This article is written in response to requests from readers of my latest published article on safe retirement withdrawal from a dividend fund portfolio. The readers were concerned over the relatively short backtest period. In this article, I selected the Vanguard mutual funds with long historical record that allowed me to perform a back test over 27 years instead of just 9 years in my previous study.
The portfolio is comprised of the following four funds:
 Vanguard Long Term Treasury Fund (MUTF:VUSTX)
 Vanguard Equity Income Fund (MUTF:VEIPX)
 Vanguard Morgan Growth Fund (MUTF:VMRGX)
 Vanguard International Growth Fund (MUTF:VWIGX)
The portfolio is managed based on quarterly asset reallocation as dictated by a meancovariance optimization algorithm. On the first trading day of each quarter, we estimate the covariance matrix of the returns over the previous 65 trading days, roughly corresponding to the latest threemonth period. Based on the means and volatilities of the returns, as well as the correlation between the asset returns, the algorithm determines the optimal allocation of the assets that would have produced the highest total return without exceeding a given level of volatility of the returns. This allocation is maintained until the first trading day of the next quarter when a new allocation is determined.
We performed the simulation under two target levels of the volatility of the returns. The first one we call the "low volatility", the other  the "high volatility". The low volatility is suitable for conservative investors while the high volatility is for aggressive investors.
The data for the study were downloaded from Yahoo Finance on the Historical Prices menu for all the tickers mentioned above. We use daily price data from March 1998 to July 2015, adjusted for dividend payments. Since we used three months of data for parameter estimation, the simulation started on June 20, 1988, and ended on July 31, 2015. We performed simulations under the following two scenarios:
 No withdrawals of any money are made. We call this "0% withdrawal ". All the dividends are reinvested.
 At the beginning of each quarter a fixed inflationadjusted amount of money is withdrawn from the account. At the start, on July 1, 1988, $1,250 is withdrawn, that is 1.25% of the initial capital of $100,000. Subsequently, the amount withdrawn is increased to account for inflation at a 2% annual rate. By doing this adjustment, the amount withdrawn on July 1, 2015, was $2,153. We call this scenario "5% withdrawal". Most of the time the withdrawal is made out of dividends and the surplus of dividends is reinvested by buying additional fund shares, but when dividends do not suffice to cover the withdrawal, fund shares are being sold.
In table 1, we show the performance of the portfolios under the 0% withdrawal rate. We list the total dollar return, the compound average growth rate (CAGR%), the maximum drawdown (maxDD%), the annual volatility (VOL%), the Sharpe ratio and the Sortino ratio.
Table 1. Performance of portfolios with 0% withdrawals
Total return 
CAGR 
maxDD 
VOL 
Sharpe 
Sortino 

Low volatility 
1,203% 
9.93% 
14.72% 
10.40% 
0.95 
1.35 
High Volatility 
1,310% 
10.25% 
29.86% 
13.77% 
0.74 
0.99 
As can be seen in table 1, the portfolio with high volatility target had a slightly higher return but much higher maximum drawdown. The riskadjusted return of the low volatility target is much better than the one for high volatility target. Based on this result, we think that using a low volatility target was the better strategy.
In table 2, we give the results for the 5% annual withdrawal scenario. Here we list the total excess return after the 5% annual withdrawals.
Table 2. Performance of portfolios with 5% annual withdrawals
Total excess return 
CAGR 
maxDD 
VOL 
Sharpe 
Sortino 

Low volatility 
397.70% 
6.09% 
19.53% 
10.51% 
0.58 
0.81 
High Volatility 
404.34% 
6.15% 
34.15% 
13.87% 
0.44 
0.59 
Both portfolios were capable of delivering an annual 5% withdrawal rate and still end up with sizable gains. Again, the portfolio with high volatility target had a slightly higher return but much higher maximum drawdown and higher volatility.
We performed additional simulations to determine what would have been the highest annual withdrawal rate that would still result in an equity no less than the initial capital. The low volatility target strategy with an annual withdrawal rate of 7% achieves a final equity of $175,500. The high volatility target with an annual withdrawal rate of 7% ends up with $141,900. This result is counterintuitive and it is caused by larger withdrawals when total equity of the high volatility portfolio was depressed. It demonstrates again that at critically high withdrawal rates, volatility of the returns counts. Without withdrawals, the level of volatility has much lower effect on the total returns.
In Figures 1 and 2 we show the equity curves of the portfolios.
Figure 1. Equity curves of the low volatility portfolio
Source: This chart is based on Excel calculations using the adjusted daily closing share prices of securities
Figure 2. Equity curves of the high volatility portfolio
Source: This chart is based on Excel calculations using the adjusted daily closing share prices of securities
Conclusion
The adaptive allocation strategy, especially with low volatility targets, performed well over a long time period that included two severe bear markets. The strategy with high volatility targets performed quite well during the 200809 bear market, but not so well during 200103 one. Both strategies allowed safe annual withdrawal rates of up to 7% of the initial investments.
Additional disclosure: The article was written for educational purposes and should not be considered as specific investment advice.
Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.
I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.