfy client needs and expectations, a few changes can be made, including:

• Increasing contributions to goal.
• Reducing the goal.
• Delaying the timing of a goal.
• Adopting an investment strategy with higher expected returns.

Again, MCS does not predict outcomes with 100% accuracy, rather it is a tool that should be used as a complement to the portfolio management process. It can accurately predict the viability of a given plan.

Question

$$ \begin{array}{c|c}
\textbf{Percentile} & \textbf{Year 10 Portfolio Value} \\ \hline
\bf{50th} & \$2,188 \\ \hline
\bf{75th} & \$1,921 \\ \hline
\bf{95th} & \$1,838 \\ \hline
\textit{Successful Trials} & \bf{98\%}
\end{array} $$

Based on the MCS output above, the client definition of a successful outcome must have been:

1. $1,838.
2. Above $1,838.
3. Below $1,838.

Solution

The correct answer is C.

According to the simulation, a final portfolio value of $1,838 was achieved in 95% of all trials performed. Since the successful amount (whatever that was) was reached in 98% of all trials, it means that something less than $1,838 was achieved, as it occurred more often than the 95^th percentile amount.

A higher ending value becomes less probable as the percentile in the table moves toward zero. Imagine that the 1^st percentile would be the rarest (the highest) portfolio ending value, as it would only occur in one out of 100 trials.

While most clients would likely be satisfied with a 98% success rate, it is still a subjective criterion. It could be possible that a client would want a 99%, or 100% success rate, although this would mean lowering the final portfolio value that would be deemed a success.

Portfolio Construction: Learning Module 4: Overview of Private Wealth Management; Los 4(g) Evaluate capital sufficiency in relation to client goals