MSNBC.com columnist Bob Sullivan wrote a book Stop Getting Ripped Off: Why Consumers Get Screwed, and How You Can Always Get a Fair Deal. It was published around Christmas time last year. He spent five pages in the book trying to explain how credit card companies use the average daily balance method to calculate interest and how that method maximizes the revenue for the bank.

With the help of a spreadsheet created by blogger NCN at No Credit Needed, Sullivan showed that when a consumer doesn’t have a grace period because he’s carrying a balance, if he charged $3,000 on the 5th of the month (assuming the billing cycle runs from the 1st to the 30th), he would owe five times more interest than if he charged the same $3,000 on the 25th of the month. The author announced the surprise discovery:

"Putting off big-ticket purchases for twenty days can cut your interest charges by 80 percent!" [p. 85]

With that insight, our consumer advocate came up with a strategy: pay early, buy later.

Sullivan thinks there’s something unfair there — that the credit card companies use the average daily balance method to rip off consumers. After all, the title of the book is Stop Getting Ripped Off.

"Banks hire mathematicians to spend a lot of time trying to cook up formulas that are extremely advantageous to the banks." [p. 84]

"Spreading interest-rate charges over the maximum amount of days is a clever way to increase revenue." [p. 89]

I find it amazing how such a simple matter can get so convoluted. The whole exercise through the spreadsheet and all just showed he didn’t quite get how interest is supposed to work.

The basic principle for lending and borrowing is really simple:

If you use other people’s money, you pay interest.

In this basic form, it’s very easy to understand and I think everybody would agree that’s the way it should be. If you borrow money, you pay interest. If you borrow more money, you pay more interest. If you borrow the same amount of money for longer time, you pay more interest. If the amount and time are the same but the interest rate is higher, you pay more interest.

After you understand the basic principle, why is it any surprise that interest on a charge made on the 5th would be five times more than the same charged on the 25th? The charge on the 5th is borrowed for 25 days while the charge on the 25th is borrowed for 5 days. 25 days is five times of 5 days. Q.E.D.

I have a mathematical proof showing that calculating the interest by the amount borrowed times the number of days borrowed is exactly the same as applying the daily rate to the average daily balance for the month. In other words, the average daily balance method is consistent with the basic principle of lending and borrowing.

For the math inclined, let Ci be a charge and Di be the number of days borrowed. Let r be the daily interest rate and M be the number of days in a month. The interest for the month should be:

   SUM(Ci * Di * r)
= (SUM(Ci * Di) / M) * M * r
= Average Daily Balance * M * r

There is nothing unfair about the average daily balance method. Once one understands the basic principle of lending and borrowing, "pay early buy later" becomes so obvious — you don’t pay interest if you stop using other people’s money.

The average daily balance method isn’t the problem. Carrying a balance is. Don’t carry a balance. Enough said.

[Links to Amazon.com are affiliate links. Amazon pays me 4% - 6.5% if you make a purchase within 24 hours.]

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But the conventional wisdom is wrong. I patiently waited until I can have a real life example.

After Vanguard published the blog post, Ella posted on the Bogleheads investment forum and asked if she should invest in two ETFs right away or wait until the ex-dividend date.

OK to buy an ETF just before the dividend?

The ex-dividend date is the date when the investor will not receive the dividend. Not receiving the dividend means not paying the tax on the dividend now but paying a higher capital gains tax in the future. In effect, the tax is deferred, but not avoided.

Ella got the conventional wisdom answer from the forum participants: don’t buy a distribution; wait until the ex-dividend date. One of the replies came from Taylor Larimore. Taylor is a respected forum leader and the lead author of two Bogleheads books. On December 10, Ella decided to wait.

The two ETFs Ella asked about were Vanguard Total Stock Market ETF (ticker VTI) and Vanguard Europe Pacific ETF (ticker VEA).

On December 10, VTI traded between a low of $55.61 and a high of $55.97 a share. Let’s take an average and call it $55.79. The ex-dividend date for VTI is December 22. On that day, VTI traded between $56.30 and $56.59. Let’s take an average and call it $56.45.

If Ella bought VTI on Dec. 10, for every $10,000 she could have bought $10,000 / $55.79 = 179 shares. Those 179 shares were worth $56.45 * 179 = $10,105 on Dec. 22. In addition, she would also receive a dividend of $0.358 per share. That’s $0.358 * 179 = $64 in dividends. Together with a leftover $13 from the share purchase, Ella would have $10,182 in shares and cash if she bought on Dec. 10, versus $10,000 if she bought on Dec. 22.

The conventional wisdom market timing advice cost Ella $182 for the sake of deferring tax on the $64 dividend, which comes out to $10 at 15% qualified dividend tax rate. Giving up $182 to defer $10 is penny wise pound foolish.

The story on VEA is a little better. VEA’s ex-dividend date was December 24. Doing the same math shows Ella was worse off by $98 for the sake of deferring $34 tax.

Although the story “don’t buy a distribution” sounds credible, its base assumption “ignoring market appreciation/depreciation” is false. The market appreciation/depreciation is many times the size of the tax effect on distributions. It can’t be ignored. Worrying about the tax effect while ignoring the market movement is missing the forest for the tree leaves.

Of course someone can argue the market could’ve gone the other way and Ella would be better off waiting. But that’s precisely my point. Whether some one is better off waiting is determined by the market movements, not by buying before or after the ex-dividend date. Trying to be clever about the distribution and the ex-dividend date is unproductive in the face of market movements.

If an investor is going to time the market on the purchases, he/she should time on market movements, not on distributions and ex-dividend dates, because the former’s effect is a magnitude larger. Of course we all know one shouldn’t time the market. Therefore, don’t worry about the distributions and ex-dividend dates when their effect is just a tiny blip overwhelmed by daily volatility.

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Double-Cycle Billing Persists, Legal or Not

It’s another "banks are out there to get you" article. It alleges that some banks are exploiting a loophole in the Credit Card Accountability Responsibility and Disclosure Act of 2009 ("CARD Act") for double-cycle billing.

I’m sorry to say that the journalist was misled by her sources. Whoever fed her the story either lack basic understanding of how loans and interest work or they understand it but choose to ignore it.

The basic rule for loans and interest is if you use someone else’s money, you pay interest. The amount of the interest depends on the amount borrowed, the time in possession, and the interest rate. The reverse works when you deposit money into a bank. If they use your money, they pay you interest. I think everybody would agree to this as the basic principle of lending and borrowing.

When there are exceptions to this basic rule, the exceptions are granted by the lender out of other business considerations. The basic rule still applies. A borrower pays interest to the lender, for the amount and time borrowed.

At issue in the SmartMoney article are Macy’s and Bloomingdale’s credit cards issued by Citibank. These cards don’t have a grace period. Interest accrues from day one. The bank gives one exception to this rule: interest paid will be credited back if the borrower pays the principal and interest in full by the payment due date.

Let me put this in a picture. For simplicity’s sake, let’s assume:

• A month is always 30 days.
• Payment due date is 21 days after the end of the month.
• The interest rate is 1.5% per month, or 0.05% per day.

Suppose a consumer charges $500 on Day 1 on a brand-new card. No additional charges are made during the month. On Day 30, when the bank issues the billing statement, the amount borrowed is $500. The payment due date is Day 51. By that time, the consumer will have borrowed $500 for 50 days. The interest will be $500 * 0.05% * 50 = $12.50. Therefore the payoff amount is $500 + $12.50 = $512.50.

If the consumer pays $512.50 on or before Day 51, the bank credits back $12.50. If the consumer pays any less, the bank does not credit anything back.

I fail to see how this arrangement is unfair to the consumer. The bank said up front the card will accrue interest for each day the money is borrowed, to which the bank is fully entitled. The bank also created an exception to give an incentive to the consumer for behavior the bank desires: pay the bill in full by the due date. The bank didn’t have to create that exception. It did because it wants its customers to pay it back in full.

The SmartMoney article says if the consumer makes a partial payment, this arrangement is equivalent to double-cycle billing, which will be illegal under the CARD Act. Let’s look at the picture again. Suppose the consumer pays $412.50 instead of $512.50 on Day 51:

From the $412.50 payment, $12.50 will be applied toward interest for $500 borrowed for 50 days. $400 will be applied toward principal balance. $100 is still outstanding, accruing interest from Day 51 onward. The bank does not credit anything back.

I still don’t see anything wrong in this scenario. The basic rule for loan and interest is satisfied: pay interest for amount and time borrowed. The consumer doesn’t get an extra credit back from the bank because the consumer didn’t take up the bank’s offer (pay in full).

To be honest I’m very annoyed by these consumer advocates. They complain about the consumer having to pay interest on the $400 but they ignore the fact that the consumer indeed borrowed that $400 for 50 days. I trust they have good intentions but it seems they don’t understand the basic rule for loans and interest.

These consumer advocates are looking at the bark through a magnifying glass. They miss the forest and they miss the tree. As a result, they are advocating for the wrong thing. The issue is moot if the consumer didn’t finance their purchase at Macy’s or Bloomingdale’s. If they pay for the purchase with their own money, they won’t pay interest. Everybody should understand this simple fact.

To take it one step further, not buying whatever they bought at Macy’s or Bloomingdale’s will save the consumer a lot more than the $10 interest the bank allegedly took through a legal loophole.

I don’t work for Macy’s, Bloomingdale’s, or Citibank.

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“Also, never ever borrow against your 401k plan because you will pay double taxation on the money you borrow. Because you don’t pay taxes on the money you put into a 401k, when you pay back the loan (which you must do within five years, or 15 years if used to buy a home), you pay it back with money you have paid taxes on. Then, when you retire and take the money out again, you end up paying taxes on it a second time.”

This allegation is all over the place — MSN, USA Today, The Motley Fool, Moolanomy blog. It is a myth because there is NO double taxation. It’s a mind trick similar to that well-known “where’s the missing dollar” puzzle.

“Three men went into a hotel. The manager said the room was $30 so each man paid $10. A while later the manager realized the room was only $25 so he sent the bellboy to the 3 guys’ room with $5. The bellboy only gave each man $1 back and kept the other $2 for himself. Now 3 men paid $9 each for the room, which is $27. Add the $2 that the bellboy kept, and that’s $29. But the 3 men paid $30 originally. Where is the other dollar?”

I was able to find a good explanation for this puzzle. The $30 number is irrelevant. The correct math is $27 – $2 = $25. It makes no sense to add $2 to the $27 because it’s already a part of the $27. The $2 should be subtracted from the $27.

Now, back to our 401k double taxation myth. The fact that the loan has to be repaid with after-tax dollars is irrelevant, just like the $30 number in the hotel puzzle. If you didn’t borrow from the 401k plan but you borrowed from a bank, you’d have to pay the bank back with after-tax dollars as well. If you didn’t borrow from your 401k plan but you dipped into your own savings, you have to replace those savings with after-tax dollars too. What it really means is that a 401k loan is not tax deductible, just like any other consumer loan except a mortgage or a HELOC. Instead of saying you will be double taxed, they should just say that a 401k loan is not tax deductible, plain and simple.

I have this post in draft for a long time but Jonathan at My Money Blog beat me to it recently with two posts trying to debunk this myth (post 1, post 2). After so much discussion some folks are still not convinced. I think this issue is best illustrated by this chart below:

The left hand side represents a typical consumer loan, like a car loan. The arrows represent “borrows from” and “pays back to.” You borrow from a bank. The bank borrows from the financial market. Your 401k invests in the financial market. I think we all agree there is no double taxation in this case. You pay after-tax dollars to the bank for both principal and interest. Your 401k earns from the financial market but the earnings have to be taxed when you withdraw from your 401k.

The right hand side represents a 401k loan. Now, if you put an imaginary box in the middle on the right hand side, it becomes exactly the same as the left hand side. You borrow from an imaginary middleman and pay after-tax dollars for both principal and interest. This imaginary middleman then borrows from your 401k and passes the same dollars it receives from you to your 401k. All of a sudden you are not double taxed any more because it looks exactly the same as a car loan on the left hand side. Because this middleman is only imaginary, it follows that you are not double taxed with a 401k loan, whether for the principal repayments or for the interest.

Whether or not you are mathematically better off with a 401k loan depends on how these three rates play out:

• your alternative after-tax interest rate from a bank loan
• what bond funds in your 401k are expected to earn from the market
• the interest rate on your 401k loan

Suppose your alternative after-tax interest rate from a bank loan is 7% and the interest rate on your 401k loan is 5%. If you borrow from your 401k, you save 2% in interest cost in after tax dollars. But also suppose the bond funds in your 401k are expected to earn 8%. If you borrow from it, your 401k plan can only earn 5% from you. So your 401k plan account is 3% worse off in before-tax dollars. Between 2% better off after tax and 3% worse off before tax, it can become a wash. The reason you have to compare it with what bond funds can earn is because the 401k loan payments are not subject to market fluctuation. If you do borrow from your 401k, increase your allocation to stocks for what’s left in the plan.

While there is no double taxation on a 401k loan, there are other negatives on borrowing from your 401k plan. The biggest negative is that if you change jobs (voluntarily or involuntarily), you often have to repay the outstanding balance of the loan within a short period of time, like 60 days. Some plans actually allow you to continue the loan repayment even after you terminate employment, but not all plans do that. If you really need cash and you don’t have any other source except your 401k, taking out a 401k loan is at least better than taking a hardship withdrawal from the plan. Just be absolutely sure you will be able to repay the loan and you won’t change jobs before paying off the loan. And don’t reduce your regular 401k contributions while you are paying off the loan.

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A financial service charges no fee if you have less than $100,000 with them. If your account has $100,000 or more, they charge you $100 a year account maintenance fee. If you create multiple accounts, each with less than $100,000, then you will pay no fee for all your accounts.

The answer: What is Legacy Treasury Direct?

“Legacy Treasury Direct is a program in which investors buy Treasury bills, Treasury notes, and Treasury Inflation-Protected Securities (TIPS) directly from the U.S. Treasury, without a broker.

Established in 1986, Legacy Treasury Direct allows customers to conduct transactions through the Web, over an automated phone system, or by mail.

… …

If your account holds more than $100,000, we charge an annual fee of $100.”

Most financial services reward their larger accounts with freebies or lower fees because larger accounts are less costly to maintain and more profitable to the business. Not U.S. Department of Treasury. They punish their larger customers with a fee other customers don’t pay. If you break up your large account into several small ones, then you avoid the fee altogether. Don’t you love how our government runs its business?

This question came up on Bob Brinker’s Money Talk program on the radio two weekends ago. A woman caller said she got a notice from the Treasury Department about the fee being increased from $25 a year to $100 a year(!). She asked Brinker what to do. Bob Brinker totally blew the question. He said she would have to transfer the account to a broker and pay maintenance fees and commissions or buy CDs instead of Treasurys. Not true. There are several options for avoiding the fees and still investing in Treasurys if that’s what the woman wants.

• Stay with Legacy Treasury Direct but break up the account into two or more smaller accounts, each with less than $100k.
• Migrate to the new TreasuryDirect, although she will lose the ability to conduct business by phone or by mail because the new TreasuryDirect is online only.
• Transfer the Treasury securities to Fidelity or Schwab, neither of which charges annual maintenance fees or commissions for purchasing Treasury securities online at auction or on the secondary market.

You can’t trust what’s being said on the radio or TV, even if the person sounds like an expert.

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The rationale behind these proposals is that the mortgage interest deduction and the property tax deduction benefit only the well-off. They say people who don’t itemize their deductions don’t get those deductions. From Obama’s Tax Fairness Plan:

"Owning a home is the culmination of the American dream that so many Americans work so hard for. The tax code is supposed to encourage home ownership with a mortgage interest deduction, but it goes only to people who itemize their tax deductions. Like so much in our tax code, this tilts the scales toward the well-off. The current mortgage interest deduction excludes nearly two-thirds of Americans who do not itemize their taxes."

Is that so? On the surface, yes. If you don’t itemize your deductions, you use the standard deduction, which in 2008 is $5,450 for single and $10,900 for married filing jointly. If you pay mortgage interest and/or property tax, but if they are not large enough, you still use the standard deduction. That’s why by definition Americans who don’t itemize their deductions don’t show a mortgage interest deduction on their tax return.

However, to say that those Americans don’t benefit from the mortgage interest deduction or the property tax deduction is a misunderstanding of how taxes and math work. The tax law says everybody is allowed to itemize their deductions. Everybody starts out listing their mortgage interest, property tax, state income tax, plus any other deductions they are allowed. Say for a married couple filing jointly, those deductions add up to $6,000, then the IRS tells them

"Guess what, you are lucky. We are going to let you deduct even more than what you’ve already got here. Would you like us to top off your deductions to $10,900?"

Now they can take the IRS up on the offer or say "no thanks" and stick to their original list of deductions, which include their mortgage interest, property tax, state income tax, and everything else. In reality, when one has less in deductions than the standard deduction, nobody declines the sweet offer from the IRS because they get to deduct all the deductions they are allowed, plus a bonus deduction offered by the IRS.

Now tell me who’s better off? The taxpayers who don’t itemize their deductions but end up deducting even more than their deductions, or the taxpayers who itemize their deductions? The non-itemizers get to deduct everything they are allowed plus a bonus deduction they receive from the IRS. Itemizers don’t receive such bonus. The non-itemizers are already better off than the itemizers. If we allow a new property tax deduction under the proposed housing legislation or a new "universal mortgage credit" under Obama’s tax plan, the non-itemizers will deduct their mortgage interest and property tax twice, plus taking a bonus deduction from the IRS. Does that sound fair to you?

I’m afraid our legislators and presidential candidates don’t understand how taxes and math work because they don’t do their own taxes.

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“While you’re correct that this overstates the problem in that people won’t miss just the 10 best days of the market, you’re forgetting that the biggest days often come in the earliest stages of a recovery.

“For example, looking over the past 25 years, three of the 10 biggest days came in the week and a half following Black Monday, and two more of them occur in close succession at the very tail end of the dot bomb debacle. Thus, these days are concentrated into periods when people are especially likely to have bailed on the market and not gotten back in.

“Consider the scenario in which sometimes gets smacked on Black Monday, jumps out of the market to lick their wounds, and then immediately misses gains of 9.3%, 5.3% and 4.9%. They’ve now locked in a huge loss that they had little chance of avoiding in the first place, and they also missed out on a huge recovery.

“Calculating the probability that people will randomly miss the ten best days is a *huge* oversimplification, and it casts doubt on your entire argument.”

I want to thank Nickel for the comments and address the issue of best days coming right after the stock market bottom. Since he brought up Black Monday in 1987 and the dot com bubble, let’s take a closer look.

Black Monday was October 19, 1987. The S&P 500 dropped a whopping 20.5% on a single day, from 282.70 to 224.84. Let’s say a nervous investor sold the very next day on the open. The price was 225.06, close to the bottom made on the previous day. In the next 10 days, he would’ve missed 3 of the 10 best days in the next 20 years, which had returns of +5.33%, +9.10%, and +4.93% respectively. Does it mean this investor missed a total of (1 + 5.33%) * (1 + 9.10%) * (1 + 4.93%) – 1 = 20.6% of returns? No, after 3 best days passed, S&P 500 closed at 244.77 on 10/29/1987, up 8.8%, not 20.6%, from the 225.06 level he sold at. A little over a month later, on 12/3/1987, the market returned to 225.21, which was about the same level as the previous bottom. Now, having missed 3 of the 10 best days in the next 20 years, this investor didn’t suffer any damage if he got back in a month and half later.

Now, let’s look at the same for the 2 best days in 2002. On 7/24/2002 and 7/29/2002, the S&P 500 had two best days, up 5.73% and 5.41% respectively. By then the bear market had gone on for over two years. If an investor was nervous, he would’ve sold way before then, perhaps in early 2001 when the S&P 500 dropped to 1,300 from 1,500 in the previous year, or in early 2002 when the S&P 500 dropped more than 20% in two years. For argument’s sake, let’s say our unlucky investor sold right before the best days, on 7/23/2002, at the close of 797.70. After two of the 10 best days in 25 years, the market closed on 7/29/2002 at 898.96, up by 12.7%. Was that a permanent loss of opportunity if the investor missed those two best days? Once again, no. 2 months and 10 days later, on 10/7/2002, the S&P 500 went back to 785.28, lower than the 797.70 price before the best days.

Will the market always return to the previous low before the best days? I don’t think anybody has an answer to that. The market is volatile and unpredictable. I continue to believe that (a) it’s impossible to miss only the 10 best days; and (b) even if some best days were missed, the damage isn’t nearly as bad as those meaningless stats imply.

Suppose calculating random odds is a *huge* oversimplification like Nickel said, and because the best days often come in the early recovery days, I’m off by a factor of a billion. That is huge, right? Say instead of one in 2.8 billion billion billion, the odds of missing the 10 best days in 10 years is actually only one in 2.8 billion billion. That is still 100 times less likely than winning 2 consecutive Powerball jackpots with the same set of numbers. If I write about what I would do if I won 2 consecutive Powerball jackpots with the same numbers, nobody will take me seriously because it’s meaningless to talk about impossible events. Well the stats on missing the 10 best days in 10 years fall into the same camp. They are not worth the attention given to them.

Trust me, I don’t advocate timing the market. I just think this missing the 10 best days in 10 years thing is over-hyped by at least a factor of a billion. My question to Nickel and all other readers, if it’s not one in 2.8 billion billion billion, or one in 2.8 billion billion, what do you think the odds are for missing the 10 best days in 10 years and how do you prove it?

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There’s a chart like this in a recent issue of Schwab’s On Investing magazine (sorry, no online link):

It said the S&P 500 Index returned on average 8.4% a year between July 1, 1997 and June 30, 2006. Based on an average of 252 trading days a year, if someone missed the best 10 trading days in those 10 years, the return would’ve been only 3.4% a year. In dollars, 8.4% a year means $10,000 invested in 1997 would turn into $22,402 in June 2006, for a cumulative gain of 124%. If one missed the best 10 days, $10,000 in 1997 would only turn into $13,970 in 2006, or only a 40% cumulative gain. If someone missed the best 40 days, the return would’ve become -6.4%, which means $10,000 in 1997 would turn into $5,161, for a cumulative loss of 48%. Hmm … 124% gain or 40% gain, perhaps even a 48% loss, night and day, huh? Unbelievable.

These striking stats are used as arguments against market timing because they illustrate the risk of being out the market. Market timing means investing in the market when the conditions are considered favorable and getting out of the market when the conditions are considered as unfavorable. There are various schemes of market timing. Some are based on seasonality, some on chart shapes, some on valuation metrics. It is argued that if someone is out of the market for even a short period of time, 10 days or 40 days in the example above, and if they happen to be out on the wrong days (best X days in Y years), the long term return would suffer, a lot.

Although I haven’t double checked the statistics myself, I don’t doubt their accuracy. The stats are technically true however this piece of information is meaningless. Why? Let’s see what the stats really say. Being out of the market on the 10 best days in 10 years means that

1. Someone is out of the market for 10 and only 10 days out of 2,520 trading days in 10 years; AND
2. Those 10 days happen to be the best 10 days in 10 years.

If someone is going to be out of the market for 10 days, how likely is it that he/she will cherrypick 10 random days which in hindsight happen to be the best 10 days in 10 years? Very unlikely. How unlikely though? A math exercise will tell us.

The math formula for our calculation is called combination. We are calculating the number of ways you can choose 10 days from 2,520 trading days in 10 years. There is only one possible way those 10 days happen to be the 10 best days.

C(2520, 10) = 2520 * 2519 * 2518 * … * 2511 / 10! = 2.796E+27

You will need a scientific calculator for this. The ! symbol means factorial. If you use Excel, enter this formula and you will get the same result.

=COMBIN(2520,10) = 2.796E+27

The symbol E here represents scientific E notation. That’s 2.796 * 10²⁷, or 2,796 followed by 24 zeros. A billion is 10⁹. What we have here is that this unlucky market timer has one in 2.8 billion, billion, billion chance for missing the best 10 days in 10 years. In other words, IMPOSSIBLE. What about missing the best 40 days? Don’t even go there.

What’s the point of zeroing in on this impossible event? I don’t know. Shock and awe, perhaps. Nobody should care what happens if the chance of it happening is one in 2.8 billion billion billion. If some other one in 2.8 billion billion billion event happens to me, I will be a million times richer than Bill Gates and Warren Buffett combined. The meaningless stats don’t support effectively what they are supposed to prove. The really meaningful stats are those for the average or median impact to one’s long term return if someone is out of the market for 10 random days, or 10 random consecutive days, not the 10 best days. I’ve never seen stats for those scenarios. Perhaps because they don’t support what they are trying to tell you. My guess is that the average impact of being out of the market for 10 random days or 10 random consecutive days in 10 years is practically zero.

Does this mean it’s OK to time the market then? No, just the cited evidence doesn’t support the case. There are other valid reasons for not timing the market, but this 10 days out of 10 years thing isn’t one of them. At least one shouldn’t be too worried about being out of the market for a few days when they have a 401k rollover being moved from one place to another. Relax. It’s not a big deal as some make it out to be.

Related Posts:

• Avoiding the Worst Days and Missing the Best Days
• More On Missing The 10 Best Days

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You invest in VUL. The money in the policy grows tax deferred. You get to choose what you invest in, stocks, bonds, international, you name it. It’s like a super IRA, only way better. When you need money after you retire, you can first withdraw what you put in, then borrow from it, all tax free. When you die, your beneficiaries receive money tax free.

Sounds good? Tax deferred investing plus tax free income after retirement. Who wouldn’t go for it? If you’d like to read the full pitch, here’s an example: Variable Universal Life: Flexibility at Its Best by New York Life, whose slogan is “the company you keep.” It’s very enticing but you will see the real story at the end of this post.

VUL appeals to people who hate taxes (who doesn’t?), especially to people who have higher income and therefore in higher tax brackets. After you hear about this wonderful clever way of avoiding taxes on your investment, you go “sign me up!” Uh oh, big mistake. Let’s take a look at a real life example, from this thread on the Bogleheads forum.

Poster John and his wife each bought a VUL policy from a “friend” who works as a financial “advisor” at a “well known financial planning organization” (I’m guessing it’s Ameriprise or formerly American Express Financial Advisors). After 9 months into their policies they put in about $5,000 each for a total of $10,000. Now they realize that their VUL policies have high fees and expenses, to the tune of $1,100 a year. But, if they get out before 5 years, they will lose ALL of the $10,000 they paid into the policies (?!?!) because the first $8,300 in each policy goes toward a “surrender charge” or better put, early termination fee like that on a cell phone contract. In other words, if John and his wife put $3,300 more into each policy, the policies will still suck it all in like a black hole with nothing coming out. They paid $10,000 into two policies but they only filled a little more than half way up the big hole that the VUL policies dug for them.

Despite all the help from other posters on the forum, John’s options are still limited because the policies are designed to trap them in good with high fees and various charges. John and his wife can:

1. Keep paying into the policies and get plucked by high fees (not good); or
2. Cancel the policies now and receive nothing back (not good); or
3. Stop paying premiums and let the policies wind down by themselves (not good)

None of the three options is good. The 3rd option is perhaps the least of all evils. Basically they will let what they already paid pay for the insurance and whatever is left over stays in some mediocre investment options with high fees. Every month more money is deducted from the investments part towards the insurance part and fees. After the 5-year surrender period is over, I doubt there will be anything left. Their policies may end even before 5 years because all the money will have been depleted by insurance charges and fees. That $10,000 is gone. They won’t ever see it again. What an expensive lesson!

I feel really sorry for John and his wife. Having this done to them by a “friend” is even more sad. This VUL saga plays out over and over. It’s almost always the same story. I personally know a small business owner who was sold a VUL policy by his “financial advisor” who is also an insurance agent. The “advisor” has nice sounding credentials like CLU and ChFC. The business owner was quite mad at the “advisor” after I pointed out the fees and expenses printed in black and white in the prospectus. Of course he didn’t read the prospectus because he was busy running his business and he trusted that his so-called “advisor” would act in his best interest. The same “advisor” also sold him load funds, an expensive 401(k) plan for his business, limited partnerships that were impossible to get out of … — altogether the “advisor” cost him more than $200k.

Now let’s get back to the wonderful VUL policies New York Life sells. Here’s the 80-page prospectus (PDF, 476kB) of their NYLIAC Variable Universal Life 2000 product. Fees and expenses start on page 9.

• 4.5% – 6% charge up front for each deposit, like a load; plus
• $120 a year contract fees; plus
• 0.5% – 0.7% a year for M&E and admin charges; plus
• ~0.8% a year for expenses on investment options

Does it look like a good way of investing money? I like what poster ole meph said [1] on the Bogleheads forum:

“The only way you can benefit from this product is by dying fairly soon.”

Oh wonderful. I’m sure the clients didn’t want to pursue that route when they bought into the VUL policies.

[1] ole meph has been a veteran insurance agent and manager himself for over 40 years.

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a * b = b * a

This basic law of arithmetic is taught in the second grade in elementary school. Yet it is very useful when you evaluate the relative merits between Traditional 401k, Roth IRA, and the new Roth 401k.

Blogger Trent writes the popular blog The Simple Dollar, which is one of the most successful personal finance blogs. Unfortunately Trent made the mistake of not recognizing the Commutative Law of Multiplication. In his post The New Roth 401(k) Versus The Traditional 401(k): Which Is The Better Route? he said Roth 401k is better even if the tax rate in the future is lower than the tax rate at present. His reasoning was

“Basically, by paying $2,800 a year now in extra taxes, Joe saves himself $14,000 a year in retirement.”

Wrong. It matters not how much tax you pay at different times. What matters is how much money you have left after all the taxes are paid. Sadly when more than one commenters pointed out the problem with Trent’s math, he still insisted that his math was correct. You would think a blogger writing about finance and investment should “get it,” but I guess not.

In case someone out there is still confused, here’s how the math works. Let t₀ be the marginal tax rate now, and t₁ be the marginal tax rate at retirement time. Suppose through successful investing, you are able to grow each dollar to $n when you are ready to retire. For each dollar you invest in a Traditional 401k, you will have $n before tax, and n * (1 – t₁) after tax. In a Roth IRA or Roth 401k, for each dollar before tax, you pay tax first and have (1 – t₀) dollars left after tax. Growing the money to the same degree, you will have (1 – t₀) * n when you are ready to retire. If the tax rate now (t₀) is the same as the tax rate at retirement time (t₁), we have

n * (1 – t₁) = (1 – t₀) * n

There, is the Commutative Law of Multiplication.

If the tax rate at retirement time is lower, t₁ < t₀, Traditional 401k will be better than Roth 401k because the value on the left hand side is larger than the value on the right hand side. The opposite is true if the tax rate at present is lower, t₀ < t₁.

Of course nobody knows what the future tax rates will be or whether they will be higher or lower than today’s. In choosing between a Traditional 401k and a Roth 401k, you just have to take a guess or do a little of both. For me, my money is on the Traditional 401k. I think the Roth 401k is a device for the current government to maximize its current revenue at the cost of robbing revenues from the future government. When the future government needs money, it will find ways to raise revenue including taxing on Roth withdrawals either directly or indirectly. The laws on Roth IRA and Roth 401k only say withdrawals from them today are not taxed. They don’t say withdrawals won’t ever be taxed. Tax laws can be changed by the legislature in the future.

Related Post: The Case Against Roth 401(k)

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