Annuities Rant Part II – Low Returns and High Fees

Editor’s Note: Please see Annuities Part I here.

Another reason I don’t like fixed rate, fixed index, and variable annuities is their low returns and high costs. These are directly related. The higher the costs to you, the lower your returns.

To begin with the simplest of the three types, fixed rate annuities are the exception in that they do not charge high fees. In fact, generally they don’t charge you any fees at all. Instead, they offer you very low returns. 

I recently pulled some quotes from my preferred insurance company. For amounts less than $100,000 I could earn 2.6% guaranteed on a fixed rate annuity for the next five years, and I could earn 3% if I invested more than $100,000. I checked rates with another provider online and received quotes in the similar range of 2.8% and 2.95% respectively. That rate changes over five years. Mine had a minimum reset rate of 1.3%, after the five year term. 

What should we think about these rates?

With a product like this, you should always reasonably expect that the annual return on a fixed rate annuity, adjusted for inflation and taxes, will be approximately zero. That’s not a typo. That’s just a rule of fixed rate annuity products and risk-less products in general.

Now, figuring the returns of fixed index and variables annuities is trickier because they are somewhat market driven and depend on what you pick as underlying investments and risks. But we can understand what the costs are, and therefore their expected underperformance versus comparable assets you could buy from a brokerage company.

With a variable annuity you have the chance to purchase mutual funds similar to funds at a brokerage account. Costs will weigh down your returns, however. 

The management fees of mutual funds offered inside a typical variable annuity are typically very high. In the 2018 Brighthouse Financial Life (formerly MetLife) policy variable annuity contract I reviewed, the costs of mutual funds ranged from a low of 1.56% to a high of 2.71%. Hello? 1987 just called, and it wants its mutual fund fees back.

The cheapest 1.56% fund was a stock index fund which low-cost brokerages offer at 0.05% – or 31 times cheaper elsewhere. I really didn’t enjoy the 1.66% fees quoted on the Blackrock Ultra Short Bond Portfolio. That fund has a 10 year return of 0.39% – meaning you could have locked in huge losses after fees for the past decade, on a product supposedly meant to preserve capital. These types of egregious fund management costs are the rule, not the exception, when it comes to most variable annuity fund offerings I’ve reviewed. The Teacher’s retirement System (TRS) in Texas just capped mutual fund fees inside variable annuities at 1.75% following a “reform” in October 2017, to go into effect in October 2019. These fees are, in a word, bad. Even after that “reform.”

Why are the fees so high? I have a theory, and it goes something like this.

Insurance companies can impose huge fees on variable and fixed index annuities because they have selected their customers very carefully. Only people who don’t know what they are doing would select these providers and these products. So in essence they can charge whatever they like.

They employ psychology similar to how the “Nigerian Prince” scam artist who supposedly wants to wire you $10 million will purposefully misspell words in the solicitation email. The Nigerian Prince scammer knows that any target victim who replies has no powers of discernment. The misspelling in the email is a purposeful selection process by which the scammer chooses the right kind of victim.

Seems legit, right?

Similarly, whenever a public school employee sets up a “finance and retirement discussion” meeting with a commissioned insurance salesperson, the salesperson can have high confidence that the teacher has absolutely no idea what they are doing financially. The result: high fees, with impunity!

Of course, there are more fees after that. 

Arguably the main service an insurance company provides with variable and fixed index annuities is a lifetime guarantee of payments, because they employ actuarial math that helps them make educated guesses about how long you’ll live. That seems like a service. And the insurance company seems to be taking a risk on you.

Ah, but they aren’t, not really. These complex annuities also charge a fee on your account called the “mortality and expense risk charge” – offloading that specific risk that you live too long – to you. 

The 2018 Brighthouse contract I reviewed charged 1.2% per year for this “mortality and expense risk,” and the industry range is an extra 0.4 to 1.75% per year on these products. The lesson: If you charge high enough fees, you don’t end up taking a risk.

Finally, here’s my least favorite of all the low-return/high cost features of fixed index annuities.

This gets a bit technical, but bear with me, because this is really how the sausage is made.

The insurance company calculates the ‘growth’ in your fixed index account value based on the change in value of a stock market index over a year, but does not take into account dividends or the reinvestment of dividends that you would get, were you invested in the market directly through a brokerage account. 

Over long periods of time working towards retirement – I’m talking about decades – the growth of your investment may be in substantial part due to dividends. Because of the way the company calculates returns, however, you probably don’t get the return on dividends from a fixed index annuity. 

Does this matter? Oh yes.

Let’s say you had $100,000 in an S&P 500 brokerage account beginning in May 1989, held until May 2019. The return on the index over 30 years, considering only index price changes, is 7.7%.

However, the return on the index over 30 years, including the reinvestment of dividends, is 9.9%.

Hmm. Is that annual 2.2% difference a big deal? Yes it is. It’s the difference between ending up 30 years later with $818,000 or $1.6 million. But if you, as a fixed index annuity investor don’t get the credit for dividends or the reinvestment of dividends, who kept that money? Do I have to spell this out for you?

Over a long period of time, you may be leaving half your investment gains with the insurance company.

When you are a hammer, everything looks like a nail. Similarly, when you are an insurance company or commissioned insurance salesman, the investment solution everyone needs for retirement is an annuity. It’s what you sell.

As I do not sell annuities, all I can say is: Don’t buy these.

A version of this rant ran in the San Antonio Express News and Houston Chronicle.

Please see related posts:

Annuities Rant Part I – The Complexity

Annuities Rant Part III – Condoning in Some Ways

Annuities – Death Eaters

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Annuities Rant, Part I – On Complexity

Fixed rate annuities, fixed index annuities, variable annuities – how do I hate thee? 

I’m not recommending this book. I haven’t read it. I just like the double-entendre of “Cons” = Convicts and “Pros = Only professional salespeople could like this.

Let me count the ways, for they are plural.

Let’s start with annuities’ complexity. In a future post I will address their mediocre returns and high fees. 

Complexity matters because of a basic rule of financial products I just made up which, if you read it out loud, will sound a lot like your Miranda Rights:

“You and your money have the right to simplicity. Whatever you can’t understand can and will be used against you by the financial service provider.”

Annuities come in three main flavors. 

The vanilla flavor – fixed rate annuities – are actually decently simple. These are not evil. You give money to the insurance company, either all at once or over time, and they agree to give you back your money in equal monthly payments, either for a fixed amount of time or more typically for the rest of your life, guaranteed. The only fancy complex math going on in the background of fixed rate annuities is an actuarial guess about when you’ll die.

The other two flavors – the confusingly named fixed-index annuity, and its close cousin the variable annuity – are far more complex. Their structures vary from company to company, so in describing them I can point out the possible complications, but the specifics will be hidden from you somewhere in the fine print of your contract. Like an Easter egg hunt, but far, far more costly.

The other flavors start out with opaque calculations as the insurance company collects your money over time. At some point when you’re done giving money over they morph into a simpler fixed annuity. In this way, the fixed index and variable annuities are like hungry fuzzy caterpillars, disgusting to look at. Eventually, however, they annuitize and become simpler fixed rate annuity butterflies.

In prepping this review I read every word of some of the most boring variable annuity product plan documents you can imagine. Three different company contracts from 2008, 2014, and 2018, plus The National Association of Insurance Commissioner’s Buyer’s Guide To Deferred Annuities.

So, about the complexity of fixed index annuities, and their variable annuity cousins. Both give the buyer exposure to “the market,” but in an indirect way.

With a fixed index annuity you give your money to an insurance company and they promise to credit your account with some of the gains associated with a stock market index, such as the S&P500 of large cap companies or the Russell 2000 index of small cap companies. But exactly how they do that is usually calculated in a complex way. The basic value proposition from the insurance company is that they say you can participate on the upside when the stock mark appreciates, but they will provide some protection from loss when the stock market drops below the amount you put in, or drops below the previous year’s highwater amount. It’s a kind of “some market upside and some safety” combo platter. Sometimes that protection is against a 10% drop in the market, sometimes it’s against any loss of principle.

But how do they provide this “safety?” A bunch of ways. Sometimes the contract limits your upside by a “participation amount,” like 80% of the index gains. So if the market index returns 10%, you get credit for just an 8% annual gain. Another feature might be a “performance cap” that limits the amount an insurance company will need to credit you with, in a bull market. The market went up 12%? Sorry, your gains are only 9%. You might pay a “Spread Rate” which is a % of market gains, by which your insurance company subtracts your returns. Spread Rate doesn’t sound like a fee, but that’s what it is.

A particularly devious way to limit your returns is to only credit the price change of an index, but not the dividends you would have received if you owned the index in a brokerage account. As I’ll explain in a future column, that might mean you’ve left half your gains on the table.

with guaranteed benefit riders. Helping to Protect your Income. in Unpredictable Markets. Variable Products: Are Not a Deposit of Any Bank • Are Not FDIC Insured by Any Federal Government Agency • Are Not Guaranteed by Any Bank or Savings Association • May Go Down in Value. ML

How does the company handle all this complexity? 

As Jefferson Bank’s contract clearly states, “Subsequent Accumulation Unit Values for each Sub-Account are determined by multiplying the Accumulation Unit Value for the immediately preceding Valuation Period by the Net Investment Factor for the Sub-Account for the current period.”

It goes on like this for a couple of pages. I’ve read all the words and my head hurts.

Let’s go to the AXA Equitable document, to figure out our “Guaranteed Annual Withdrawal Amount” or (GAWA). Well, you see it’s, the, um:

  1.  “The sum of contributions that are periodically remitted to the PIB variable investment options, multiplied by the quarterly Guaranteed Withdrawal Rate (GWR) in effect when each contribution is received, plus
  2. The sum of (i) transfers from non-PIB investment options to the PIB variable investment options and (ii) contributions made in a lump sum, including but not limited to, amounts that apply to contract exchanges, direct transfers from other funding vehicles under the plan, and rollovers) that are allocated to the variable investment options, multiplied by the Guaranteed Transfer Withdrawal Rate (GTWR) in effect at the time of the transfer or contribution, plus
  3. The sum of any Ratchet Increase.”

Got it? As the teens would say: “Ratchet, dude”

Ok, here’s what you do need to know. You can’t independently observe their math. You own rights to a complex derivative – that’s not what they call it, but that’s what it is – and only they can tell you what that derivative is worth.

Variable Annuities should come with a 2-word review “Shit Sandwich”
Nigel Tufnel: “They can’t print that!”

With a regular brokerage account, by contrast, you would see an observable market price for a mutual fund, or a stock or a bond, or an ETF. 

Remember, anything you don’t understand can and will be used against you.

Do you want your money back yet? You can’t have it. 

Generally once you’ve annuitized, you can’t accelerate or change your fixed rate annuity. Prior to annuitization, you can have some, but you will probably pay surrender or withdrawal charges on any fixed index or variable annuity that you want to get out of. You may be able to get 10% of your money back each year without penalty, but for additional money you should expect to pay a 5% fee under many contracts, with a slowly declining penalty amount per year.

So that’s the story on complexity and illiquidity. I’ll tell you next time about the bad returns and the high fees.

A version of this post ran in the San Antonio Express News and Houston Chronicle.

Please see related posts

Annuities Rant Part II – Low Returns, High Fees

Annuities Rant – Part III – I partly take it back, but not really

Ask an Ex-Banker about Annuities – Death Eaters

Variable Annuities – Shit Sandwich

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403(b) Plans in TX – The Terrible Problem of Choice


RetirementSchool district employees in Texas attempting to fund their own retirement – through 403(b) defined contribution plans – face a garbage fire of bad choices.

A neutral and expert observer – anyone not directly benefitting from insurance industry money – can look at the retirement options mandated by school districts and see a rigged game.

Problem of Choice

How is the game rigged? Let’s start with the 403(b) plan problem of “choice.”

School district employees typically have access to a 403(b) plan – a tax-advantaged retirement savings plan through automatic payroll deduction. 403(b) plans as designed and regulated in Texas appear uniquely suited to make a lot of money, not for school district employees, but rather for the insurance industry.

Here’s the first problem with the 403(b) options, because of regulatory and legislative restrictions. In Texas, as in other states like California and Ohio, school districts may not be proactive or selective about what retirement companies and products teachers may access. This is known as an “any willing vendor” rule, according to school district retirement consultant Cecile Russell.

I imagine this “any willing vendor” idea was once sold to legislators as reasonable because it encouraged “choice,” which sounds appealing at first glance. What it actually does is stuffs the menu of investment options to a ridiculous point with insurance companies and insurance products.

Better Design

A better program design, better than this “any willing vendor” model, would involve limiting choices in 403(b) plans to low-cost and appropriate retirement products. A better plan would be designed by experts with fiduciary responsibility looking out for the best interest of school employees. Just as private sector 401(k) designers have to do. School districts in Texas are not allowed to do this with their 403(b) plans.

trsIn Texas the Teachers Retirement System has approved 65 separate vendor companies. There are actually 74 approved vendors listed by TRS but some of those are affiliated companies.  These vendors in turn offer 10,520 eligible investment products to school district employees.

That’s the first problem. Having 10,520 choices is not good. It’s a behavioral finance nightmare which produces what an economist would call “The Paradox of Choice” but which we could also understand more simply as “The Deer in the Headlights” response. For some, their 403(b) plan contributions stay stuck in a money market account earning no return. For others, they use the random dartboard approach to investing. The third option, by design, is that school district employees invest according to the plan of that nice insurance salesman offering free pizza in the teacher’s lounge. All of these are bad results in their own way.

At least two-thirds of approved 403(b) vendors in Texas are insurance companies or have insurance affiliates. Do you want to guess the result of having insurance companies as the dominant providers for 403(b) plans?

A study by independent consultancy Aon Hewitt estimated in 2016 only 24 percent of 403(b) investments are in mutual funds (the preferable products), compared to 43 percent in fixed annuities (the inappropriate product) and 33 percent in variable annuities (the abominably high-cost product.) Those last two products are specifically insurance-company products, whereas mutual funds are typical brokerage company products.

aon_hewittThe result of these asset allocation choices, AON Hewitt estimated, is $10 billion in extra costs paid by 403(b) participant investors, as compared to a comparable 401(k) style investment platform available to private sector workers and products. This is a multi-billion dollar fiduciary failure involving many responsible parties.

One way to understand the asset allocation problem is to understand the effect of compounding different returns over a long career. A school employee who managed to put away $50,000 in her 403(b) by age 30 faces a vastly different retirement depending on what she chooses as her primary investment vehicle. A 4% return on that investment would become worth $240,000, as compared to an 8% return becoming worth $1.08 million by age 70. Differences in returns, when compounded over 40 years, lead to massive divergences in results. Costs and investment products matter tremendously.

Before 1974, only insurance companies could provide investment products to 403(b) plans, giving them a head start with these types of plans. But 45 years later, the relative absence of mutual fund providers stands out as a shocking result. After so many years that result must be considered a feature, not a bug, of 403(b) plan design. It suits the insurance industry to keep this territory for itself, at the great expense of public school employees.

Can reasonable people disagree reasonably?

Now, I haven’t yet explained yet why insurance products are particularly pernicious in Texas 403(b) plan platforms. Many nice people, including especially insurance company employees, believe these to be fine products.

They are not.

I am not anti-Insurance. I buy insurance. It has an important role to play in all of our financial lives. Fixed and variable annuities are not good products, however, for a retirement plan. They are specifically inappropriate within a Texas public school employee’s retirement account. But they account for 75% of the products!

I don’t work for any finance or brokerage company. This is precisely why, even if you don’t understand my point straight away, you should at least believe that I don’t have an ax to grind, except to state the truth as I understand it.

I would go so far as to say that any independent fiduciary for a teacher’s retirement plan – and by independent again I mean someone not paid by any finance company – would agree that these are not the best products for public school district 403(b) plan participants.

And yet, they are the dominant products. Why is that?

In subsequent posts I will lay out the plausible explanation for this result, which is a perfectly legal  – but ought to be illegal – crime hidden in plain site.

A version of this post ran in the San Antonio Express News and Houston Chronicle.

See Related posts:

403(b) Plans – Failed Reform Only An Insurance Company Could Love

Teachers and Their Retirement Problems

Public Policy Debate on Teacher’s Retirement in TX

Nobody Advocating to Fix Teachers’ 403(b) Plans in TX

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John Oliver Does Us All A Service

john_oliver_retirementWe know from Mary Poppins that a spoonful of sugar helps the medicine go down and, similarly, a healthy dose of humor is the best way to learn about something as baleful as personal finance. John Oliver does us all a good 20-minute service in nailing key points about retirement, in this bit from a few weeks ago.


The video is worth watching and includes such key points as:

  1. Annuities suck (Especially variable annuities, I should add).
  2. Financial Advisor” is a meaningless title that tells you nothing about their qualifications.
  3. Fees matter a lot. A lot. A  lot.
  4. Suze Orman has a crazed look on her face (ok that’s my own editorializing right there).
  5. Actively managed funds tend to lag passive funds, by approximately the amount of extra fees.
  6. Insurance companies are particularly egregious fee-chargers when it comes to financial services.
  7. Personal investing – despite the best efforts of the financial infotainment industrial complex – can be made startlingly simple.

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Guest Post – Annuities Are Expensive

lars-Kroijer-on-TVAnnuities are an important and sometimes dominant part of the investment portfolio for millions of savers.  While in certain instances there is a requirement for pension scheme participants that they put a part of their pension savings into an annuity, others decide to have them because they find great comfort from having a secured cash flow until they die (some annuities continue payments for dependants).

I certainly don’t have a problem with annuities.  There is great intangible value to be had in knowing that you are going to be ok in your old age, regardless of how old you become.  Particularly if you have an annuity that is adjusted for inflation (some adjust for changes in the retail price index), you have a very good picture of your spending power in retirement, without worrying about the oscillations of the markets or dying with a lot of money that you may have no use for (you’ll be dead…).

But there are a couple of things I would encourage you to think about when purchasing an annuity.

 Who guarantees your payment in the future and what is their credit quality?

Keep in mind that you will be expecting payments many years into the future.  If you buy an annuity at age 50, with some luck you’ll be looking for a payment half a century into the future, and at that time your quality of life may greatly depend on actually receiving that payment.  In most cases annuity providers are insured by a government backed scheme, but you want to make absolutely sure that this is the case.  You certainly don’t want to be in a case where a Lehman style bankruptcy means that you are left with nothing in retirement when your earnings potential has greatly diminished (keep in mind that annuity providers are likely to be struggling exactly when markets are tough and you probably need them the most).

 The price of the annuity may be very high – be sure you need it!

You are essentially lending money to the insurance company for a very long time.  You can try to figure out at what rate the following way for a standard (non-inflation adjusted) annuity:

  1. Figure out your life expectancy. There are many life expectancy calculators on the internet[1] – it will be more accurate if you can incorporate where you live, etc.  This will give you a good idea of how long the insurance company expects you to pay your annuity for (make sure you tell them all the bad health stuff – as morbid as it sounds in this case you want them to think you are going to die soon).  I was surprised by how long I can expect to live, which according to a friend in insurance is a common reaction.
  2. Search around for the best annuity and be sure that the payments are in fact guaranteed by someone other than the annuity provider’s general corporate credit. Assume we are doing an annuity that you buy for £100; what will your yearly payments be?
  3. Figure out the internal rate of return (IRR) on your payment. Your IRR is the rate that the insurance company effectively borrows from you at.  So year zero: -£100, year 1: +3.75, year 2: +3.75, etc.  You can do this in excel.  Keep in mind that unlike a bond you don’t get the principal back at the end (there are annuities that do this, but the interim payments are just lower to reflect this).
  4. Figure out the average time to future payments (the duration – also use excel); depending on your circumstances it will perhaps be 15-20 years. If you start receiving the annuity payments now this will be half the years you are expected to have left to live.
  5. Compare your IRR to a government bond of a maturity similar to the duration and in the same currency (your average time to payment in 4 above).
  6. Apply some sort of discount to the annuity IRR to reflect the inflexible nature of the product and perhaps stiff penalties if you try to get out of the annuity. Depending on the policy these penalties can very stiff and you should discount the value of the annuity accordingly.

Consider any tax advantages of the annuity; these are at times significant.

As an example, when I did the above exercise as a potential annuitant, the IRR I received on my investment was slightly lower than the equivalent UK government bond.  So I essentially would be lending money to the annuity provider decades into the future at a lower rate than I would the UK government, ignoring the flexibility I would have in trading the UK government bonds if my circumstances changed.  In other words, the insurance I received from the annuity provider against running out of money in very old age was very costly.

It is not surprising that the IRR for your annuity is not great.  Annuity products are expensive to manage, and not necessarily great business for the insurance companies, as you deal with the administration of cash transfers to thousands of annuitants, in addition to marketing, overhead, re-insurance that the annuity provider will be able to pay you, and their profit and capital requirements of the annuity provider.  Just think that it costs money every time someone calls up to complain that they have not received their £300 and multiply that by a million customers – even if you are not the costly customer you share in paying for those costs by being on the same annuity platform.

My conclusion on annuities is that if you don’t have a lot of savings and worry about having enough into old age, annuities are well worth the poor return they promise on your investment.  If you don’t have a lot there is great value in knowing exactly what you have and that it will be enough.  An annuity can give you that.

If you have more assets and are highly likely to leave an estate for your descendants then perhaps reconsider annuities.  After adjusting for potential tax or other benefits the return on the assets you put into an annuity is mostly quite poor and you could make more money investing on your own.  You will of course not have the guarantee of additional payments if you live beyond your life expectancy, but considering your other assets you will be fine even without those additional monies.  Also annuity providers make large sums from the hefty penalties from changing or cancelling annuities and if there is any chance that you may be doing that do consider that in evaluating an annuity (a lot can change in decades ahead so even if you consider that unlikely now that may change in the future).  This could include if you wanted out because you no longer considered the future annuity payments secure.  Just imagine how you would feel if your old age living cost was promised by a Greek insurance company that was backed by the Greek government in case it defaulted.  You would hopefully have run for the hills a long time ago.

As evidenced by the IRR on the annuity the return profile is extremely low risk/return and that may not suit your risk profile – if you can afford greater risk in pursuit of greater returns in your portfolio an annuity may lock you in to lower return expectations for decades ahead.

[1] I used a couple including one from University of Pennsylvania:


Editor’s note: I like annuities even less than Lars. For example, please see my related posts on annuities:

Ask an Ex-banker: Annuities!

Using Discounted Cash Flows to Understand Annuities

 And please see related posts by or about Lars Kroijer:

Book Review: Investing Demystified by Lars Kroijer

Podcast with Lars Kroijer on Having an ‘Edge’ in Markets

Podcast with Lars Kroijer on Global Diversification

The Simplest Investment Approach Ever, by Lars Kroijer

Don’t Buy Too Much Insurance, by Lars Kroijer

Agnosticism Over Edge Can Earn You 7 Porsches, by Lars Kroijer



[1] I used a couple including one from University of Pennsylvania:

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Part V – Discounted Cash Flows, using an annuity to learn the math

PiggyPlease see my earlier posts

Part I – Why don’t they teach this in school?

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Part IV – Discounted cash flows – an example using a pension buyout


In the last post I used the example of a pension buyout to show how the discounted cash flows formula worked, and I argued that discounted cash flows are the key to all investing decisions.[1]  Everything else you get inundated with – from the Financial Infotainment Industrial Complex – is just a whole lot of hype, gimmicks, tricks and tips.[2]

Which makes it all the more odd that almost nobody outside of the financial industry has ever heard of discounted cash flows, never mind actually using the formula in their investment life.

So, allow me to peel back the curtain a bit more, using the example of an annuity investment.[3]


“Life’s but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more”


Another example using discounted cash flows, to value an annuity

Is that guaranteed monthly income annuity offered by an insurance company a good deal or not?  To answer the question you’d need to know how to discount cash flows to put yourself on an equal footing with your insurance company offering you the annuity.  Which I did on my site once before.[4]

Let me break down some of the numbers, by way of example, or possibly by way of inspiration to others who want to start calculating discounted cash flows in their own life.

I just went on my preferred insurance provider’s website[5] and asked for a quote on a 15-year fixed time-period annuity.  In exchange for a $100,000 lump sum from me, the insurance company offered me $641.15 per month, guaranteed, for the next 180 months.  The question I ask is whether that is an attractive investment for my $100,000?

To answer the question I’m going to use the discounted cash flows formula Present Value = Future Value/ (1+Yield/p)N.

I offer a bit more explanation of these variables in a footnote[6]

I can discount exactly 180 different future payments of $641.15, by dividing each of them by (1+ Yield/12)N.

For the first cash flow, N is 1.  For the second, N is 2.  For the 180th monthly payment, N is 180.

This looks like this table in my spreadsheet, which contains 180 rows of numbers and discounted cash flows formulas:

N Period Monthly Payment Formula: PV = FV/(1+Y/p)N
1 $641.15 =$641.15/(1+Y/12)1
2 $641.15 =$641.15/(1+Y/12)2
3 $641.15 =$641.15/(1+Y/12)3
$641.15 =$641.15/(1+Y/12)
180 $641.15 =$641.15/(1+Y/12)180


Once I have programmed a spreadsheet to calculate 180 individual discounted values for $641.15, I next program the spreadsheet to add up all 180 payments.[7]

Next I can input a value for Y, or Yield, to try to figure what kind of deal I’m offered by my annuity company.

I compare the sum of all 180 values to my original $100,000 investment.  To come up with a comparable yield on the annuity, I input different values for yields into my spreadsheet.  For my purposes I can find the ‘yield’ through ‘iteration,’ basically trying different values until I match up the sum of discounted annuity payments to a final value of $100,000.

If I assume Y is 2%, as I’ve shown in the table below, it turns out the sum of all cash flows is too small and does not quite add up to $100,000.

N Period Monthly Payment Formula: PV = FV/(1+Y/p)N Calculation
1 $641.15 =$641.15/(1+0.02/12)1 $640.08
2 $641.15 =$641.15/(1+0.02/12)2 $639.02
3 $641.15 =$641.15/(1+0.02/12)3 $637.95
180 $641.15 =$641.15/(1+0.02/12)180 $475.09
TOTAL $115,407.00 $99,633.46 $99,633.46


If I instead assume Y is 1.5%, it turns out the sum of all cash flows is too large and adds up to more than $100,000.

N Period Monthly Payment Formula: PV = FV/(1+Y/p)N Calculation
1 $641.15 =$641.15/(1+0.015/12)1 $640.35
2 $641.15 =$641.15/(1+0.015/12)2 $639.55
3 $641.15 =$641.15/(1+0.015/12)3 $638.75
180 $641.15 =$641.15/(1+0.015/12)180 $512.04
TOTAL $115,407.00 $103,287.51 $103,287.51



So I keep trying to find, using my spreadsheet, the value that makes all 180 discounted payments of $641.15 equal to $100,000.  Once I find that, I know what kind of yield, or return, my insurance company offers me on my annuity investment

It turns out, through iteration, that 1.92% is the yield I get by investing $100,000 today and receiving $641.15 per month guaranteed for the next 15 years.

The fact that 1.92% is an absolutely pathetic return is not surprising, nor notable.  As I’ve written before, insurance companies are in the business of buying money cheaply and selling money expensively, and retail annuities are the ultimate source of cheap money for them.

What is notable is that we, as consumers, have no way of evaluating the return on an annuity if we can’t do discounted cash flows.

Which is why I say, ask not what you can do with your insurance company.  Ask what your insurance company is doing to you.

Just like credit card companies do not want you to know that the average American household, carrying the average credit card balance, at an average interest rate, will pay $2.6 million over 40 years because of compound interest[8], similarly, insurance companies can build massive skyscrapers in major cities because they know how to use the discounted cash flow formula to get money cheaply.

And you don’t.

Please see earlier posts

Part I – Why don’t they teach this in school?,

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Part IV – Discounted cash flows – Pension Buyout Example

Part VI – Conclusion, or why everyone needs to know this math for the good of society

and Video Posts

Video Post: Compound Interest Metaphor – The Rainbow Bridge

Video Post: Time Value of Money Explained



Be Rational Get Real

[1] Put it this way, if you’re an individual (I will exempt broker-dealers, HFT and many professional investors from this next statement because they are often doing something different) and you’re not employing a discounted cash flows formula, you’re gambling, not investing.  Which is to say, 99.5% (and I rounded down to be conservative) of us are gambling when we purchase an individual stock.

[2] Are the Chinese buying it?  Is your gym-budding selling? Will baby-boomer demographic trends boost this?  Is Bill Ackman short the stock?  Is it a breakthrough miracle drug?  Will nano-technology make it obsolete?  All hype.

[3] I’m using an annuity to illustrate the use of the discounted cash flow formula because it’s easier to talk about the straight math of future annuity cash flows than it is to talk about modeling future stock dividends and profits.  That involves a longer conversation about equities actually just being a series of future cash flows, which most people will not want to wrap their head around at this time.

[4] By the way, I just re-read my piece on annuities from six months ago.  You should go read it.  It’s good.

[5] I mentioned USAA before in my piece on annuities, because their customer service is awesome.  I have no relationship to them other than as a customer and I just like them.  I assume their quote is standard for an annuity provider, neither better nor worse than the competition.  As I wrote you before, USAA, you should totally make me your President Palmer, peddling life insurance for you.  Call me, maybe.

[6] This time with the formula I’ve introduced the variable p, which is the number of times per year that money gets compounded.  In the case of monthly payments, p is 12, because I have to take into account compounding 12 times per year.  N remains the number associated with each payment, from 1 to 180 in our example, unique to each monthly payment.  Yield, also known as Discount Rate, is the variable I’m going to solve for, to figure out whether the investment is a good deal or not.

[7] Those of you reading this who have spreadsheet experience will note that it’s very simple to create 180 nearly identical rows of formulas simply by a click-and-drag of a single formula.  Similarly, adding up 180 different discounted cash flows is as easy as typing “=sum()” into a spreadsheet cell and referencing the correct cells.  Out pops the answer.

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