Savings equals 87% off?

[johnhkc]

If something costs $10 per month every month on a regular basis over the next 45 years, the total cost is $5,400.
If I add in inflation (I used the CAGR of actual recorded inflation since 1973), it comes to $14,045.74.
But I don't want to pay $14K so I take $2,001.80 and shove it into an investment which grows at 5.773%. This generates the same $10 per month plus inflation over the 45 years.


Thus, $2K today equals $14K in a stream. 7/8 the cost is paid by investment returns and 1/8 is paid by my input.



Does this make sense?


(The 5.773% comes from an inflation-adjusted, recession-adjusted RoR. 9.826% nominal minus 4.053% general inflation = 5.773%)
The nominal rate is the CAGR of a 70/30 investment from 1973 onwards.

 

[Texas Proud]

Have not looked too closely but it seems you have inflation in both number... that does not make sense to me...


IOW, you stream takes into account the inflation so you do not need to add to get to $14K...

 

[Gumby]

Using the nominal return and inflation rate you stated, compounding monthly (i.e. - every month the bill goes up by the rate of inflation (4.053% annual/.33613% monthly, and every month you get paid interest at 9.826% annual/.78412% monthly), and assuming you put the money in at the beginning of month 1 and pay the bill at the end of month 1 and at the end of every subsequent month, you would need to deposit $2014.54 at the beginning of month 1 to support the monthly draw for all 45 years. You would have 36 cents remaining.

NB - this calculation assumes that inflation never varies and your return never varies, which is not a realistic assumption. A period of high inflation, low returns, or both, would deplete your asset prior to the end of the period, especially if these things occurred early in the period (known in retirement planning as the sequence of returns risk).

 

[johnhkc]

Have not looked too closely but it seems you have inflation in both number... that does not make sense to me...


IOW, you stream takes into account the inflation so you do not need to add to get to $14K...

The 5.773 real rate of growth is 9.826 nominal minus 4.053


Yes, I compensated for inflation by subtracting it from the nominal rate of return. That rate was 70/30 stock bond which is computed from a basket of mutual funds dating back to the 1930s. I used intermediate bond funds and a mix of growth and value equity funds. I don't know anything about bonds so maybe I messed up on that.

 

[johnhkc]

Using the nominal return and inflation rate you stated, compounding monthly (i.e. - every month the price goes up by the rate of inflation (4.053% annual/.33613% monthly, and every month you get paid interest at 9.826% annual/.78412% monthly), and assuming you put the money in at the beginning of month 1 and pay the bill at the end of month 1 and at the end of every subsequent month, you would need to deposit $2014.54 at the beginning of month 1 to support the monthly draw for all 45 years. You would have 36 cents remaining.

NB - this calculation assumes that inflation never varies and your return never varies, which is not a realistic assumption. A period of high inflation, low returns, or both, would deplete your asset prior to the end of the period, especially if these things occurred early in the period (known in retirement planning as the sequence of returns risk).

Is there a way to compensate for likely SORR by oversaving (like a downturn hedge)? I have a 33.33% "recession risk" item in my budget. It's 1/3 of all core expenses excluding health stuff which is a different fund due to wildly different inflation numbers.


Also, do you know if anyone on this site has any experience in insurance? I'd like to learn how premiums are calculated and what assumptions go into them.

 

[Gumby]

Is there a way to compensate for likely SORR by oversaving (like a downturn hedge)? I have a 33.33% "recession risk" item in my budget. It's 1/3 of all core expenses excluding health stuff which is a different fund due to wildly different inflation numbers.


Also, do you know if anyone on this site has any experience in insurance? I'd like to learn how premiums are calculated and what assumptions go into them.

I thought you might be going in this direction. You are probably wondering why the Trinity Study and Bengen use an inflation adjusted 4% annual safe withdrawal rate, instead of the 6% that you have calculated ($120 yr/$2000). It is precisely because inflation and returns vary.

 

[Dtail]

I thought you might be going in this direction. You are probably wondering why the Trinity Study and Bengen use an inflation adjusted 4% annual safe withdrawal rate, instead of the 6% that you have calculated ($120 yr/$2000). It is precisely because inflation and returns vary.

Yup, the SWR% if you take out the worst ~6 retire starting year scenarios is around 6.5%.

 

[Sunset]

Must be nice to live in a tax free world, wouldn't the earnings also be taxed ?

 

[johnhkc]

Must be nice to live in a tax free world, wouldn't the earnings also be taxed ?

Roth.

 

[pb4uski]

If something costs $10 per month every month on a regular basis over the next 45 years, the total cost is $5,400.
If I add in inflation (I used the CAGR of actual recorded inflation since 1973), it comes to $14,045.74.
But I don't want to pay $14K so I take $2,001.80 and shove it into an investment which grows at 5.773%. This generates the same $10 per month plus inflation over the 45 years.


Thus, $2K today equals $14K in a stream. 7/8 the cost is paid by investment returns and 1/8 is paid by my input.



Does this make sense?


(The 5.773% comes from an inflation-adjusted, recession-adjusted RoR. 9.826% nominal minus 4.053% general inflation = 5.773%)
The nominal rate is the CAGR of a 70/30 investment from 1973 onwards.

Pretty close. =PV((9.826%-4.053%)/12,45*12,-10)=$1,922.95

 

[pb4uski]

Must be nice to live in a tax free world, wouldn't the earnings also be taxed ?

Roth.

Or 0% bracket qualified income or combination of Roth and 0% qualified income.

 

[pb4uski]

I thought you might be going in this direction. You are probably wondering why the Trinity Study and Bengen use an inflation adjusted 4% annual safe withdrawal rate, instead of the 6% that you have calculated ($120 yr/$2000). It is precisely because inflation and returns vary.

John's hypothesis shows the danger of using averages.

Some of the reason is that the 4% rule is effectively based on historical bad case scenarios (not the worst case scenario because the 4% rule concedes that there will be some failures even at 4%... it was ~95% confidence level IIRC) so the average rate of return for those bad case scenarios was probably a lot less than 9.826%. Plus, the 9.826% is for a 100% equity portfolio and IIRC the 4% rule was based on a 60/40 AA or something along those lines.

A 6% WR may work "on average", but for many lower than average bad SORR they will fail dramatically and by definition 50% will be above average and 50% will be below average.

If I plug the OP's scenario into FIRECalc... $2,001,800 portfolio. $120,000 spending, 100% equities and 45 year time horizon... I get a 40% success rate... right on average would be 50% successes and 50% failures...change the AA to 60% equities and the success rate drops to 21%... change the spending to $80,000 (4%) and the success rate increases to 75.2%... change the time horizon to 30 years and the success rate increases to 95.8%... consistent with the 95% level of confidence for the 4% rule.

 

[Gumby]

Some of the reason is that the 4% rule is effectively based on historical bad case scenarios (not the worst case scenario because the 4% rule concedes that there will be some failures even at 4%... it was ~95% confidence level IIRC) so the average rate of return for those bad case scenarios was probably a lot less than 9.826%. Plus, the 9.826% is for a 100% equity portfolio and IIRC the 4% rule was based on a 60/40 AA or something along those lines.

A 6% WR will work on average, but for many historical bad SORR they will fail dramatically.

If I plug the OP's scenario into FIRECalc... $2,001,800 portfolio. $120,000 spending, 100% equities and 45 year time horizon... I get a 40% success rate... right on average would be 50% successes and 505 failures...change the AA to 60% equities and the success rate drops to 21%... change the spending to $80,000 (4%) and the success rate increses to 75.2%... change the time horizon to 30 years and the success rate increases to 95.8%... consistent with the 95% level of confidence for the 4% rule.

Thanks for following up with FIRECalc. Those results are what I would have expected.

 

[pb4uski]

Is there a way to compensate for likely SORR by oversaving (like a downturn hedge)? I have a 33.33% "recession risk" item in my budget. It's 1/3 of all core expenses excluding health stuff which is a different fund due to wildly different inflation numbers.


Also, do you know if anyone on this site has any experience in insurance? I'd like to learn how premiums are calculated and what assumptions go into them.

Google "rising equity glide path".

https://www.kitces.com/blog/should-...is-a-rising-equity-glidepath-actually-better/

 

[pb4uski]

P.S. It is so nice to have a non-COVID thread active!

 

[Gumby]

Plus, the 9.826% is for a 100% equity portfolio and IIRC the 4% rule was based on a 60/40 AA or something along those lines.

Just went back and noticed that John says his rate of 9.826% is for a 70/30 portfolio, not 100% equities. Your point about the Trinity Study using 60/40 is still well taken, but the difference due to asset allocation alone would be smaller.

 

[pb4uski]

Yup... I missed that... thanks. Doesn't make much difference.

John's hypothesis shows the danger of using averages.

Some of the reason is that the 4% rule is effectively based on historical bad case scenarios (not the worst case scenario because the 4% rule concedes that there will be some failures even at 4%... it was ~95% confidence level IIRC) so the average rate of return for those bad case scenarios was probably a lot less than 9.826%. Plus, the 9.826% is for a [-]100% equity[/-] 70/30 portfolio and IIRC the 4% rule was based on a 60/40 AA or something along those lines.

A 6% WR may work "on average", but for many lower than average bad SORR they will fail dramatically and by definition 50% will be above average and 50% will be below average.

If I plug the OP's scenario into FIRECalc... $2,001,800 portfolio. $120,000 spending, [-]100% equities[/-] 70/30 AA and 45 year time horizon... I get a 31% success rate... right on average would be 50% successes and 50% failures...[-]change the AA to 60% equities and the success rate drops to 21%...[/-] change the spending to $80,000 (4%) and the success rate increases to [-]75.2%[/-] 78.1%... change the time horizon to 30 years and the success rate increases to 95.8%... consistent with the 95% level of confidence for the 4% rule.