HDBR80T2 Returns versus Earnings Yield
Posted: Thu Dec 16, 2004 12:19 pm
These are the final balances of the HDBR80T2 portfolio at years 10, 14, 18, 22, 26 and 30 when there are no withdrawals and when the initial balances are all $100000.
The HDBR80T2 portfolio consists of 80% stocks and 20% TIPS at 2% interest. It is rebalanced annually. Expenses are 0.20%. All dividends are reinvested. There were no withdrawals. The initial balances were all $100000.
Curve fit equations
These are the equations for fitting a straight line to the final balances as a function of Professor Robert Shiller's P/E10.
P/E10 is the current value of the S&P500 index (in real dollars) divided by the average of the most recent ten years of (real) earnings.
Excel calculated the curve fit equations as a function of the percentage earnings yield 100E10/P.
The calculator uses dummy data with heavy stock market losses after 2002. I excluded all sequences that ended after 2002.
Curves from sequences beginning in 1923-1984
At year 10: Final balance = 1642800/[P/E10] + 58294 and R-squared equals 0.3702.
At year 14: Final balance = 3293200/[P/E10] - 10682 and R-squared equals 0.5666.
At year 18: Final balance = 4688200/[P/E10] - 45165 and R-squared equals 0.5553.
Curves from sequences beginning in 1923-1972
At year 22: Final balance = 5581300/[P/E10] - 31825 and R-squared equals 0.4879.
At year 26: Final balance = 5115800/[P/E10] + 90712 and R-squared equals 0.3359.
At year 30: Final balance = 5711000/[P/E10] + 175812 and R-squared equals 0.3211.
Predictability
Look at R-squared. We see that P/E10 (actually, 100E10/P) predicts a portfolio's return best in the medium-term.
There is considerable randomness in the short-term.
We cannot rely upon significant portfolio gains prior to year 18. [Put today's P/E10 of 28 or so into the equations. While you are at it, put in a P/E10 of 44 to see what happened at the top of the bubble (in December 1999).]
Valuations always matter. We can take best advantage of them in the medium term.
At a 4% earnings yield (with P/E10 = 25), the calculated balances at years 10, 14 and 18 are all very close at $124K, $121K and $142K respectively. They separate considerably as the earnings yield increases (and as P/E10 decreases). At a 10% earnings yield (and P/E10 =10), the calculated balances are $223K, $319K and $424K, differences of $96K and $105K. The downward scatter is about $100K. Even though the likelihood of a higher balance increases with time, there is considerable overlap until the earnings yield has increased to 6% (with P/E10 = 17).
By years 22, 26 and 30, the lines are almost parallel. This is can be seen by looking at their slopes (which are the numbers just before the "/[P/E10]"Â terms). They are all close to 55000. The calculated balances at a 4% earnings yield (with P/E10 = 25) are $201K, $295K and $394K respectively with differences of $94K and $99K. It is arguable as to whether it is worth waiting 4 years for the earnings yield to increase from 4% (with P/E10 = 25) to 6% (with P/E10 = 17). It is not worth waiting for 8 years.
Relationship with previous findings
In the New Tool we found that knowing a portfolio's total return at year 14 allowed us to estimate its 30-year Historical Surviving Withdrawal Rate with the greatest accuracy. R-squared was around 90%. When we waited much later to make estimates, R-squared was much lower. There was almost no variation of Historical Surviving Withdrawal Rates at year 30 based upon a portfolio's 30-year total return.
These results help to explain why. We have only a limited ability to estimate total returns as a function of earnings yield before year 10 and after year 22. Years 14 and 18 are best, but year 22 is also good.
Considering only the predictability of returns, we would expect the best estimate at year 14, but year 18 is almost as good. Historical Surviving Withdrawal Rates are most sensitive to the returns during the earliest years. This pulls the best number of years for predicting Historical Surviving Withdrawal Rates forward slightly, favoring 14 years over 18.
Have fun.
John R.
The HDBR80T2 portfolio consists of 80% stocks and 20% TIPS at 2% interest. It is rebalanced annually. Expenses are 0.20%. All dividends are reinvested. There were no withdrawals. The initial balances were all $100000.
Curve fit equations
These are the equations for fitting a straight line to the final balances as a function of Professor Robert Shiller's P/E10.
P/E10 is the current value of the S&P500 index (in real dollars) divided by the average of the most recent ten years of (real) earnings.
Excel calculated the curve fit equations as a function of the percentage earnings yield 100E10/P.
The calculator uses dummy data with heavy stock market losses after 2002. I excluded all sequences that ended after 2002.
Curves from sequences beginning in 1923-1984
At year 10: Final balance = 1642800/[P/E10] + 58294 and R-squared equals 0.3702.
At year 14: Final balance = 3293200/[P/E10] - 10682 and R-squared equals 0.5666.
At year 18: Final balance = 4688200/[P/E10] - 45165 and R-squared equals 0.5553.
Curves from sequences beginning in 1923-1972
At year 22: Final balance = 5581300/[P/E10] - 31825 and R-squared equals 0.4879.
At year 26: Final balance = 5115800/[P/E10] + 90712 and R-squared equals 0.3359.
At year 30: Final balance = 5711000/[P/E10] + 175812 and R-squared equals 0.3211.
Predictability
Look at R-squared. We see that P/E10 (actually, 100E10/P) predicts a portfolio's return best in the medium-term.
There is considerable randomness in the short-term.
We cannot rely upon significant portfolio gains prior to year 18. [Put today's P/E10 of 28 or so into the equations. While you are at it, put in a P/E10 of 44 to see what happened at the top of the bubble (in December 1999).]
Valuations always matter. We can take best advantage of them in the medium term.
At a 4% earnings yield (with P/E10 = 25), the calculated balances at years 10, 14 and 18 are all very close at $124K, $121K and $142K respectively. They separate considerably as the earnings yield increases (and as P/E10 decreases). At a 10% earnings yield (and P/E10 =10), the calculated balances are $223K, $319K and $424K, differences of $96K and $105K. The downward scatter is about $100K. Even though the likelihood of a higher balance increases with time, there is considerable overlap until the earnings yield has increased to 6% (with P/E10 = 17).
By years 22, 26 and 30, the lines are almost parallel. This is can be seen by looking at their slopes (which are the numbers just before the "/[P/E10]"Â terms). They are all close to 55000. The calculated balances at a 4% earnings yield (with P/E10 = 25) are $201K, $295K and $394K respectively with differences of $94K and $99K. It is arguable as to whether it is worth waiting 4 years for the earnings yield to increase from 4% (with P/E10 = 25) to 6% (with P/E10 = 17). It is not worth waiting for 8 years.
Relationship with previous findings
In the New Tool we found that knowing a portfolio's total return at year 14 allowed us to estimate its 30-year Historical Surviving Withdrawal Rate with the greatest accuracy. R-squared was around 90%. When we waited much later to make estimates, R-squared was much lower. There was almost no variation of Historical Surviving Withdrawal Rates at year 30 based upon a portfolio's 30-year total return.
These results help to explain why. We have only a limited ability to estimate total returns as a function of earnings yield before year 10 and after year 22. Years 14 and 18 are best, but year 22 is also good.
Considering only the predictability of returns, we would expect the best estimate at year 14, but year 18 is almost as good. Historical Surviving Withdrawal Rates are most sensitive to the returns during the earliest years. This pulls the best number of years for predicting Historical Surviving Withdrawal Rates forward slightly, favoring 14 years over 18.
Have fun.
John R.