**Is the Raddr Methodology Analytically Valid?**dated Fri Oct 01, 2004.

http://nofeeboards.com/boards/viewtopic.php?t=2986

http://nofeeboards.com/boards/viewtopic ... 192#p24192

Proceeding on this theme, I have collected accumulation phase data.hocus2004 wrote:What makes this confusing is that SWR analysis has generally been designed to be applicable only to retirees. It is not appropriate for non-retirees to draw conclusions from SWR studies as to how to invest during the asset accumulation stage. Everyone understands this is so as a technical matter. The reality, however, is that many have improperly drawn inferences from SWR analyses as to how to invest during the accumulation stage. There are many posts in the archives showing this to be the case.

In our Safe Withdrawal Rate studies, we normally look at the effect of steady withdrawals during the distribution phase of a retirement account. In this case, I am reporting the effect of dollar cost averaging during the accumulation phase. This is the exact opposite of what one does during retirement.

I started with an initial balance of $1000. I deposited $1000 per year in subsequent years.

We are already aware of the prospects of a retirement account when the balance is left untouched at 15 and 30 years. These results compare switching portfolio allocations with sticking with a 100% stock portfolio. I investigated using 2.0% TIPS, 2.0% ibonds and commercial paper as the component other than stocks.

I used my latest Deluxe Calculator V1.1A07, a modified version of the Retire Early Safe Withdrawal Calculator Version 1.61, dated 7 November 2002. I started with an initial balance of $1000. I deposited $1000 per year by setting the initial withdrawal rate to (100%), that is, minus 100%. I set the expenses to 0.00%. I adjusted the deposits to match inflation as measured by the CPI-U. I rebalanced all portfolios annually.

I used the optimal switching program from previous studies for the distribution phase. The P/E10 thresholds were 9-12-21-24 and the corresponding stock allocations were 100-50-30-20-0%. I set the interest rate for TIPS and ibonds at 2.0%.

I have attached tables with the detailed results. The annualized real returns are all based on the initial $1000. These are the rates that would cause a $1000 portfolio to grow to the calculated final balance in the appropriate number of years, N = 15 or 30.

**30-Year Results**

With rare exceptions, an investor was much better off sticking with 100% stocks. Even with the exceptions, any advantage in favor of switching was small. The worst case was 1952. The all-stock allocation had a final balance of $45231. Switching with 2% TIPS, 2% ibonds and commercial paper produced balances of $53121, $53044 and $51289, respectively. Balances with 100% stocks frequently exceeded $100000. The best cases were $215873 in 1932 and $202734 in 1970. With switching, there were only a handful of final balances above $100000.

Ibonds produced the best results with switching.

Final balances were almost entirely independent of the percentage earnings yield 100E10/P. R-squared values were less than 0.01.

With 2% TIPS the relationship between the final balances with switching and with 100% stocks in the modern era (1923-1972) was y = 0.1303x+59011. By looking at a graph of the data, I noticed the 1952 results (approximately) define the lowest values of x and y. This means that there is a general penalty with switching because of this and the fact that the slope is less than 1.0.

Switching improved the worst case results only a small amount while taking away the upside.

**15-Year Results**

The behavior at 15 years was different in many respects.

The 100% stock portfolio's final balances increased with the percentage earnings yield 100E10/P. The equation was y = 2794.7x+9956.9 and R-squared was 0.3279. My visual estimates of the confidence limits are plus $20000 and minus $15000 at lower levels of earnings yield and minus $25000 at high levels of earnings yield. The slope shows that there is a general penalty with switching since it is less than 1.0.

With 2% TIPS and switching, the equation was y = 460.18x+21200 and R-squared was 0.1132. My visual estimates of the confidence limits are plus $8000 and minus $5000.

A plot of switching results with 2% TIPS versus using 100% stocks produces the equation y = 0.0733x+22442 with an R-squared of 0.0685. My visual estimates of the confidence limits are plus and minus $7000. Switching is superior when the final balances are low. If the final balance without switching exceeds $30000 or so, switching severely limits returns.

In essence, switching produces a non-trivial improvement when overall stock returns are low, but with a serious penalty on the upside. The entire decade of the 1960s produced better results with switching than without. The decade from 1925-1934 favored switching as well.

The percentage earnings yields [at the very start of a historical sequence] during which switching produced better results was typically between 4% and 6% (i.e., P/E10s of 17 and above).

The 15-Year results favor switching at today's valuations, but not at valuations typically found in the historical record.

Have fun.

John R.