[Calculating future Social Security benefits: How do I adjust the discount rate?]

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[Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by afan » Sun Aug 05, 2018 8:12 am

[Moved into a new thread from: "Open Social Security" calculator: feature requests, bug reports, etc --admin LadyGeek]

This is not a feature request or bug report, but I don't know where else to bring it up.

I think one needs to consider that the 20 TIPS may not be the appropriate discount rate. For TIPS, one has an explicit promise from the federal government to pay the interest and the principal. From SS one has a promise to pay current benefits, but future benefits are slated to go down absent some sort of action by Congress. No one knows what, if any, action Congress might take, or when. The point of my post is not to speculate about what those changes might be. It is simply to point out that there is an uncertainty built into the structure of the program.

That uncertainty argues for a higher discount rate than TIPS. I don't know how much higher, but the optimal claiming strategy for a benefit to be paid over decades is highly dependent on the discount rate.

Mike Piper does discuss these issues in his post.
https://obliviousinvestor.com/the-polit ... -until-70/

In it, he argues that some of the potential changes in SS would not affect the claiming decision. However, some of the changes could have a major effect of lower future benefits.

Without speculating here about what future changes might occur, my question is "How should one adjust the discount rate, taking into account the risk of possible future benefits reductions?"

Looking for thoughts on this subject.
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Re: "Open Social Security" calculator: feature requests, bug reports, etc

Post by ObliviousInvestor » Sun Aug 05, 2018 9:36 am

afan,

I think that's a great topic for discussion, and I too would be interested to hear other people's thoughts. Would you consider making it a new thread though, as it is not directly related to the bugs/features discussion for the calculator but more broadly about Social Security decisions in general? (You'd probably get more replies in a new thread also, as opposed to the question being buried on page 3 here.)
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by LadyGeek » Sun Aug 05, 2018 11:37 am

^^^ I got it.

afan - If you want to change the thread title further, just edit the Subject: line in post #1.

As a reminder, this is a "no politics" forum. Speculation on the "future of Social Security" requires a change in legislation and is therefore a political discussion and off-topic. See: Politics and Religion
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by tfb » Sun Aug 05, 2018 11:48 am

afan wrote:
Sun Aug 05, 2018 8:12 am
Without speculating here about what future changes might occur, my question is "How should one adjust the discount rate, taking into account the risk of possible future benefits reductions?"
There's already an item on the to-do list for enhancing the Open Social Security tool:
5) Option to include an assumption with regard to "trust fund will be depleted as of [date] and benefits will be cut by [percentage]"
When implemented, wouldn't that take care of the possible future benefits reductions without changing the discount rate?
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by afan » Sun Aug 05, 2018 12:01 pm

Completely understand and agree that speculation about future legislation is not up for discussion.

This topic is about choosing a discount rate when the cash flows are not guaranteed. In this unusual case, the institution that will be paying the money has essentially a perfect ability to pay. But the terms of how much it pays are expected to change, in an uncertain way.

Using the calculator it is clear that increasing the discount rate by half a percent changes our optimal claiming ages by several years. That means the discount rate is so important that it is worth worrying about.

It also calls for reevaluating periodically as the discount rate changes.

For now, I have used half a percent as my add to the discount rate to reflect this uncertainty, but this is an arbitrary figure.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by afan » Sun Aug 05, 2018 12:06 pm

tfb wrote:
Sun Aug 05, 2018 11:48 am
afan wrote:
Sun Aug 05, 2018 8:12 am
Without speculating here about what future changes might occur, my question is "How should one adjust the discount rate, taking into account the risk of possible future benefits reductions?"
There's already an item on the to-do list for enhancing the Open Social Security tool:
5) Option to include an assumption with regard to "trust fund will be depleted as of [date] and benefits will be cut by [percentage]"

When implemented, wouldn't that take care of the possible future benefits reductions without changing the discount rate?
That begins to address the question, but, without going into off limits details, there are other potential changes that one has to consider. Right now everyone knows that the trust fund will be depleted if there are no changes to the law. The trustees estimate when that will happen. They update this regularly.

One could enter the current estimate of the depletion date without taking care of the rest of the issues.

This is really about how far to increase the discount rate to reflect the uncertainty.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by FiveK » Sun Aug 05, 2018 12:38 pm

afan wrote:
Sun Aug 05, 2018 8:12 am
Mike Piper does discuss these issues in his post.
https://obliviousinvestor.com/the-polit ... -until-70/
Claiming Social Security Early to Invest It: What Rate of Return (Discount Rate) Should We Assume? — Oblivious Investor may be another pertinent post to reference.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by FiveK » Sun Aug 05, 2018 1:16 pm

In the article linked in the previous post, one finds (emphasis added) "...when deciding whether to delay Social Security or claim it now and invest the money, you have to make some assumption about the rate of return that you would earn on invested benefits."

That seems the correct way to say it, but there is an interesting difference between the word "would" and the word "should".

For example, what of people who have a 100% stock asset allocation? We can debate whether they should have such an allocation, but given that they do, what then should they assume about the rate of return they would earn on invested benefits?

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by afan » Sun Aug 05, 2018 1:33 pm

FiveK wrote:
Sun Aug 05, 2018 1:16 pm

For example, what of people who have a 100% stock asset allocation? We can debate whether they should have such an allocation, but given that they do, what then should they assume about the rate of return they would earn on invested benefits?
The standard reasoning would say they should assume a rate of return they think is expected from such a portfolio, then apply a discount rate that is high enough to reflect the high risk of 100% stock.

Predicting stock returns even over long term, is difficult and the results vary a lot. So one should pick a higher discount rate.

The discount rate for SS claiming is almost certainly lower than for a stock portfolio but I don't know how much lower. Even increasing the rate by half a percent has a huge effect on the NPV and optimal age.

For us, as I assume for many bogleheads, the risk of having lower payments in advanced old age is not catastrophic. Social Security would be a nice addition to RMDs and income from the taxable portfolio. Losing SS altogether would not mean living on the street or eating dog food. Thus, it is not like life insurance. As Piper points out, for life insurance the expected value is negative but the financial consequences of an uninsured parent dying young could be catastrophic. So you buy insurance.

This is a straight NPV problem. It is just a matter of of finding the correct range of discount rates to consider.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Sun Aug 05, 2018 3:30 pm

It's an interesting question, but a tricky one.

Social Security clearly has a degree of political risk. And TIPS clearly do not carry that same risk. But it's not easy to quantify via discount rates.

On the other hand, delaying Social Security provides a degree of risk reduction that TIPS do not provide (via the longevity insurance aspect).

But even that is complicated, because the value of such risk reduction varies from one person to another. For example, it's common to see Bogleheads who face virtually no risk of portfolio depletion, given their portfolio size and desired spending level. For them, the risk reduction value is trivial. For other Bogleheads, it will be quite valuable.

I think a range of answers would be reasonable, with yields for TIPS of a similar duration probably being somewhere in the middle-ish portion of that range. But I find it hard to be much more concrete than that.

I do think, though, that people who use stock-like returns for the discount rate -- or even returns one would expect from a 60/40 balanced fund for example -- are usually doing a mistaken analysis. The answer in that case is almost always, "it reduces my expected result!" (Duh. "Expected" results do generally worsen when swapping high-risk/expected-return assets for low-risk/expected-return assets.)

The much more interesting (and usually more applicable) question is whether to spend down one's bond holdings to delay Social Security.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by afan » Sun Aug 05, 2018 4:12 pm

ObliviousInvestor wrote:
Sun Aug 05, 2018 3:30 pm
It's an interesting question, but a tricky one.
...
On the other hand, delaying Social Security provides a degree of risk reduction that TIPS do not provide (via the longevity insurance aspect).

But even that is complicated, because the value of such risk reduction varies from one person to another. For example, it's common to see Bogleheads who face virtually no risk of portfolio depletion, given their portfolio size and desired spending level. For them, the risk reduction value is trivial. For other Bogleheads, it will be quite valuable.

I think a range of answers would be reasonable, with yields for TIPS of a similar duration probably being somewhere in the middle-ish portion of that range. But I find it hard to be much more concrete than that.
This gets at the question. I am finding it hard to see how the discount rate could be lower than that for TIPS. Is that because you reduce your risk of running out of money?

For those who have little risk of that, it seems one should value that insurance aspect as zero and not have it influence the discount rate at all. I agree the value of that longevity insurance could be meaningful to some people, so they would end up with a different discount rate for SS. The only way to incorporate that insurance value in this calculation is by reducing the discount rate, but I have no idea by how much.

I agree that the expected return for stocks is not a reasonable discount rate for SS. To estimate the NPV of a stock portfolio, one should use a high discount rate to reflect the high level of risk. It would not make sense to use the same discount rate for SS, even with its uncertainties. Different projects, different risks, different discount rates.

Age at death- no one who is not at death's door knows this. But one can get pretty good estimates from actuarial tables and tweak them based on private knowledge of one's own health. The estimate will be far from perfect, but at least it is quantitative.

I am grateful to the Oblivious Investor for this tool. It highlights that the biggest factor for us is not when we plan to retire (after 70). It is not the unknowable age at death. The big factor is discount rates.

For now, I am using discount rates of 1.0-2.0 percent. But the range from the 20 yr TIPS rate, 0.92% as I write, and 1.5 or 2% produces very different conclusions about when to claim. And that is only based on today's rates. Let the TIPS rate vary and the problem gets even worse.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by LadyGeek » Sun Aug 05, 2018 4:31 pm

How do commercial companies calculate the discount rate when they make their "lump sum or annuity" pension payment options to employees who are about to retire? Are they basing it on company performance or something else?

I'm just wondering if there's anything in common that may have been overlooked.

==================
To new investors, the basics of "NPV" is in the wiki: Comparing investments
The first important property of present value is that the higher the interest rate (or discount rate[3]), the lower the present price.[4]

3. Calculating the present value is also referred to as discounting. The interest rate is referred to as the discount rate and present value is also known as discounted value.
We want to estimate what the value of Social Security would be today (Present Value) - what interest rate should be used?

The "Net" part of NPV means that more than one cash flow is included in the calculation.

Also google for "Time value of money" calculations. (If I got anything wrong, please correct me.)
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by afan » Sun Aug 05, 2018 7:35 pm

Same broad principles, but the insurance company faces a simpler problem. They don't care about the life expectancy of any one person or couple, which is hard to predict. All they need to know is the actuarial probabilities for the population of people to whom the sell annuities. They know what amounts they are promising to pay. They know, on average which is all that matters, how long those commitments will last.

The situation for an individual is more like the government offering to buy an annuity from the insurance company while reserving the right to change the terms at some point in the future.

Imagine the government decided to hire an insurance company to manage SS. Social Security taxes would go to the company and the insurer would pay the benefits. They would be given the demographics of the population, the promises currently made, the unlimited COLA provisions and the "premiums" being charged.

The insurance company would quickly figure out that this was unsustainable. The company, hearing that there were no plans at this point of how to get out of the problem would decline to bid on the job. At least, I find it hard to see how they could. The uncertainty would make it impossible to price.

At this point estimating a discount rate is guess work. "Substantially more than TIPS" is as far as I can get.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Sun Aug 05, 2018 8:22 pm

afan wrote:
Sun Aug 05, 2018 4:12 pm
ObliviousInvestor wrote:
Sun Aug 05, 2018 3:30 pm
It's an interesting question, but a tricky one.
...
On the other hand, delaying Social Security provides a degree of risk reduction that TIPS do not provide (via the longevity insurance aspect).

But even that is complicated, because the value of such risk reduction varies from one person to another. For example, it's common to see Bogleheads who face virtually no risk of portfolio depletion, given their portfolio size and desired spending level. For them, the risk reduction value is trivial. For other Bogleheads, it will be quite valuable.

I think a range of answers would be reasonable, with yields for TIPS of a similar duration probably being somewhere in the middle-ish portion of that range. But I find it hard to be much more concrete than that.
This gets at the question. I am finding it hard to see how the discount rate could be lower than that for TIPS. Is that because you reduce your risk of running out of money?
Yes, exactly. For most people, it's a very significant risk reduction in that regard.

I agree, though, that for people for whom the longevity protection is irrelevant, the discount rate should be higher than TIPS yields.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by LadyGeek » Sun Aug 05, 2018 8:29 pm

afan wrote:
Sun Aug 05, 2018 7:35 pm
Same broad principles, but the insurance company faces a simpler problem. They don't care about the life expectancy of any one person or couple, which is hard to predict. All they need to know is the actuarial probabilities for the population of people to whom the sell annuities. They know what amounts they are promising to pay. They know, on average which is all that matters, how long those commitments will last.

The situation for an individual is more like the government offering to buy an annuity from the insurance company while reserving the right to change the terms at some point in the future.

Imagine the government decided to hire an insurance company to manage SS. Social Security taxes would go to the company and the insurer would pay the benefits. They would be given the demographics of the population, the promises currently made, the unlimited COLA provisions and the "premiums" being charged.

The insurance company would quickly figure out that this was unsustainable. The company, hearing that there were no plans at this point of how to get out of the problem would decline to bid on the job. At least, I find it hard to see how they could. The uncertainty would make it impossible to price.

At this point estimating a discount rate is guess work. "Substantially more than TIPS" is as far as I can get.
That's helpful, thanks.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by FiveK » Sun Aug 05, 2018 8:48 pm

ObliviousInvestor wrote:
Sun Aug 05, 2018 8:22 pm
I agree, though, that for people for whom the longevity protection is irrelevant, the discount rate should be higher than TIPS yields.
And for those looking to do Roth conversions at lower tax rates, when looking at overall finances it may be better to delay SS benefits. Might be difficult to capture that effect in a discount rate, other than qualitatively by decreasing whatever the discount rate should be without the Roth conversion effects.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Wed Aug 08, 2018 1:38 pm

tfb wrote:
Sun Aug 05, 2018 11:48 am
afan wrote:
Sun Aug 05, 2018 8:12 am
Without speculating here about what future changes might occur, my question is "How should one adjust the discount rate, taking into account the risk of possible future benefits reductions?"
There's already an item on the to-do list for enhancing the Open Social Security tool:
5) Option to include an assumption with regard to "trust fund will be depleted as of [date] and benefits will be cut by [percentage]"
When implemented, wouldn't that take care of the possible future benefits reductions without changing the discount rate?
This option is now available on the calculator, for anybody interested in testing how it affects their planning:
https://opensocialsecurity.com/

(Check the "advanced options" checkbox at the top. Then the related input will be below the input for discount rate.)
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by LadyGeek » Wed Aug 08, 2018 2:15 pm

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by dconrath » Wed Aug 08, 2018 2:26 pm

Mike:

Thanks again for the great work as it is very helpful!

One thing I noticed that you may want to adjust.

When I run using the "Advanced Options" and select "Yes" for "Assume that Social Security benefits will be cut in the future?" as expected the primary results are impacted.

However, when I subsequently run the "Test an alternative claiming strategy", it does not seem to use the reduced social security benefits that would be expected based on the "yes" selection, but instead I still get the same results I would have if I had selected "no".

I hope the explanation of this observation is clear to you.

Thanks again.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Wed Aug 08, 2018 2:34 pm

dconrath wrote:
Wed Aug 08, 2018 2:26 pm
Mike:

Thanks again for the great work as it is very helpful!

One thing I noticed that you may want to adjust.

When I run using the "Advanced Options" and select "Yes" for "Assume that Social Security benefits will be cut in the future?" as expected the primary results are impacted.

However, when I subsequently run the "Test an alternative claiming strategy", it does not seem to use the reduced social security benefits that would be expected based on the "yes" selection, but instead I still get the same results I would have if I had selected "no".

I hope the explanation of this observation is clear to you.

Thanks again.
Hmm. Thank you for bringing this up. In testing it myself, it is accounting for the assumed benefit cut in the "alternative strategy" output. (For example if above I entered that benefits would be cut by 50% -- to make the math easy -- in 2034, the output in the alternative strategy table does include a 50% benefit cut beginning in 2034.)

Perhaps could you provide the inputs you used?
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by galeno » Wed Aug 08, 2018 2:40 pm

So????????????

What discount rate should we use?

When I learned finance in the 1990s we always used 6%. That WAS the yield of a 10 yr USA treasury bond.

Today's SEC Yield on the 10 yr USA treasury note is 2.97%.

Should we use 2.97% as the discount rate for the NPV calculation of SS benefits?
AA = 40/55/5. Expected CAGR = 3.8%. GSD (5y) = 6.2%. USD inflation (10 y) = 1.8%. AWR = 4.0%. TER = 0.4%. Port Yield = 2.82%. Term = 33 yr. FI Duration = 6.0 yr. Portfolio survival probability = 95%.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by galeno » Wed Aug 08, 2018 2:49 pm

The yield on 20 yr TIPS is 0.92%.

So should we use 2.97% or 0.92% as the discount rate for a stream of SS monthly payments?

Also the term should be noted. 30 yr? 25 yr? 20 yr?
AA = 40/55/5. Expected CAGR = 3.8%. GSD (5y) = 6.2%. USD inflation (10 y) = 1.8%. AWR = 4.0%. TER = 0.4%. Port Yield = 2.82%. Term = 33 yr. FI Duration = 6.0 yr. Portfolio survival probability = 95%.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by dconrath » Wed Aug 08, 2018 2:56 pm

Mike: I tried again with the "advanced options" and the "reduced social security" and then the "Test an alternative claiming strategy" and it worked. So I think it was user error :-)

I think what I did differently is that previously I was reusing a previous calculation where I was not selecting reduced social security and then performed the alternate strategy. Then in the same web page I changed the upper selection to reduce social security, hit the upper submit and then either didn't hit or missed the lower submit button for the alternate strategy, and that alternate strategy was left the same as originally calculated.

Sorry for any confusion my feedback may have caused.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Wed Aug 08, 2018 2:58 pm

dconrath wrote:
Wed Aug 08, 2018 2:56 pm
Mike: I tried again with the "advanced options" and the "reduced social security" and then the "Test an alternative claiming strategy" and it worked. So I think it was user error :-)

I think what I did differently is that previously I was reusing a previous calculation where I was not selecting reduced social security and then performed the alternate strategy. Then in the same web page I changed the upper selection to reduce social security, hit the upper submit and then either didn't hit or missed the lower submit button for the alternate strategy, and that alternate strategy was left the same as originally calculated.
Ahh.. OK. :sharebeer
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by galeno » Wed Aug 08, 2018 5:40 pm

I used the calculator below:

https://www.bankrate.com/calculators/re ... lator.aspx

Term of 83-61=22 yr for me and 85-61=25 yr for my wife. Discount rate used is 0.92% and 2.97%. COLA of 2.0%. Retire at age 62. Monthly benefit $1000.

Got $258K and $207K respectively.
AA = 40/55/5. Expected CAGR = 3.8%. GSD (5y) = 6.2%. USD inflation (10 y) = 1.8%. AWR = 4.0%. TER = 0.4%. Port Yield = 2.82%. Term = 33 yr. FI Duration = 6.0 yr. Portfolio survival probability = 95%.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by afan » Thu Aug 09, 2018 10:22 am

Yes, higher discount rates will lead to lower NPV.
The alternative to raising the discount rate would be assuming one knew what the changes will be and when they will come. Calculate the optimal claiming strategy and the resulting NPV. Then change the assumptions and repeat. With the addition to the calculator this is now easy to do.

I think it will illustrate that these assumptions about future benefits will dominate the claiming strategy for most people who can afford to delay SS.

They will dominate it so severely that the "current law" assumptions will be meaningless.

One would have a range of strategies that depend on different assumptions about future changes. One would have no idea what probabilities to assign to those assumptions.

This would be an interesting exercise but it would be effectively the same as varying the discount rate. The more uncertainty you dial in about the future the higher discount rate you would use.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by siamond » Sun Jun 09, 2019 9:34 am

FiveK wrote:
Sun Aug 05, 2018 12:38 pm
afan wrote:
Sun Aug 05, 2018 8:12 am
Mike Piper does discuss these issues in his post.
https://obliviousinvestor.com/the-polit ... -until-70/
Claiming Social Security Early to Invest It: What Rate of Return (Discount Rate) Should We Assume? — Oblivious Investor may be another pertinent post to reference.
Although I understand where Mike is coming from, I don't think this is quite right. The discount rate should be the expected return (in the statistical sense) of one's AA, over the full retirement period. The money you keep invested by getting SS income (hence not having to withdraw such $$ from your savings) is invested in your portfolio (DUH!). One *may* decide to adjust the bond (and/or TIPS) exposure based on SS benefits as Mike is suggesting, but one doesn't have to. We all have a web of highly personal reasons for setting our AA and the level of SS benefits is only one input among many. What matters is the conclusion (AA) you derive from your overall situation. Personally, there is just no way I would change my AA whether I claim SSA at FRA or at 70...

Please note that I am not necessarily suggesting to change the current default value in the calculator (even though I really don't like it!), but those of us with PV knowledge may want to (should?) proceed a bit differently. Note that the calculator's recommendations are highly sensitive to the discount rate, just playing with a range of 'reasonable' values with my own situation, the calculator suggested to claim at 62 in some cases or postpone until 70 in other cases...

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Sun Jun 09, 2019 10:11 am

siamond wrote:
Sun Jun 09, 2019 9:34 am
Although I understand where Mike is coming from, I don't think this is quite right. The discount rate should be the expected return (in the statistical sense) of one's AA, over the full retirement period. The money you keep invested by getting SS income (hence not having to withdraw such $$ from your savings) is invested in your portfolio (DUH!).
siamond, I imagine you know by now that I respect your intelligence, input, and so on.

I am going to respectfully suggest here that you are not fully understanding what I'm saying.

When you use the expected return of your overall portfolio as the discount rate, you will often conclude, "I should not spend down my overall portfolio in order to delay Social Security." This is what you are getting at in the above quote. And it is a valid and useful conclusion.

But there's another question you still have to ask yourself. You have to ask, "should I spend down one part of my portfolio, in order to delay Social Security?" -- because you have that option as well. And when you consider the option to spend down just bonds, the answer is often, "yes, I should spend down my bonds in order to delay Social Security."

In fact, it's super common that for many people the answer to the one question (spend down overall portfolio?) is "no" and the answer to the other question (spend down bonds?) is "yes." That's why most analyses actually begin by asking the second question.

When we talk about delaying Social Security, the default assumption is that we're talking about spending down fixed-income in order to delay Social Security -- because more often than not, if we're going to spend down something in order to delay (or annuitize in general), that's what we want to spend down. That's why the calculator defaults to a low discount rate (while still offering the option to adjust the discount rate, in order to ask other questions).

In other words, I would rephrase the following quote:
siamond wrote:
Sun Jun 09, 2019 9:34 am
One *may* decide to adjust the bond (and/or TIPS) exposure based on SS benefits as Mike is suggesting, but one doesn't have to.
...as "one *may* decide not to adjust the bond (and/or TIPS) exposure, but one doesn't have to."
Last edited by ObliviousInvestor on Sun Jun 09, 2019 10:18 am, edited 1 time in total.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Sun Jun 09, 2019 10:18 am

The following paper from David Blanchett and Michael Finke may be of interest:
https://www.onefpa.org/journal/Pages/NO ... ation.aspx
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by siamond » Sun Jun 09, 2019 11:07 am

ObliviousInvestor wrote:
Sun Jun 09, 2019 10:11 am
I am going to respectfully suggest here that you are not fully understanding what I'm saying. [...]
Hey Mike, first off, all respect to you. We had an entire chapter meeting yesterday (Metro-Boston) dedicated to Social Security. References & compliments about the work you've been doing over the years kept coming every few minutes. One presenter used numerous slides you were kind enough to share with me a few weeks ago, thanks a lot for that, this put the meeting on the right track.

Back to the topic... thanks for elaborating on your thinking. What you said is actually consistent with the understanding I had of your line of reasoning. But what I was trying to convey is that you may be putting the cart in front of the horses (and I insist on the plural form! :D).

SOME people may decide to spend bonds to assist their strategy of delaying social security (in other words, to have the SS delaying strategy drive a change in their AA), granted. OTHER people (including myself), driven by a set of personal reasons which go way beyond SS considerations, may decide to NOT do so or to do something different. That is just a simple hard fact, we're all making our own AA choices, driven by many personal factors.

Now in presence of such variability, what is the thing that stays constant? It is the simple fact that money not withdrawn from one's portfolio stays invested in said portfolio (with the AA chosen by the owner)... Therefore the discount rate should be the AA's expected return. Please note that a proper PV assessment should actually take in account multiple cash flows (e.g. SS, Pension, SPIA, inheritance, name it), and the same principle applies.

I know this topic of choosing the proper PV rate is a mind bender. I circled around it myself for quite a while, so please believe me, I understand the struggle. My mind finally cleared up (and my math became consistent) when I made sure to use a discount rate directly associated with the way $$ are invested when not spent (which, by the way, is exactly how companies assess strategic investments like M&A and the likes; I actually used to work in a strategy & planning team before I retired and for whatever reason, I didn't make the connection with my personal finances for a while, DUMB!). This is how we can compare multiple strategies.

Stepping back a bit, the very disturbing thing is the level of sensitivity associated with such discount parameter. An interesting observation though is that if one reflects on an OVERALL retirement plan, including a full PV assessment and a PMT-based variable withdrawal method (+ the fixed income flows), the discount rate in the PV math is counter-balanced by the expected return rate in the PMT formula (which really should be the same rate), and then the parameter's sensitivity level suddenly drops like a rock. Relief! But this line of thought is going way beyond your calculator (here is a thread when we went quite in depth about it)...

Anyhoo, you had to make a choice about the default value, and since there is just no good generic answer, I am not going to push back hard... I just wanted to point out that PV-minded folks should really take advantage of the flexibility you provided, allowing to override such default value, and use whatever logic they are more comfortable with.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by #Cruncher » Sun Jun 09, 2019 1:33 pm

siamond wrote:
Sun Jun 09, 2019 11:07 am
SOME people may decide to spend bonds to assist their strategy of delaying social security (in other words, to have the SS delaying strategy drive a change in their AA) ,,, (underlines added)
In this post I examined funding the age 62 to 70 delay while keeping the asset allocation (50% stocks : 50% fixed income broadly defined) the same. It shows that about 90% of the funding comes from selling bonds; only about 10% from selling stocks. Here is an extract from the large table in that post.

Code: Select all

        Capitalized SS       Portfolio Value          Bond Value          Stock Value
      -----------------   --------------------    -----------------    -----------------
Age     62       70          62         70          62       70          62        70
---   -------   -------   ---------  ---------    -------   -------    -------   -------
 62   327,029   317,714   1,000,000  1,000,000    336,486   341,143    663,514   658,857
 70   246,614   434,041   1,022,128    850,467    387,757   208,213    634,371   642,254
                                       -------              -------              -------
Chg                                   (149,533)            (132,930)             (16,603)
The key is that fixed income "broadly defined" includes the capitalized value of expected future Social Security benefits. I realize that whether one should do this or not is a quasi-theological subject on this forum; and I don't want this thread to degenerate into the "yes, it makes sense" / "no, it's ridiculous" back and forth I've seen in several other threads over the years. So let me be clear: I'm not here claiming one should include capitalized SS in fixed income. I'm only saying,
if one includes the present value of SS as part of fixed income, then one may be able to fund the age 62 to 70 delay almost entirely by selling bonds, while keeping the stock : fixed income allocation the same.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by siamond » Sun Jun 09, 2019 3:49 pm

#Cruncher wrote:
Sun Jun 09, 2019 1:33 pm
The key is that fixed income "broadly defined" includes the capitalized value of expected future Social Security benefits. I realize that whether one should do this or not is a quasi-theological subject on this forum; and I don't want this thread to degenerate into the "yes, it makes sense" / "no, it's ridiculous" back and forth I've seen in several other threads over the years.
I have no desire for a 'theological' debate either. What you describe is one perfectly reasonable approach. All I am saying is that it is only one approach among many others.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Sun Jun 09, 2019 4:24 pm

Thanks for your reply siamond.
siamond wrote:
Sun Jun 09, 2019 11:07 am
SOME people may decide to spend bonds to assist their strategy of delaying social security (in other words, to have the SS delaying strategy drive a change in their AA), granted. OTHER people (including myself), driven by a set of personal reasons which go way beyond SS considerations, may decide to NOT do so or to do something different. That is just a simple hard fact, we're all making our own AA choices, driven by many personal factors.
I agree with this. (I also agree of course with the assertion that the analysis is very sensitive to the discount rate used. Hard to disagree about that.)
siamond wrote:
Sun Jun 09, 2019 11:07 am
Now in presence of such variability, what is the thing that stays constant? It is the simple fact that money not withdrawn from one's portfolio stays invested in said portfolio (with the AA chosen by the owner)... Therefore the discount rate should be the AA's expected return.
But I enthusiastically disagree with this (the bolded part, specifically).

Let me try one more time to win you over to my way of thinking. If we still disagree, OK fine.

Let's consider an analogy.

Imagine for a moment that your portfolio is the following:
40% Vanguard Total Stock Market Index Fund
20% Vanguard Total International Stock Index Fund
40% Vanguard Total Bond Market Index Fund

And let's also imagine that Vanguard has just released a new bond fund, and that the fund sounds like something that's at least worth considering for your portfolio. So you do some analyses to see what would happen if you allocated 20% of your portfolio to the new fund.

You consider what would happen if you took the 20% out of your Total Stock Market holding. You conclude that it probably wouldn't be advantageous.
You consider what would happen if you took the 20% out of your international holding. Doesn't seem advantageous.
You consider what would happen if you took the 20% pro-rata from each of the three existing holdings. Again, doesn't seem advantageous.
But you also consider what would happen if you took the 20% out of your Total Bond holding. And in this case, it does look like doing so would improve the portfolio.

Do you decide to add the new fund? Presumably, you do, because you have concluded that selling half of your Total Bond holding to buy the new fund would result in an overall improvement.

Point being, when deciding whether to add the new fund, you consider the most advantageous way of doing so. And that is the basis on which you judge whether or not the fund merits inclusion. (Sort of a "highest and best use" line of thinking.)

And of course what I'm getting at here is that when deciding whether to "buy more" Social Security, you ultimately want to consider: when done in the most advantageous way possible, do I want to spend down some assets to get more of this Social Security asset?

For most people, "the most advantageous way possible" means selling bond holdings. (For more on that, see the Blanchett/Finke paper I linked to above.) That's why the calculator defaults to using bond-based discount rates.

That said, there certainly are some cases in which "the most advantageous way possible" does actually mean selling stocks or a combination of stocks and bonds (obvious example: a person whose portfolio is already 100% equity). And that's why the calculator allows the user to choose, ultimately.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by Big Dog » Sun Jun 09, 2019 4:37 pm

My mind finally cleared up (and my math became consistent) when I made sure to use a discount rate directly associated with the way $$ are invested when not spent (which, by the way, is exactly how companies assess strategic investments like M&A and the likes;
Our megacorp did not do it that way. We had numerous internal 'hurdle' rates, one for international projects, one (higher) for international projects in higher risk countries (Russia, China), one for US R&D, and a much lower one for more of a domestic cash play. For example, we used the latter when we were buying known/proven cash flows.

That is similar to what Mike is saying (I think).

fwiw: I just ran OpenSS with default rate, and then changed it to 2%. With my and wife's ages/numbers, it only moved the claiming strategy by several months. Since I'm planning on doing tIRA-Roth conversions,I'll stick with the later default rec. (The NPV delta is meaningless to me, as I look to OpenSS more for claiming timing.)

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by siamond » Sun Jun 09, 2019 5:29 pm

Big Dog wrote:
Sun Jun 09, 2019 4:37 pm
My mind finally cleared up (and my math became consistent) when I made sure to use a discount rate directly associated with the way $$ are invested when not spent (which, by the way, is exactly how companies assess strategic investments like M&A and the likes;
Our megacorp did not do it that way. We had numerous internal 'hurdle' rates, one for international projects, one (higher) for international projects in higher risk countries (Russia, China), one for US R&D, and a much lower one for more of a domestic cash play. For example, we used the latter when we were buying known/proven cash flows.

That is similar to what Mike is saying (I think).
I was reflecting on why Mike and myself are speaking past other. I think you might have just explained it.

I suspect it is a case of being so used to a given (valid) methodology that we have troubles opening our mind to another (valid) methodology which happens to share the same mathematical tools, but used in another way... What you just explained (and this appears to match how Mike explains his views) seems to attempt to capture the risk of a given investment/project through the discount rate - am I correct?

The way I proceeded (and still proceed) is to take a given scenario for a possible investment/project and to use the discount rate to compare to (or complement) a more regular form of investment with a given return rate (both rates being -by design- equal). And the risk/variability dimension is captured by defining variants of such scenarios (e.g. bad luck, average luck, good luck!), hence changing the expected cash flows and their timing.

The first way doesn't seem terribly flexible to me (risk being so multi-faceted), but I realize that I am probably stuck in my own way of thinking.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by afan » Sun Jun 09, 2019 5:38 pm

Using the same discount rate for all investments cannot work.

Although the expected return of the total portfolio is an interesting figure, it hardly serves as a discount rate for all other investments.

Consider two hypothetical investmens.

One is a full faith and credit treasury that pays a fixed annual real return. So indexed to inflation with no cap on the rate. This has effectively zero risk. You probably cannot find such a bond anywhere, but it helps illustrate the point.

The other is a 3X leveraged fund based on the 10th decile of the total stock market. So microcaps only. Extremely risky.

Using the expected return of the overall portfolio as the discount rate, one would apply the same rate to both investments. Which is wildly inaccurate.

There is no way to calculate a present value of an income stream without applying a discount rate.
The discount rate always has to apply to the risk of that particular income stream.
Applying the discount rate from a different investment with different risk will always lead to the wrong answer.

No easy way around this for SS. I am still at "higjer discount rate than TIPS, but I don't know how much higher." Even if you use the option to reduce benefits as currently expected in the trustees report, you have not eliminated all of the risk in SS.

There is no assurance that the current projections are the only bad outcome. Some proposals would hit those who have saved well throughout their careers much worse than a 23% benefit cut.

One cannot do a responsible job of evaluating the promised benefit without taking this into account.
Last edited by afan on Sun Jun 09, 2019 6:23 pm, edited 1 time in total.
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by Big Dog » Sun Jun 09, 2019 5:55 pm

Even if you use the option to reduce benefits as currently expected in the trustees report, you have not eliminated all of the risk in SS.
Even then, you'd have to age your exceptions (pun intended) based on your estimates of whose ox gets gored, i.e., will the cuts apply across the board to everyone (as current law seems to indicate), or will those say, 75+ be spared and therefore those <50 take a larger hit? (Don't want to get into politics, but coming up with the 'proper' discount rate requires a decent estimate of what cut and when and to whom.)

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by siamond » Sun Jun 09, 2019 6:17 pm

ObliviousInvestor wrote:
Sun Jun 09, 2019 4:24 pm
Point being, when deciding whether to add the new fund, you consider the most advantageous way of doing so. And that is the basis on which you judge whether or not the fund merits inclusion. (Sort of a "highest and best use" line of thinking.) [...]
I think you're making two points:

a) the existence and size of fixed income future flows should have a strong bearing on one's asset allocation (the AA of one's savings/portfolio) => I do not disagree (and John Bogle clearly had the same view), but I do NOT draw as direct a relationship as you do because many people (including myself) factor in many other considerations. I will notably NOT change our AA when I'll start claiming SS or when my wife will start getting her state pension, nor will we sell more bonds than stocks in the mean time. This might not seem logical to you, but I am very set on this set-my-AA-and-keep-it-that-way simple approach, and heck, this is my choice (and I believe I am far from being alone in this camp)...

b) then I think (?!) you view the use of discount rate in a radically different way than mine (see the exchange with Big Dog) and I have troubles to bend my mind to your way and you (and afan) have troubles to bend your mind to my way. This doesn't mean that either of us is wrong. We probably just use present-value and risk/return concepts in a different manner.

Anyhoo, I think this entire discussion shows that you made the right decision by making the discount rate a variable parameter.

PS. and yes, I might have been too hasty in asserting that using the portfolio's expected return as discount rate should be a constant in any case. I need to think a bit more about it...

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by ObliviousInvestor » Sun Jun 09, 2019 7:10 pm

siamond wrote:
Sun Jun 09, 2019 6:17 pm
ObliviousInvestor wrote:
Sun Jun 09, 2019 4:24 pm
Point being, when deciding whether to add the new fund, you consider the most advantageous way of doing so. And that is the basis on which you judge whether or not the fund merits inclusion. (Sort of a "highest and best use" line of thinking.) [...]
I think you're making two points:

a) the existence and size of fixed income future flows should have a strong bearing on one's asset allocation (the AA of one's savings/portfolio) => I do not disagree (and John Bogle clearly had the same view), but I do NOT draw as direct a relationship as you do because many people (including myself) factor in many other considerations.
I have likely not been sufficiently clear on this point: I agree that many factors should be considered. I am not making the case that "Social Security is a bond," as some people do. Rather what I am saying is that, after considering whichever factors you choose to consider, it often happens to be the case that spending down bonds (or primarily bonds) is more advantageous than spending down stocks or a pro-rata stock/bond combination when delaying Social Security. (This is what the Blanchett/Finke paper speaks to. This Pfau/Tomlinson/Vernon paper does as well.)
siamond wrote:
Sun Jun 09, 2019 6:17 pm
b) then I think (?!) you view the use of discount rate in a radically different way than mine (see the exchange with Big Dog) and I have troubles to bend my mind to your way and you (and afan) have troubles to bend your mind to my way. This doesn't mean that either of us is wrong. We just use present-value and risk concepts in a different manner.
I think (?!) that we would all agree that discount rate is used to represent the opportunity cost. That is, a dollar in the future is worth less than a dollar today (i.e., it needs to be discounted), because getting that dollar in the future means that we can't invest it in the interim.

And I agree with afan that risk is a critical factor in the selection of discount rate (because in order to determine the opportunity cost, we have to figure out what else we'd be doing with the money -- which necessarily involves a discussion of risk).
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by #Cruncher » Mon Jun 10, 2019 4:44 pm

siamond wrote:
Sun Jun 09, 2019 9:34 am
Note that the calculator's recommendations are highly sensitive to the discount rate, just playing with a range of 'reasonable' values with my own situation, the calculator suggested to claim at 62 in some cases or postpone until 70 in other cases...
How sensitive depends on the particulars. Consider the following table. It calculates, at discount rates of 0.0% to 5.0%, the present value (PV) of expected benefits if SS is begun at each of the 9 whole number ages 62 to 70. It assumes a single person born in 1960 with a Primary Insurance Amount (PIA) of $1,000 who lives until age 85 (23 years [1] beyond age 62). [2]

For each discount rate it determines which starting age produces the highest PV. These are listed in the "Best" column. At low discount rates the best age isn't very sensitive to the discount rate. E.g. The best year remains at 69 for any discount rate from 0.6% to 2.0% . It remains at 68 for any discount rate from 2.2% to 3.2%. But the best age becomes more sensitive for higher discount rates. E.g., It falls four years from 66 to 62 for only a small increase in the discount rate from 4.0% to 4.4%.

Code: Select all

Row  Col A          Col B
  1  Born            1960
  2  NRA               67
  3  PIA            1,000
  4  Years @ 62        23

Code: Select all

  5  Start age                                 62      63      64       65      66      67       68      69      70
  6  Years collect                             23      22      21       20      19      18       17      16      15
  7  Years delay                                0       1       2        3       4       5        6       7       8
  8  Percent PIA     ------- Range ------   70.00%  75.00%  80.00%   86.67%  93.33% 100.00%  108.00% 116.00% 124.00%
Row   Rate  Col Best Overall Before After  --------------- P r e s e n t  V a l u e  a t  A g e  6 2  --------------
     Col A ColB ColC   Col D  Col E Col F    Col G   Col H   Col I    Col J   Col K   Col L    Col M   Col N   Col O

Code: Select all

 10  0.00%    9   70  30,000    480        193,200 198,000 201,600  208,000 212,800 216,000  220,320 222,720 223,200
 11  0.20%    9   70  27,546    248        188,639 193,132 196,445  202,478 206,942 209,843  213,825 215,937 216,186
 12  0.40%    9   70  25,193     29        184,228 188,423 191,460  197,139 201,281 203,896  207,554 209,392 209,421

 13  0.60%    8   69  23,116  1,577   180  179,959 183,867 186,639  191,977 195,809 198,149  201,498 203,075 202,895
 14  0.80%    8   69  21,149  1,328   376  175,828 179,458 181,974  186,984 190,519 192,596  195,649 196,976 196,600
 15  1.00%    8   69  19,260  1,090   563  171,829 175,191 177,460  182,154 185,403 187,229  189,998 191,089 190,526
 16  1.20%    8   69  17,446    865   739  167,958 171,061 173,092  177,482 180,456 182,040  184,539 185,403 184,664
 17  1.40%    8   69  15,704    650   906  164,209 167,062 168,863  172,960 175,670 177,024  179,263 179,913 179,007
 18  1.60%    8   69  14,031    445 1,063  160,578 163,190 164,769  168,584 171,041 172,174  174,165 174,610 173,546
 19  1.80%    8   69  12,425    250 1,212  157,062 159,440 160,805  164,348 166,561 167,483  169,237 169,487 168,275
 20  2.00%    8   69  10,883     65 1,353  153,655 155,806 156,966  160,247 162,226 162,945  164,472 164,537 163,185

 21  2.20%    7   68   9,513  1,311   111  150,353 152,286 153,247  156,275 158,030 158,555  159,866 159,755 158,270
 22  2.40%    7   68   8,258  1,104   279  147,153 148,875 149,644  152,429 153,968 154,307  155,411 155,132 153,523
 23  2.60%    7   68   7,052    906   438  144,051 145,568 146,153  148,703 150,035 150,197  151,102 150,665 148,937
 24  2.80%    7   68   5,892    716   589  141,043 142,363 142,769  145,094 146,226 146,218  146,935 146,345 144,508
 25  3.00%    7   68   4,776    536   733  138,126 139,255 139,489  141,596 142,537 142,367  142,902 142,169 140,228
 26  3.20%    7   68   3,703    363   869  135,297 136,240 136,309  138,206 138,963 138,638  139,001 138,131 136,092

 27  3.40%    5   66   3,406    581   474  132,553 133,317 133,226  134,920 135,501 135,027  135,225 134,226 132,095
 28  3.60%    5   66   3,914    411   616  129,890 130,481 130,235  131,735 132,146 131,530  131,570 130,449 128,232
 29  3.80%    5   66   4,397    248   752  127,306 127,729 127,334  128,646 128,894 128,142  128,032 126,794 124,497
 30  4.00%    5   66   4,855     92   882  124,797 125,058 124,519  125,650 125,742 124,860  124,607 123,259 120,887

 31  4.20%    4   65   5,349    957    59  122,362 122,465 121,788  122,744 122,686 121,680  121,290 119,837 117,395

 32  4.40%    1   62   5,979           49  119,998 119,948 119,137  119,926 119,723 118,599  118,077 116,526 114,019
 33  4.60%    1   62   6,949          197  117,702 117,505 116,564  117,190 116,849 115,612  114,966 113,321 110,753
 34  4.80%    1   62   7,877          340  115,471 115,131 114,066  114,536 114,061 112,716  111,951 110,219 107,594
 35  5.00%    1   62   8,767          478  113,304 112,826 111,640  111,959 111,357 109,909  109,031 107,215 104,537
Explanation of columns using row 13 as example:
  1. Rate (0.6%): Discount rate used to compute the present value (PV).
  2. Col (8): Index into the columns "G" to "O" of the largest PV.
  3. Best (69): Starting age with the largest PV.
  4. Range overall ($23,116): From the smallest PV ($179,959 if start at 62) to the largest ($203,075 if start at 69).
  5. Range before ($1,577): How much larger is the largest PV than the PV if started a year sooner ($201,498).
  6. Range after ($180): How much larger is the largest PV than the PV if start a year later ($202,895).
  7. Present value ($179,959): Computed with Excel PV function:
    $179,959 = -12 * 1000 * PV(0.6%, 23, 70%, 0, 0) / (1.006) ^ 0
Follow these steps to do the calculation for other assumptions:
  • Select All, Copy, and Paste [3] the following at cell A1 of a blank Excel sheet:

    Code: Select all

    Born	1960
    NRA	=MIN(67,66+MAX(0,B1-1954)/6)
    PIA	1000
    Years @ 62	23
    Start age						62	63	=2*H5-G5
    Years collect						=$B$4-(G5-62)	=$B$4-(H5-62)	=$B$4-(I5-62)
    Years delay						=$B4-G6	=$B4-H6	=$B4-I6
    Percent PIA			------- Range ------			=IF(G$5<$B2,1-(5/900)*MIN(36,($B2-G$5)*12)-(5/1200)*MAX(0,($B2-G$5)*12-36),1+(8/1200)*(G$5-$B2)*12)	=IF(H$5<$B2,1-(5/900)*MIN(36,($B2-H$5)*12)-(5/1200)*MAX(0,($B2-H$5)*12-36),1+(8/1200)*(H$5-$B2)*12)	=IF(I$5<$B2,1-(5/900)*MIN(36,($B2-I$5)*12)-(5/1200)*MAX(0,($B2-I$5)*12-36),1+(8/1200)*(I$5-$B2)*12)
    Rate	Col	Best	Overall	Before	After	---------------------- Present Value at Age 62 -------------------------------
    0	=MATCH(MAX(G10:O10),G10:O10,0)	=INDEX(G$5:O$5,1,B10)	=MAX(G10:O10)-MIN(G10:O10)	=IF(B10=1,0,INDEX(G10:O10,1,B10)-INDEX(G10:O10,1,B10-1))	=IF(B10=COLUMNS(G$5:O$5),0,INDEX(G10:O10,1,B10)-INDEX(G10:O10,1,B10+1))	=-$B$3*12*PV($A10,G$6,G$8,0,0)/(1+$A10)^G$7
    0.002	=MATCH(MAX(G11:O11),G11:O11,0)	=INDEX(G$5:O$5,1,B11)	=MAX(G11:O11)-MIN(G11:O11)	=IF(B11=1,0,INDEX(G11:O11,1,B11)-INDEX(G11:O11,1,B11-1))	=IF(B11=COLUMNS(G$5:O$5),0,INDEX(G11:O11,1,B11)-INDEX(G11:O11,1,B11+1))	=-$B$3*12*PV($A11,G$6,G$8,0,0)/(1+$A11)^G$7
    =2*A11-A10	=MATCH(MAX(G12:O12),G12:O12,0)	=INDEX(G$5:O$5,1,B12)	=MAX(G12:O12)-MIN(G12:O12)	=IF(B12=1,0,INDEX(G12:O12,1,B12)-INDEX(G12:O12,1,B12-1))	=IF(B12=COLUMNS(G$5:O$5),0,INDEX(G12:O12,1,B12)-INDEX(G12:O12,1,B12+1))	=-$B$3*12*PV($A12,G$6,G$8,0,0)/(1+$A12)^G$7
  • Format for readability.
  • Copy cells I5:I8 right to column O.
  • Copy celld G10:G12 right to column O.
  • Copy cells A12:O12 down to row 35.
  • Update year born in B1, PIA in B3, and life expectancy in B4 as desired.
  1. According to the SSA 2016 Period Life Table the life expectancy of a woman age 62 is 22.94 years.
  2. The table approximates the results from Mike's calculator. The latter is more precise because it evaluates starting SS each month not just at the start of each year. It is also more accurate because, instead of just assuming benefits continue at full for the specified number of years, it calculates the survival-weighted benefits for every possible year. But its sensitivity to the discount rate is roughly the same. E.g., while my table shows the "Best" age falling from 69 to 68 when the discount rate rises from 0.6% to 2.0%, Mike's calculator shows it falling, for a female with the same mortality table, from 69+11 mo to 68+7 mo for the same increase in discount rates. My table shows it falling from 66 to 62 when the discount rate rises from 4.0% to 4.4%. Mike's calculator shows it falling from 65+5 mo to 62+2 mo when the discount rate rises from 3.6% to 4.0%.
  3. If you have trouble pasting, try "Paste Special" and "Text".

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by TimeRunner » Mon Jun 10, 2019 6:51 pm

#Cruncher, that is some seriously impressive conformational spreadsheet work. Tip 'o the hat to you. :beer
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by LadyGeek » Mon Jun 10, 2019 9:24 pm

^^^ I agree.

I have replicated #Cruncher's results and have added the post to the wiki: Social Security: member contributions
#Cruncher wrote:
Mon Jun 10, 2019 4:44 pm
If you have trouble pasting, try "Paste Special" and "Text".
You need one more step:

Paste Special --> Text --> Tab delimited
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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by siamond » Tue Jun 11, 2019 5:03 pm

#Cruncher wrote:
Mon Jun 10, 2019 4:44 pm
How sensitive depends on the particulars. Consider the following table. [...]
Nice work, thank you for sharing. This actually reinforces me in my attempt to better rationalize the discount rate to be used in such SS/pre-SS calculations. I swapped a few e-mails with Mike as we seemed to be quite at odds with each other on this matter, and we discovered that we're actually reasonably in sync, once underlying assumptions were spelled out and mental frameworks were clarified.

Before I explain, I believe it is worth making more explicit what a discount rate really is. Let's think forward first. Say we have a given amount of money ('PV', present value). Say we invest it with an annual rate of return of 'R'. After a few years ('N'), the final value ('FV') is:
FV = PV * (1+R)^N

Nobody will disagree, I'm sure, this is quite obvious. Now let's solve for PV, doing a tiny bit of algebra:
PV = FV / (1+R)^N

Why am I going through that? The key point is that the semantics of 'R' did NOT change in those two (equivalent) equations. People call it 'discount rate' in a PV calculation, which I find rather confusing, but the truth this is the rate of return of the $$ being involved during this period of time, and whether the math is done forward or backward doesn't change this simple truth.

Personally, my trick when going through a Present-Value reasoning is to always turn it on its head and think forward instead of backward. Quite magically, the usual mind-binder becomes much clearer. After doing a local BH chapter presentation, I actually wrote a multi-part blog article on the matter, centered on future cash flows and early retirement. It came with a shared spreadsheet and fairly simple corresponding formulas for numbers-minded readers. Mike made me realize I was making some implicit assumptions though... See next post!

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by siamond » Tue Jun 11, 2019 6:17 pm

A few posts ago, I stated the following - and started to get some flak... :wink:
siamond wrote:
Sun Jun 09, 2019 11:07 am
Now in presence of such variability, what is the thing that stays constant? It is the simple fact that money not withdrawn from one's portfolio stays invested in said portfolio (with the AA chosen by the owner)... Therefore the discount rate should be the AA's expected return.
After discussing offline with Mike, I realize that although I stand by my statement, a few qualifiers were badly missing to account for a broader range of strategies. So I reworded it by making a very direct association with the PV = FV / (1+R)^N formula:

The proper discount rate is the (expected) rate of return of the part of the portfolio that will be used to compensate for the lack of SS income in pre-SS years. Note that I am wording this in SS terms, but this is actually a subset of a broader strategy about future cash flows (incl. pensions, etc).

The 'part of' qualifier is the key to make the statement more broadly applicable. Mike seemed to agree, although he preferred the following wording, making an association with the 'opportunity cost' of such pre-SS expense:

Proper discount rate is the expected return forgone on the part of the portfolio spent down that would not have otherwise been spent down.

Let me illustrate by taking two somewhat opposite examples.

1. I am squarely in the probabilistic camp. The idea of partitioning my portfolio based on one goal or another is complete anathema to me. I also plan to stick to a fixed AA for the rest of my life, no glide path or whatever. Finally, I am an early retiree who has a 40+ years time horizon (without even counting the bequest goal) and is currently more than a decade away from claiming SS.
=> my strategy maps very exactly to what I explained in the blog article. The Harry and Sally example wasn't too far from my situation!
=> I compute a Present-Value of future cash flows (SS and more), using a discount rate equal to the (real, inflation-adjusted) expected return of my portfolio during retirement, itself derived from my fixed AA.
=> before SS/etc, I will complement my regular portfolio withdrawals by extra withdrawals, essentially annuitizing the future cash flows (using the same rate, of course).
=> now, being very concrete, what money will be invested and spent in pre-SS years? Well, my portfolio, of course. So if you switch the 'backward' logic of the PV math into a 'forward' logic of the $$ being involved, it should be clear that the discount rate is the AA expected return.
=> there are a few more considerations to accommodate for variability of returns, variability of withdrawals and short-term risk management, but the main point is there, the proper discount rate is the (unpartitioned) portfolio's AA.

2. Other people are more aligned with an LMP/RP kind of philosophy and would find anathema to plan for anything else than the very constant and very guaranteed stability of SS income. They will therefore partition their portfolio in pre-SS years, quite possibly creating a TIPS ladder, and the SS-equivalent income in pre-SS years will come from there. The rest of their portfolio remains totally separate from this TIPS bucket.
=> to be fair, if you're just a few years from claiming, I can understand that. In my case, when I early-retired in my early 50s, there was no way I would create a (very expensive) 18-years TIPS ladder, but every situation is unique. Others might think differently and I respect that.
=> so... what is the proper discount rate, then? Well, switch the backward logic to the forward logic, the $$ being involved are the part of the portfolio being allocated to the TIPS ladder, and the expected rate of return is the corresponding yield.
=> funny, that is the default setting Mike uses in his calculator. Which I now understand and agree with.

Although those two examples reflect very distinct philosophies and ways to address the pre (and post) SS years, the generic statements about the discount rate above (either mine or Mike's) remain applicable.

Then there are of course all sorts of variations in-between. Mike seems quite keen on the idea of spending bonds for such pre-SS income, creating some sort of upward glide path. I can't say that I find much appeal in such approach, but that's his view and I respect it. Then the proper discount rate would be the (real) expected return on those bonds (optionally mixed with a small dollop of stocks as he mentioned in a previous post).

PS. one last point. What about the risk of SS funding shortage and similar fears? Well, this has nothing to do with the $$ from your savings that you will invest/spend in pre-SS years. Therefore, this has nothing to do with the discount rate (which is simply a rate of return). The way to model this is to do some scenario analysis and using reduced SS benefits (i.e. cash flows) to feed in the PV math while keeping the discount rate unchanged. And what about any form of pension or inheritance or else? Same reasoning applies.

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Re: [Calculating future Social Security benefits: How do I adjust the discount rate?]

Post by #Cruncher » Wed Jun 12, 2019 12:55 pm

Nerd alert! This post just examines the arithmetic of present value and future value calculations.
siamond wrote:
Tue Jun 11, 2019 5:03 pm
Say we have a given amount of money ('PV', present value). Say we invest it with an annual rate of return of 'R'. After a few years ('N'), the final value ('FV') is:
FV = PV * (1+R)^N
Nobody will disagree, I'm sure, this is quite obvious. Now let's solve for PV, doing a tiny bit of algebra:
PV = FV / (1+R)^N
Yes indeed. For example, row 27 from the table in my previous post shows, by coincidence, that if one lives to age 85, the benefits from starting SS at age 62 or 70 have about the same present values ($132,553 or $132,095 respectively) at age 62 when discounted at 3.4%. Using siamond's first formula above we can see that the future values 23 years later at age 85 are also close:
$285,997 = 132553 * 1.034 ^ 23
$285,010 = 132095 * 1.034 ^ 23

The following little table shows how, if invested with a 3.4% return, the Social Security benefits would grow, year by year, to these values:

Code: Select all

Rate       3.40%
PIA        1,000
Begin         62        70
Pct PIA   70.00%   124.00%
Benefit    8,400    14,880

Age            Grows To               
---       ----------------
 63        8,400         0
 64       17,086         0  17,086 = 1.034 *  8400 +  8400
 65       26,067         0  26,067 = 1.034 * 17086 +  8400
 66       35,353         0  etc.
 67       44,955         0
 68       54,883         0
 69       65,149         0
 70       75,764         0
 71       86,740    14,880
 72       98,089    30,266  30,266 = 1.034 * 14880 + 14880
 73      109,825    46,175  46,175 = 1.034 * 30266 + 14880
 74      121,959    62,625  etc.
 75      134,505    79,634
 76      147,478    97,222
 77      160,893   115,407
 78      174,763   134,211
 79      189,105   153,654
 80      203,934   173,759
 81      219,268   194,546
 82      235,123   216,041
 83      251,518   238,266
 84      268,469   261,247
 85      285,997   285,010
It isn't necessary to accumulate the amounts year by year to get the ending future value (FV). This can be done with the following formula:

Code: Select all

FV       = PMT          * (((1 + r) ^ n  - 1) / r)     [1]
$285,997 = 12000 *  70% *  ((1.034  ^ 23 - 1) / 0.034)
$285,010 = 12000 * 124% *  ((1.034  ^ 15 - 1) / 0.034)
Likewise here is the formula for computing the present value (PV). Note that for the case of starting SS at 70, a second step is needed to compute the present value at age 62.

Code: Select all

PV       =  PMT           * ((1 - 1 / (1 + r) ^ n)  / r)     [1][2]
$132,553 =  12000 *   70% * ((1 - 1 /  1.034  ^ 23) / 0.034)
$172,604 =  12000 *  124% * ((1 - 1 /  1.034  ^ 15) / 0.034) [PV age 70]
$132,095 = 172604 / 1.034 ^ 8                                [PV age 62]
One doesn't have to fool with these formulas for either single amounts or a repeated annuity. Both are encapsulated in the Excel FV and PV functions. [3]
  1. Just as a little algebra converts the present value of a single amount formula to the corresponding future value formula, the same can be done with the formulas for the present and future values of a repeated annuity. Just multiply the present value formula by (1 + r) ^ n.

    Code: Select all

    FV =  PV                                            * (1 + r) ^ n
       = (PMT * (( 1          - 1 / (1 + r) ^ n)  / r)) * (1 + r) ^ n
       =  PMT * (((1 + r) ^ n - 1)                / r)
  2. The present value of an annuity formula can be derived from the present value of a single amount formula, but it's complicated. For example, this web page purports to do so, but it's beyond my ability to follow.
  3. For example:

    Code: Select all

          pv = -PV(rate, nper, pmt,          fv,     0 or 1)
    $132,553 = -PV(3.4%, 23,   12000 *  70%, 0,      0)
    $172,604 = -PV(3.4%, 15,   12000 * 124%, 0,      0) [PV age 70]
    $132,095 = -PV(3.4%,  8,   0,            172604, 0) [PV age 62]

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