Tapping into Portfolio Gains

Research on Safe Withdrawal Rates

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JWR1945
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Tapping into Portfolio Gains

Post by JWR1945 » Sat Oct 23, 2004 11:29 am

This survey shows us what happens if we remove a fraction of portfolio increases, but not any decreases, while making steady withdrawals.

I set up the latest version of my calculator, the Deluxe Version 1.1A07, to remove a percentage of year-to-year portfolio gains, but not losses, and determined 30-year Historical Surviving Withdrawal Rates (HSWR). I have summarized the results for 1921-1980.

The calculator is a modified version of the Retire Early Safe Withdrawal Calculator, Version 1.61, dated November 7, 2002. Use caution when looking at portfolios starting in 1973-1980. Be aware that the entries for 2003-2010 consist of dummy data with heavy losses. I have included those years because there are early failures in the decade of the 1970s.

I set up all portfolios to start with an initial balance of $100000. I set annual expenses at 0.20%. I rebalanced portfolios annually. I adjusted withdrawals to match inflation as measured by CPI-U. I reinvested all dividends and interest.

All withdrawal rates are presented as a percentage of a portfolio's initial balance.

Historical Surviving Withdrawal Rates are in increments of 0.1%. The number of failures is less than or equal to the amount shown when the withdrawal percentage is as indicated. In all cases, an increase of the withdrawal percentage by 0.1% causes the number of failures to increase to an amount higher than indicated.

All of these results are for the 1921-1980 time frame. There are 60 historical sequences. Six failures represent 10%. Twelve failures represent 20%.

These are the results when stocks take up 50% of the portfolio.

These are the results when using 0.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.7%.
2) For 6 failures, the withdrawal rate is 4.0%.
3) For 12 failures, the withdrawal rate is 4.2%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.4%.
2) For 6 failures, the withdrawal rate is 3.7%.
3) For 12 failures, the withdrawal rate is 3.9%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.2%.
2) For 6 failures, the withdrawal rate is 3.4%.
3) For 12 failures, the withdrawal rate is 3.6%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.1%.
3) For 12 failures, the withdrawal rate is 3.3%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.7%.
2) For 6 failures, the withdrawal rate is 2.9%.
3) For 12 failures, the withdrawal rate is 3.0%.

These are the results when using 1.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.9%.
2) For 6 failures, the withdrawal rate is 4.3%.
3) For 12 failures, the withdrawal rate is 4.5%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.6%.
2) For 6 failures, the withdrawal rate is 4.0%.
3) For 12 failures, the withdrawal rate is 4.2%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.4%.
2) For 6 failures, the withdrawal rate is 3.6%.
3) For 12 failures, the withdrawal rate is 3.8%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.1%.
2) For 6 failures, the withdrawal rate is 3.3%.
3) For 12 failures, the withdrawal rate is 3.5%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.9%.
2) For 6 failures, the withdrawal rate is 3.1%.
3) For 12 failures, the withdrawal rate is 3.2%.

These are the results when using 2.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.2%.
2) For 6 failures, the withdrawal rate is 4.5%.
3) For 12 failures, the withdrawal rate is 4.8%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.9%.
2) For 6 failures, the withdrawal rate is 4.2%.
3) For 12 failures, the withdrawal rate is 4.4%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.6%.
2) For 6 failures, the withdrawal rate is 3.8%.
3) For 12 failures, the withdrawal rate is 4.1%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.3%.
2) For 6 failures, the withdrawal rate is 3.6%.
3) For 12 failures, the withdrawal rate is 3.7%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.1%.
2) For 6 failures, the withdrawal rate is 3.3%.
3) For 12 failures, the withdrawal rate is 3.4%.

These are the results when using 3.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.5%.
2) For 6 failures, the withdrawal rate is 4.9%.
3) For 12 failures, the withdrawal rate is 5.1%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.1%.
2) For 6 failures, the withdrawal rate is 4.4%.
3) For 12 failures, the withdrawal rate is 4.7%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.8%.
2) For 6 failures, the withdrawal rate is 4.1%.
3) For 12 failures, the withdrawal rate is 4.3%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.6%.
2) For 6 failures, the withdrawal rate is 3.8%.
3) For 12 failures, the withdrawal rate is 4.0%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.3%.
2) For 6 failures, the withdrawal rate is 3.4%.
3) For 12 failures, the withdrawal rate is 3.6%.

These are the results when using 4.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.7%.
2) For 6 failures, the withdrawal rate is 5.1%.
3) For 12 failures, the withdrawal rate is 5.4%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.4%.
2) For 6 failures, the withdrawal rate is 4.7%.
3) For 12 failures, the withdrawal rate is 5.0%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.1%.
2) For 6 failures, the withdrawal rate is 4.3%.
3) For 12 failures, the withdrawal rate is 4.6%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.8%.
2) For 6 failures, the withdrawal rate is 4.0%.
3) For 12 failures, the withdrawal rate is 4.2%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.4%.
2) For 6 failures, the withdrawal rate is 3.6%.
3) For 12 failures, the withdrawal rate is 3.8%.

These are the results when using commercial paper.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.9%.
2) For 6 failures, the withdrawal rate is 4.4%.
3) For 12 failures, the withdrawal rate is 4.5%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.7%.
2) For 6 failures, the withdrawal rate is 4.0%.
3) For 12 failures, the withdrawal rate is 4.2%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.5%.
2) For 6 failures, the withdrawal rate is 3.7%.
3) For 12 failures, the withdrawal rate is 3.9%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.3%.
2) For 6 failures, the withdrawal rate is 3.4%.
3) For 12 failures, the withdrawal rate is 3.7%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.2%.
3) For 12 failures, the withdrawal rate is 3.3%.

These are the results when stocks take up 80% of the portfolio.

These are the results when using 0.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.7%.
2) For 6 failures, the withdrawal rate is 4.2%.
3) For 12 failures, the withdrawal rate is 4.6%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.3%.
2) For 6 failures, the withdrawal rate is 3.7%.
3) For 12 failures, the withdrawal rate is 4.1%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.3%.
3) For 12 failures, the withdrawal rate is 3.6%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.7%.
2) For 6 failures, the withdrawal rate is 2.9%.
3) For 12 failures, the withdrawal rate is 3.2%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.3%.
2) For 6 failures, the withdrawal rate is 2.5%.
3) For 12 failures, the withdrawal rate is 2.7%.

These are the results when using 1.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.8%.
2) For 6 failures, the withdrawal rate is 4.3%.
3) For 12 failures, the withdrawal rate is 4.7%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.4%.
2) For 6 failures, the withdrawal rate is 3.8%.
3) For 12 failures, the withdrawal rate is 4.2%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.1%.
2) For 6 failures, the withdrawal rate is 3.4%.
3) For 12 failures, the withdrawal rate is 3.7%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.8%.
2) For 6 failures, the withdrawal rate is 3.0%.
3) For 12 failures, the withdrawal rate is 3.3%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.4%.
2) For 6 failures, the withdrawal rate is 2.6%.
3) For 12 failures, the withdrawal rate is 2.8%.

These are the results when using 2.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.9%.
2) For 6 failures, the withdrawal rate is 4.4%.
3) For 12 failures, the withdrawal rate is 4.8%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.5%.
2) For 6 failures, the withdrawal rate is 3.9%.
3) For 12 failures, the withdrawal rate is 4.3%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.2%.
2) For 6 failures, the withdrawal rate is 3.5%.
3) For 12 failures, the withdrawal rate is 3.8%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.8%.
2) For 6 failures, the withdrawal rate is 3.1%.
3) For 12 failures, the withdrawal rate is 3.3%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.4%.
2) For 6 failures, the withdrawal rate is 2.6%.
3) For 12 failures, the withdrawal rate is 2.9%.

These are the results when using 3.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.0%.
2) For 6 failures, the withdrawal rate is 4.5%.
3) For 12 failures, the withdrawal rate is 4.9%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.6%.
2) For 6 failures, the withdrawal rate is 4.0%.
3) For 12 failures, the withdrawal rate is 4.4%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.2%.
2) For 6 failures, the withdrawal rate is 3.5%.
3) For 12 failures, the withdrawal rate is 3.9%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.9%.
2) For 6 failures, the withdrawal rate is 3.1%.
3) For 12 failures, the withdrawal rate is 3.4%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.5%.
2) For 6 failures, the withdrawal rate is 2.7%.
3) For 12 failures, the withdrawal rate is 2.9%.

These are the results when using 4.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.1%.
2) For 6 failures, the withdrawal rate is 4.6%.
3) For 12 failures, the withdrawal rate is 5.1%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.7%.
2) For 6 failures, the withdrawal rate is 4.1%.
3) For 12 failures, the withdrawal rate is 4.5%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.3%.
2) For 6 failures, the withdrawal rate is 3.6%.
3) For 12 failures, the withdrawal rate is 4.0%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.2%.
3) For 12 failures, the withdrawal rate is 3.5%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.6%.
2) For 6 failures, the withdrawal rate is 2.7%.
3) For 12 failures, the withdrawal rate is 3.0%.

These are the results when using commercial paper.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.9%.
2) For 6 failures, the withdrawal rate is 4.4%.
3) For 12 failures, the withdrawal rate is 4.8%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.5%.
2) For 6 failures, the withdrawal rate is 3.9%.
3) For 12 failures, the withdrawal rate is 4.2%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.1%.
2) For 6 failures, the withdrawal rate is 3.4%.
3) For 12 failures, the withdrawal rate is 3.8%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.8%.
2) For 6 failures, the withdrawal rate is 3.1%.
3) For 12 failures, the withdrawal rate is 3.3%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.4%.
2) For 6 failures, the withdrawal rate is 2.6%.
3) For 12 failures, the withdrawal rate is 2.9%.

These are the results when stocks take up 20% of the portfolio.

These are the results when using 0.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.4%.
2) For 6 failures, the withdrawal rate is 3.5%.
3) For 12 failures, the withdrawal rate is 3.6%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.3%.
2) For 6 failures, the withdrawal rate is 3.4%.
3) For 12 failures, the withdrawal rate is 3.5%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.2%.
2) For 6 failures, the withdrawal rate is 3.3%.
3) For 12 failures, the withdrawal rate is 3.4%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.1%.
2) For 6 failures, the withdrawal rate is 3.2%.
3) For 12 failures, the withdrawal rate is 3.3%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.0%.
3) For 12 failures, the withdrawal rate is 3.2%.

These are the results when using 1.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.9%.
2) For 6 failures, the withdrawal rate is 4.0%.
3) For 12 failures, the withdrawal rate is 4.0%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.7%.
2) For 6 failures, the withdrawal rate is 3.8%.
3) For 12 failures, the withdrawal rate is 3.9%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.5%.
2) For 6 failures, the withdrawal rate is 3.6%.
3) For 12 failures, the withdrawal rate is 3.8%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.4%.
2) For 6 failures, the withdrawal rate is 3.5%.
3) For 12 failures, the withdrawal rate is 3.6%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.3%.
2) For 6 failures, the withdrawal rate is 3.4%.
3) For 12 failures, the withdrawal rate is 3.5%.

These are the results when using 2.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.3%.
2) For 6 failures, the withdrawal rate is 4.4%.
3) For 12 failures, the withdrawal rate is 4.5%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.1%.
2) For 6 failures, the withdrawal rate is 4.2%.
3) For 12 failures, the withdrawal rate is 4.3%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.9%.
2) For 6 failures, the withdrawal rate is 4.0%.
3) For 12 failures, the withdrawal rate is 4.1%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.8%.
2) For 6 failures, the withdrawal rate is 3.9%.
3) For 12 failures, the withdrawal rate is 4.0%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.6%.
2) For 6 failures, the withdrawal rate is 3.7%.
3) For 12 failures, the withdrawal rate is 3.8%.

These are the results when using 3.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.7%.
2) For 6 failures, the withdrawal rate is 4.9%.
3) For 12 failures, the withdrawal rate is 5.0%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.5%.
2) For 6 failures, the withdrawal rate is 4.6%.
3) For 12 failures, the withdrawal rate is 4.8%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.3%.
2) For 6 failures, the withdrawal rate is 4.4%.
3) For 12 failures, the withdrawal rate is 4.6%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.1%.
2) For 6 failures, the withdrawal rate is 4.2%.
3) For 12 failures, the withdrawal rate is 4.4%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.9%.
2) For 6 failures, the withdrawal rate is 4.0%.
3) For 12 failures, the withdrawal rate is 4.2%.

These are the results when using 4.0% TIPS.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 5.2%.
2) For 6 failures, the withdrawal rate is 5.4%.
3) For 12 failures, the withdrawal rate is 5.5%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 5.0%.
2) For 6 failures, the withdrawal rate is 5.1%.
3) For 12 failures, the withdrawal rate is 5.2%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.7%.
2) For 6 failures, the withdrawal rate is 4.8%.
3) For 12 failures, the withdrawal rate is 5.0%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.5%.
2) For 6 failures, the withdrawal rate is 4.6%.
3) For 12 failures, the withdrawal rate is 4.8%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 4.3%.
2) For 6 failures, the withdrawal rate is 4.4%.
3) For 12 failures, the withdrawal rate is 4.5%.

These are the results when using commercial paper.
When none of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.4%.
3) For 12 failures, the withdrawal rate is 3.9%.
When 25% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.3%.
3) For 12 failures, the withdrawal rate is 3.8%.
When 50% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.2%.
3) For 12 failures, the withdrawal rate is 3.8%.
When 75% of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 3.0%.
2) For 6 failures, the withdrawal rate is 3.1%.
3) For 12 failures, the withdrawal rate is 3.7%.
When all of the portfolio gains are removed:
1) For 0 failures, the withdrawal rate is 2.9%.
2) For 6 failures, the withdrawal rate is 3.0%.
3) For 12 failures, the withdrawal rate is 3.5%.

Analysis

I will focus on portfolios containing 2.0% TIPS. They are most representative of what is available today.

With 50% stocks and 50% TIPS at a 2.0% interest rate, the Historical Surviving Withdrawal Rates with 0%-10%-20% failures (i.e., 0-6-12 out of 60) are:
1) 4.2%-4.5%-4.8% when none of the portfolio gains are removed.
2) 3.9%-4.2%-4.4% when 25% of the portfolio gains are removed.
3) 3.6%-3.8%-4.1% when 50% of the portfolio gains are removed.
4) 3.3%-3.6%-3.7% when 75% of the portfolio gains are removed.
5) 3.1%-3.3%-3.4% when all portfolio gains are removed.

With 80% stocks and 20% TIPS at a 2.0% interest rate, the Historical Surviving Withdrawal Rates with 0%-10%-20% failures (i.e., 0-6-12 out of 60) are:
1) 3.9%-4.4%-4.8% when none of the portfolio gains are removed.
2) 3.5%-3.9%-4.3% when 25% of the portfolio gains are removed.
3) 3.2%-3.5%-3.8% when 50% of the portfolio gains are removed.
4) 2.8%-3.1%-3.3% when 75% of the portfolio gains are removed.
5) 2.4%-2.6%-2.9% when all portfolio gains are removed.

With 20% stocks and 80% TIPS at a 2.0% interest rate, the Historical Surviving Withdrawal Rates with 0%-10%-20% failures (i.e., 0-6-12 out of 60) are:
1) 4.3%-4.4%-4.5% when none of the portfolio gains are removed.
2) 4.1%-4.2%-4.3% when 25% of the portfolio gains are removed.
3) 3.9%-4.0%-4.1% when 50% of the portfolio gains are removed.
4) 3.8%-3.9%-4.0% when 75% of the portfolio gains are removed.
5) 3.6%-3.7%-3.8% when all portfolio gains are removed.

Observe that the spread of the results increases as the percentage of stocks increases.

When seeking the highest levels of safety, withdrawing 25% of portfolio gains in a 50% stocks / 50% TIPS portfolio provides a withdrawal rate similar to that of an 80% stocks / 20% TIPS portfolio when no portfolio gains removed.

When seeking the highest levels of safety, withdrawing 50% of the portfolio gains from a 50% stocks / 50% TIPS portfolio provides a withdrawal rate similar to withdrawing 25% of the portfolio gains of an 80% stocks / 20% TIPS portfolio.

Comparisons at a 10% failure rate and a 20% failure rate are similar.

Caution

These calculations provide Historical Surviving Withdrawal Rates, which differ from Safe Withdrawal Rates. Current Safe Withdrawal Rates are considerably lower than those shown here because of today's high valuations.

Have fun.

John R.

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