Why aftcasting is better than efficient frontier

The Efficient Frontier (EF) is one of the pillars of current investment practice. Academics have broadened its application to other areas, including the development of what they claim is the optimal asset allocation. But EF is inadequate for finding the best allocation. Instead, aftcasting is a much better tool.

Shortcomings of Efficient Frontier

Here’s how people use EF to calculate optimal asset mix:

• Take a portfolio with a specific mix of stocks and bonds.
• Calculate its Compound Annual Return (CAR) over a specific time period: say, 10 years.
• Define risk as the standard deviation of monthly returns and calculate it using standard formulas.
• Plot that point on a chart (see Figure 1). The vertical axis indicates the CAR, the horizontal axis represents risk.
• Repeat the same calculation for various asset mixes and plot each point on the same chart.
• Connect all dots (the blue line).

To determine the EF, we plot a diagonal line that shows CAR rising 1% with every 1% increase in risk (the green line in Figure 1). Portfolios closest to the EF are considered most risk-efficient. The red dot on the chart is touching the EF, suggesting an optimal mix: 80% stocks, 20% fixed income.

If you ride along the blue line further to the right (more risk), CAR doesn’t increase as much and the asset mix becomes less efficient. If you go left of the red dot, you reduce risk, but CAR comes down even more, making the portfolio less efficient.

Let’s apply the EF-based method to market data, starting at the end of the last secular bull market, and see how it performs. Our proxy for equities is the S&P 500 index; for fixed income, we’ll use the U.S. Aggregate Bond Index. We start in 1999 and review the optimal asset mix of this fictitious portfolio no less than every three years. At each review, we use the 10-year history immediately preceding the review date.

Review in December 1999

Prior to 1999, equities and bonds were steadily increasing in value for several years. The EF analysis indicates we can use anywhere from a 70%/30% to a 100%/0% as the optimal mix.

Review in September 2002

Our second review reveals the EF didn’t work as advertised. In the 1999 review, the EF suggested an optimal equity allocation of 70% to 100%. Then markets crashed—the worst multi-year decline since 1929.

For the September 2002 review, the calculation includes the crash’s effect. The EF now indicates an optimal asset mix of 10% stocks and 90% bonds. But it appears the EF analysis was late with this guidance, because the market had peaked in 2000.

Review in September 2005

Between September 2002 and September 2005, the equity index shot up by about 50%. So, the optimal mix from the last review didn’t work so well: we had only 10% in equities, missing a good bull run. Yet the EF now indicates an optimal equity holding of 20%.

Review in September 2007

Markets appear a bit wobbly, so we don’t wait three years; we review the asset mix after two. Now, the EF analysis shows the optimal equity allocation as 10%.

Review in July 2009

After the last review, markets crashed. With only 10% equities, we avoided some large losses during the credit crisis. In this review, the EF analysis indicates a 0% allocation to equities.

Review in July 2012

It’s too bad we allocated 0% to equities. Between July 2009 and July 2012, the S&P 500 shot up by about 34%.

For this review, the EF analysis still indicates a 0% equity allocation.At the time of writing (September 2014), the index was up 102% since the end of July 2009. Anyone would be pretty upset about missing that run completely.

In almost all cases, EF was a poor market timing tool. The fundamental problem with EF is it’s based on standard deviation of returns, which uses Gaussian math.

This assumes markets always follow a normal distribution curve and that recent history will continue to repeat in the future within these limits of normalcy. But markets occasionally go beyond these limits, and that’s when big money is lost (or made). This means that most of the research and conclusions using Gaussian tools are irrelevant and unrealistic.

Aftcasting

For optimal asset allocation, it makes more sense to use actual market history, which we call aftcasting. We don’t use Monte Carlo simulators or any other Gaussian tools.

Aftcasting displays the outcome of all historical asset values of all portfolios on the same chart, and it gives a bird’s-eye view of all outcomes for a given scenario for the available data.

It provides the success and failure statistics with exact historical accuracy because it includes actual historical equity performance, inflation and interest rates, as well as the historical sequencing/correlation of these data sets. And it doesn’t overlook market extremes, as Gaussian models do. Aftcasting has two additional benefits. The first concerns time horizon; the second withdrawals.

The shorter the time horizon, the larger the impact of volatility. Even though volatility’s one of the two inputs for the EF analysis, the method can’t optimize for various time horizons. It just provides a specific asset mix until the next review. By contrast, aftcasting allows you to optimize for specific time horizons.

Factors impacting optimal asset mix are different in accumulation and distribution stages. During accumulation, volatility of returns is important and sequence of returns isn’t. During distribution, it’s the opposite: sequence of returns is extremely important and volatility of returns has only a marginal impact. Aftcasting allows you to optimize for both stages separately because it incorporates additions to and withdrawals from portfolio assets (see Table 1).

Table 1: Accumulation versus distribution under aftcasting
Portfolio Regime	Capital/Cash Flow	What do we optimize for?
Accumulation	Cash might be added to portfolio	Maximize the median portfolio value
Distribution	Cash is withdrawn from the portfolio periodically	Maximize the sustainable withdrawal rate

Canadian portfolios

Shifting focus to Canada, for the equity portion we use the S&P/TSX index. For fixed income, we have a conventional bond ladder held until maturity with no capital gains or losses.

It yields (after costs) 0.5% higher than the historical interest rate for a six-month GIC. The asset mix is rebalanced annually only if the target mix deviates by more than 3%. Figure 2 depicts an aftcast for an accumulation portfolio. Each of the green lines on the chart represents a specific starting year since 1919. It shows how each portfolio would have performed over a 30-year period for all starting years prior to 1984 and until end of 2013 for portfolios starting after 1984.

The heavy black line represents the median portfolio, where half the green lines are above it and the other half below. Note the asymmetry of the density around the median; you’ll likely not see this with any Gaussian model (such as Monte Carlo simulations).

For accumulation portfolios, we calculate the median portfolio value at various asset mixes. The optimal asset mix is where the median’s highest.

For distribution portfolios, we calculate the sustainable withdrawal rate (allowing a 10% probability of failure) at various asset mixes for different time horizons. The optimal asset mix is where the sustainable withdrawal is highest.

Table 2 summarizes our findings.

Table 2: Optimal asset mix
Time Horizon	Optimal Asset Mix Equity % / Fixed Income %
	Accumulation	Distribution
10 years	60/40	30/70
20 years	70/30	40/60
30 years	70/30	50/50

Here’s an example of how to determine the mix when the client’s time horizon isn’t exactly as shown on the table. Bob, 50, is saving for retirement until age 65. So, he has a 15-year accumulation horizon. Based on Table 2, his optimal asset mix is 65% equities and 35% fixed income—halfway between the 10-year and 20-year optimals.

If your client’s in the distribution stage and his net withdrawals are smaller than the perpetual withdrawal rate (about 2%), you can then treat his portfolio as an accumulation portfolio. (For more information on perpetual withdrawal rates, read my CE course “Perpetual Distribution Rates,” on cecorner.ca.)

If your client’s in the distribution stage and his withdrawals are larger than sustainable, using the optimal asset mix doesn’t make much of a difference on the portfolio’s longevity. In these scenarios, you need to look at guaranteed lifelong income solutions, usually offered by insurance companies.

(For more information on sustainable withdrawal rates, please refer to my CE course “Purpose-Driven Sustainable Withdrawal Rate,” on cecorner.ca.)

The optimal asset mix should be reviewed when there’s a change in your client’s financial situation—keeping in mind that risk tolerance always supersedes optimal asset mix.

ACTION STEP Use aftcasting to decide upon optimal asset allocation.