Tuesday, October 30, 2012

Value Averaging Doesn’t Work

Andrew Hallam wrote a piece in the Globe and Mail that likened enhancing performance in sports by blood doping to an investing method due to Michael Edelson called “value averaging”. Value averaging is simple enough to understand, and if you use the wrong method of evaluating its results, it seems to boost returns. However, the reality is that it doesn’t boost returns, and it drives up your investing costs.

The idea of value averaging is to keep your portfolio increasing at some target rate, regardless of what happens in the market. For example, if you target a 0.5% return each month, if the market goes up more than 0.5%, you sell some of your portfolio; otherwise, you add more cash to buy more assets. No matter what happens in the market, your portfolio rises steadily.

An immediate problem arises: where do I get this cash to pour into my investments when the market drops? The answer is that you’re supposed to keep a side pot of cash that you either put money into or take money from each month. Over time this pot of cash could either dry up or become quite large depending on how the market moves. To deal with this, the strategy calls for a reset every so often (say 3 years) where you reset the cash level to some fixed percentage of your portfolio’s size.

The selling point of value averaging is that you add money when the market is down and pull money out of the market when it’s up; buy low and sell high. This gives an internal rate of return (IRR) that beats the market return and also beats dollar-cost averaging. So far, what’s not to like?

The problem is that the IRR calculation only takes into account the money actually invested in the market. It ignores the cash that you have to keep on the sidelines. However, this cash is real money that you have to keep around earning low returns.

When you factor in the cash, value averaging gets worse returns in most markets than a simple buy-and-hold strategy. It isn’t hard to see why this is true. At any given time, a buy-and-hold investment is fully invested. However, a value averaging investment is only partially invested. The tendency for markets to go up creates an opportunity cost for the cash on the sidelines. This cost exceeds the boost that comes from a higher IRR.

One remedy for this problem might be to start with no cash on the side and plan to borrow as necessary to run the value averaging strategy. However, there is a gap between the best interest rate you can get on your cash and the lowest interest rate you can get when borrowing. This gap serves as a drag on value averaging returns. Another problem with this remedy is the possibility of becoming highly leveraged if markets drop significantly.

If you are interested in a more technical critique of value averaging, read Simon Hayley’s paper Value Averaging and How Dynamic Strategies Bias the IRR and Modified IRR. He concludes “Value averaging does not boost profits, and will in fact suffer substantial dynamic inefficiency. It also imposes additional direct and indirect costs on investors as a result of its unpredictable cashflows. The strategy thus has very little to recommend it.”

With the promise of lower returns and higher trading costs with value averaging, I’ll happily stick to my buy-and-hold approach with occasional rebalancing.

Monday, October 29, 2012

Defending ‘Homemade Dividends’

Dividend investors and indexers often disagree strongly on the relative merits of their investing strategies. Recently, the Dividend Growth Investor argued that homemade dividends produced by selling some stock are not as good as real dividends. However, we can easily show that the core of the disagreement comes down to whether or not dividend stocks have an expectation of higher total returns.

For the purposes of this discussion, let’s compare an indexed portfolio of stocks that pay a 2% dividend to a dividend stock portfolio that pays an average of 4% dividends, both in tax-advantaged accounts. For the investor who wishes to live on 4% of his portfolio each year, his choices are to go with the indexed portfolio and sell 2%1 of his shares each year, or go with the dividend portfolio and live off the 4% dividend.

Dividend Growth Investor argues that “when someone sells a portion of their portfolio, they end up with less [sic] shares.” However, if the two portfolios get the same total return, then the shares in the dividend portfolio will be worth 2% less than the index portfolio shares are worth just prior to the sale of 2% of the index shares. After this sale, the two portfolios will have the same portfolio value.

Dividend Growth Investor goes on to argue that “Sometimes share prices fall or stay flat for extended periods of time, which could spell trouble for these [index] investors.” The implication here is that the index portfolio is shrinking, but the dividend stock portfolio is not. However, this can only be true if the dividend stocks are getting a higher total return. Otherwise, if index stocks are flat, dividend stocks are suffering a 2% capital loss each year.

I could go on, but all of the arguments come down to the same thing: will carefully-selected dividend stocks get higher total returns than the index or not? If the dividend stocks outperform, then the dividend investors are right; otherwise the indexers are right. Unfortunately for the dividend investors, the apparent evidence for long-term dividend stock outperformance has significant survivorship bias. If the indexers are right, then they have the advantage of a slight boost to returns that comes from better diversification.

1 The actual percentages are slightly off these approximate figures due to compounding effects, but I’ll use the round numbers to avoid muddying the waters.

Friday, October 26, 2012

Short Takes: Pitching Leverage to Seniors, Students with Credit Cards, and more

Depth Dynamics has an interesting story of a pitch to financial advisors to get them to promote leveraged investing. They also tell the story of a couple in their 70s who lost money after being talked into using leverage. Thanks to Ken Kivenko for pointing me to this one.

Rob Carrick says that students handle credit cards better than many people think. I wonder, though, whether the various statistics Carrick quotes include the effect of parental help. Some students’ parents pay their credit card bills for them every month. And some parents pay off credit card bills for students who get themselves into debt trouble. This doesn’t always happen, but it happens often enough to skew the statistics to make it look like students handle credit cards better than they really do. You can be sure that banks know that parents are often willing to bail out students with debt problems. This makes students good candidates for credit cards (in the banks’ eyes).

Mr. Money Mustache makes a thoughtful case for why paying someone else to maintain your property and possessions doesn’t make as much sense as you might think.

Jonathan Chevreau reiterates his case for saying “financial independence” rather than “retirement”. He has a good point that the real goal ought to be financial independence. Once this is achieved, we can decide whether or not to work.

Larry MacDonald doesn’t think that housing market timers will fare any better than those who try to time the stock market.

The Blunt Bean Counter finds a humorous way to approach the morbid subject of whether your spouse has enough information to properly handle the family finances if you die.

Gail Vaz-Oxlade explains that “savings mockers” can be a bigger threat to savers than their own temptations. She manages to work in the phrase “big fat FU Account” and uses a cool word “thoil” that helps express why you can afford something but choose not to buy it.

My Own Advisor updates his progress toward his 2012 financial goals. It seems that he’s right on track without adding any new debt.

Big Cajun Man is a man of simple tastes who doesn’t see the need for a bucket list.

Wednesday, October 24, 2012

Investing with My Two Brains

The latest Carrick on Money post declared “my brain is a lame investor” and pointed to a well-written summary of 7 way your brain is making you lose money. Fortunately for me, I feel like I have two brains and only one of them is a lousy investor.

I have one brain that tends to be emotional and makes snap decisions. It’s quite good at deciding whether to zig or zag in a touch football game and helps me pick up tells on opposing poker players. Unfortunately, it stinks at investing. My other brain – the rational one that tries to think everything through and makes deliberate decisions – has turned out to be the better investor.

My years as a stock-picker began during the late 1990s tech boom. Along with almost everyone else, I was overconfident and took wild chances. I did use my rational brain to pore over company reports and accounting statements looking for useful information. However, when it came time to make a trade, it took my emotional brain to ignore the fact that there were almost certainly thousands of people around the globe doing a better job than I was at analyzing the company’s information. My rational brain would have seen the futility of trying to out-trade all these better investors.

In poker I’ve noticed that the bigger the pot, the worse my emotional brain performs. I’ve improved my results simply by taking my time and letting my rational brain work. When it comes to investing, almost all the decisions are for high stakes. I’m far better off making decisions slowly and carefully.

This doesn’t mean that all stock-pickers are acting emotionally. The rational question to ask yourself is whether you are really good enough to trade against the sharks. If you are, then stock-picking can be the rational choice. However, for the vast majority of us, active stock-picking is ignorance or hubris.

Monday, October 22, 2012

MPAC’s Tricky Request for Reconsideration Process

In Ontario, the Municipal Property Assessment Corporation (MPAC) administers the property assessments used to determine property taxes. I just discovered that MPAC’s estimated area of my property is way off. However, the official Request for Reconsideration process is onerous enough that I probably won’t bother to appeal.

My fun began when my latest property assessment arrived in the mail recently. The form contains an “access key” which allows me to look up the data MPAC has about my property at their About My Property web site. This seems quite civilized. It was after poking around on this site for a while that I discovered that MPAC thinks my property is about 24% larger than it really is. My best guess is that this has cost me about $1500 in extra property taxes over the years.

The problem is that my property is not rectangular. The way MPAC estimates the width is sensible, but the estimate of depth is way high.

In a burst of optimism, I started poking around for the forms page and the particular Request for Reconsideration form relevant to me. The form begins by requesting some sensible information to identify me and my property followed by a section allowing me to explain what is wrong with my current assessment. That’s when things went off the rails for me.

The form then asks for all kinds of information about my house and property that have nothing to do with the problem that needs addressing. MPAC would have me running around measuring all the rooms in my house, calculating areas, trying to figure out what “cladding” means, and trying to decide whether the finished part of my basement is 1/2 finished or 3/4 finished.

The optimistic side of me says that MPAC will see that the property area is wrong and drop my assessment enough to save me about $125 per year. My pessimistic side says that MPAC will likely stand by their method of estimating area with some rock-solid logic like “that’s the way we do it,” and they’ll use the random answers I give to the questions I didn’t understand properly to raise my taxes.

Based on a guess of the likelihood of different outcomes if I appeal, I think my statistical savings are small, and all the effort isn’t worth it. I’ll just keep paying taxes on a big chunk of lawn that doesn’t actually exist. Congratulations to MPAC for cleverly coupling a Request for Reconsideration with an extensive request for information that is mostly irrelevant to the problem the homeowner has identified. This must cut way down on complaints; it worked on me.

Friday, October 19, 2012

Short Takes: Massive Phone Bill, How Indexing Affects Professional Money Managers, and more

What’s a factor of 100 trillion between friends? A woman in France received a phone bill that had an extra 14 zeros added to it!

Larry Swedroe examines the claim that index investing increases correlations between stocks making “it harder for active managers to harvest the winners” and argues that it isn’t true. Even if it were true, why would I abandon indexing to lose money picking my own stocks just so some professional money manager can have a better chance to pick winners?

SquawkFox has some thoughts on how to get around the upcoming Globe and Mail paywall.

The Blunt Bean Counter put together a collection of punitive income tax provisions. Don’t get caught by any of these.

Rob Carrick says that “Asking a senior to co-sign or guarantee a loan is a form of elder abuse.”

Canadian Capitalist looks at the impact of Vanguard changing the benchmark for one of their ETFs.

Preet Banerjee says “I’ve always thought that if you really knew what you needed to know to pick the right financial adviser, you probably wouldn’t need one.” He goes on to explain what we need to know about the various professional designations.

Big Cajun Man has a list of ten things he’s actually said that have saved him money while negotiating a price.

Retire Happy Blog asks whether Freedom 35 is possible. I sort of did it at age 37, but then I gave away a lot of money. I figure that with conservative assumptions I’ve got enough money to get me into my mid-70’s. That’s why I’m back to work again. I didn’t think it was smart to wait until I’m old.

Wednesday, October 17, 2012

Fun with Studies of the Value of Financial Advisors

Do you think a financial advisor would rather take on and keep a client who already has a lot of money or a client with little savings? The answer is obvious, but this fact was missed by University of Montreal researchers who conducted a study of the value of financial advisors.

The researchers collected survey data from 3610 working-age Canadian households. They asked many questions related to income, savings, and financial advisors. Among their conclusions was the following:
“Controlling for multiple factors ... Those with 15 years or more [with a financial advisor] will have 173% more assets than if they did not have a financial advisor.”
The study’s authors offer the following thoughts on this conclusion:
“This amount is too large to be explained simply by better stock picking. One highly plausible explanation of this finding comes from the greater savings that is associated with having a financial advisor and other appropriate advice.”
Despite the fact that this 173% figure seems like conclusive proof that advisors give great value in helping their clients save and grow their money, I think there is a better explanation related to the question from the opening paragraph.

I went through the survey questions in Appendix B of the report to confirm that the researchers didn’t ask any questions about how much money advised people had before they took on an advisor or how much money non-advised people had in the past. So, previous wealth could not be part of the controlling factors. At least part of this 173% edge for advised people must come from advisors seeking out clients who already have significant assets.

Another problem is that an advisor-client relationship is more likely to sour if the client fails to save much. So, looking at people who have had an advisor for 15 years will create a large survivorship bias when you try to measure whether an advisor helps people save more money. It could be that advisors help people save more money, but it could also be that advisors dump clients who don’t save enough money.

When it comes to controversial research, it’s common for critics to focus on small problems and blow them out of proportion to unfairly discredit the work. However, in this case, the bias caused by the need for advisors to find clients with significant assets (and avoid those with little money) is potentially large enough to completely swamp the finding of a 173% edge in savings for people working with an advisor for 15 or more years. This paper adds next to nothing to the question of whether financial advisors help their clients.

Tuesday, October 16, 2012

A Mathematician Plays the Stock Market

In the late 1990s, it seemed like everyone was a stock market expert. This was fueled by the fact that it didn’t matter much which tech stock you bought because almost all of them went up. Even mathematician John Allen Paulos got caught up in the hype with WorldCom stock. In his book, A Mathematician Plays the Stock Market, Paulos weaves a humble story of his investing folly along with many understandable mathematical lessons about investing.

Like many “investors” at that time, Paulos abandoned good risk management and “invested heavily in WorldCom, as did family and friends at [his] suggestion.” He even “emailed Bernie Ebbers, then the CEO, in early February 2002 suggesting that the company was not effectively stating its case and quixotically offering to help by writing copy.” Of course, the world later found out that the real problem was “creative accounting” rather than poor marketing.

On index investing, the author makes an interesting point that despite the fact that it “generally beats the more expensive, managed funds,” investing in an index fund has a cost: “One must give up the fantasy of a perspicacious gunslinger/investor outwitting the market.”

On online trading, Paulos said “The ease with which I clicked on simple icons to buy and sell ... was always a little frightening, and I sometimes felt as if there were a loaded gun on my desk.”

There were a few not so good parts of the book, but they didn’t take away from my enjoyment of it. The author claims that the S&P 500 index suffers from survivorship bias, but I don’t think this is true. In a couple of places one of the numbers in the Fibonacci sequence is wrong. In a numerical example about compounding, one of the amounts is off by a dollar.

Overall, I thoroughly enjoyed this book and recommend it to anyone who would like clear explanations of investing matters without too much mathematical jargon, or anyone who would enjoy reading about a smart guy admitting to all of the dumb things he did while trying to get rich in the stock market.

Monday, October 15, 2012

Who Loses Money to Insider Traders?

There is no doubt that when insider traders make money illegally by buying a stock before it is about to rise or selling a stock before it is about to fall, some other traders must be losing this money. However, it can be challenging to figure out exactly who is losing money.

The following argument by John Allen Paulos1 sparked my interest in this question:
Consider “a pair of similar situations. In the first one you buy a stock ... and your earnings are $1,000 if it rises the next day and -$1,000 if it falls. (Assume that in the short run it moves up with probability 1/2 and down with the same probability.) In the second there is insider trading and manipulation and the stock is very likely to rise or fall the next day as a result of these illegal actions. You must decide whether to buy or sell the stock. If you guess correctly, your earnings are $1,000 and, if not, -$1,000. ... Your chances of winning are 1/2 in both situations. ... The unfairness of the second situation is only apparent.”
Paulos isn’t defending insider trading, but just observing that the two situations are the same from your point of view even though the second one seems unfair. However, we can’t conclude that insider trading is harmless. These scenarios are idealized and there are other traders who may have been harmed.

If an insider trader makes, say, $1 million illegally on ABC stock, who has lost this $1 million? Let’s suppose that the insider trader buys 100,000 shares of ABC stock for $20 each on a Monday knowing that big positive news is coming, and he sells the shares for $30 each on Tuesday pocketing $1 million in profit. In very simple situations we can tell who has lost the million.

Suppose that the only trades in ABC stock on Monday and Tuesday are these two trades. Suppose further that the effect of the Monday trade on the market does not influence the actions of any other traders. Suppose even more improbably that the same party (let’s call him “chump”) takes the other side of both trades. In this simple and highly unrealistic scenario it’s obvious that the chump is the one who lost the $1 million made by the insider.

But what about a more realistic scenario where there is continuous trading in ABC stock, the market impact of the Monday insider trade influences other traders’ decisions (possibly even traders of other stocks), and more than one other trader is involved in the 100,000 shares traded by the insider on both Monday and Tuesday?

It’s quite likely that the $1 million loss is shared among many traders. Even people who made no trades may have lost money because the effect of the insider’s trades caused them to change their minds about making a trade. It’s even possible that some traders made money because of the way they were influenced by the insider’s trades.

The only way I can see of determining who loses and how much they lose is by running two world histories (inspired by the many-worlds theories in physics). In one history, the insider doesn’t make any trades and in the other one he does make his trades. We could then compare the outcomes for every market participant to see how much more or less money they have in the scenario where the insider makes the trades. Of course, this many-worlds experiment is impossible and we just can’t know for certain who shares the $1 million loss. It’s even possible that the total losses of all traders other than the insider won’t add up to exactly $1 million if the insider’s actions somehow affected wealth creation somewhere.

1 Quoted from the book A Mathematician Plays the Stock Market.

Friday, October 12, 2012

Short Takes: Home as a Retirement Plan, Leaking from Your DRIP, and more

In a video interview, Malcolm Hamilton says that most Canadians should not view their homes as a source of retirement assets.

Canadian Capitalist finds another way that discount brokerages take your money with currency conversions.

The Blunt Bean Counter has some concrete suggestions for those in debt to get organized and make a complete snapshot of their debts.

Rob Carrick says that car insurers just don’t get Generation Y.

Preet Banerjee says that establishing a habit of saving is more important initially than worrying about investing fees. He’s right that the expense ratio on the funds you own becomes more important as your total assets grow.

Million Dollar Journey lists 5 types of insurance you should avoid. However, you should definitely consider the insurance I offer which covers being hit by a meteor, lightning, and an airplane simultaneously.

Big Cajun Man had some trouble canceling a Motley Fool newsletter subscription after the free period was over.

Thursday, October 11, 2012

5 Ways to Save Money on [Item]s

This is a template for a guest post on a blog. Read at your own risk.

1. Buy a Less Expensive [Item]

[Item]s can be very expensive. But, if you look around, you can find less expensive [item]s that are just as good. If you keep buying the expensive version, you could end up needing the services of [embedded link to credit-counseling business].

2. Don’t Buy So Many [Item]s

Try to extend the life of your [item] by taking care of it. If you can’t do this you could end up needing to see [embedded link to payday loan company].

3. Look for a Used [Item]

blah blah blah ... [link to random page in this blog to make this guest post seem like it belongs].

4. Another Ridiculously Obvious Suggestion

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5. Insultingly Simple Idea

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This guest post was brought to you by [link to more examples of this wonderful author’s work].

Wednesday, October 10, 2012

The Rare Triumph of Diversifying with Bonds

There are good reasons for investors to reduce the riskiness of their portfolios using bonds. However, some commentators like to point out the surprising result that a portfolio mixing stocks and bonds can sometimes beat both the all-stock portfolio and the all-bond portfolio. A recent example is a post by The Reformed Broker titled ‘The Triumph of Diversification’. I ran an experiment that shows that this kind of reporting can set up investors for unrealistic expectations.

Common sense tells us that if you start your investing year with some stocks and some bonds and make no trades, your overall return will be somewhere between stock returns and bond returns. However, by a quirk of mathematics, if you rebalance to your target portfolio mix after each year, it is possible for your multi-year returns with a mixed portfolio to outperform both an all-stock portfolio and an all-bond portfolio. Somehow your portfolio can become better than the sum of its parts.

I decided to see how often this happens. I used data since 1970 on Canadian stocks and bonds provided by Libra Investments to check the 33 rolling ten-year periods since 1970 to see how a 70/30 mix of stocks and bonds would have compared to either all stocks or all bonds.

Out of the 33 ten-year periods, the 70/30 mix won out 4 times. In each case, average yearly stock and bond returns were within 1% of each other and the 70/30 mix won by less than 0.08%. So, while a mixed portfolio can beat both stocks and bonds, it happens infrequently and the edge tends to be very small.

None of this means that a mixed portfolio is bad. It’s just that you should be considering including bonds in your portfolio for the purpose of controlling risk rather than hoping to outperform an all-stock portfolio.

Friday, October 5, 2012

Short Takes: Vanguard Changes Benchmarks, Jail Time for Mortgage Fraud, and more

Canadian Couch Potato and Canadian Capitalist report that Vanguard will be changing the benchmark it uses for several of its index ETFs to save on benchmark licensing fees.

Canadian Mortgage Trends reports that a mortgage broker who submitted fraudulent mortgage documents on behalf of his clients in an effort to improve their chances of approval will be going to jail. They say this is a good thing because questionable mortgage documentation is all too common.

Million Dollar Journey reports stock-picking contest results to the end of Q3. The average return of the 10 participants is 4.5%. This trails the TSX at 6% and the S&P 500 at 15%. I guess I’ll stick to indexing.

Big Cajun Man is worried about the looming bacon shortage. Of course, we won’t have an actual shortage; it’s just that the price is going to rise. That’s the great thing about free(ish) markets; you can always have what you want if you’re willing to pay for it.

Retire Happy Blog says that the ability to save money is a combination of nature and nurture.

Wednesday, October 3, 2012

Dealing with Layoffs

Having worked in the private sector throughout my career, I’ve seen my share of rounds of layoffs. Even the most successful company will eventually stumble and not have enough revenue to pay all of its employees. What amazes me about large layoffs is that employees are unable to see them coming and do little to prepare themselves.

Businesses have owners who invest their money to make a return. If a business misses its profit target, owners will be unhappy. A common remedy to improve profitability is to lay off employees. So, employees who see their company missing profit targets should immediately expect that layoffs are a possibility.

But most employees are shaken when they learn that layoffs are planned, despite the seemingly obvious clues. They go from feeling safe and happy to feeling afraid for their futures. If their finances can’t withstand unemployment, it makes sense to be fearful. The part that doesn’t make sense is having felt safe and happy before the layoffs were announced.

A feeling of financial safety should come from having sufficient assets to withstand a long period of unemployment, not from a misguided sense that one’s employer seems stable and isn’t planning any layoffs.

At the inevitable company-wide meeting after a round of layoffs is complete, a common question is “are there going to be more layoffs?” This question is usually pointless because its answer depends on whether future revenues improve or get worse. The people who ask this type of question tend to see layoffs as arbitrary rather than as a direct consequence of poor financial results.

I expect most readers of this article who are employed in the private sector to react with brief unease followed by rationalizing that there won’t be any layoffs at their company. A much more useful response would be to cut personal spending and build some savings. Fat bank accounts and investment portfolios are the best reason to feel financially secure.

Tuesday, October 2, 2012

What’s in a Name?

Most of my readers know of Rob Carrick, a personal finance columnist at the Globe and Mail. He does an excellent job of cutting to the important parts of just about any financial story that affects your wallet. He also has a blog consisting of his picks of the best articles related to personal finance.

The Globe and Mail ran a contest to rename Carrick’s blog. The winning name was Carrick on Money. I must say that this name sounds great to me. However, I have a nagging feeling that it seems familiar. Can anyone help me figure out why it feels like I’ve heard it before?

Kidding aside, I hope Carrick continues delivering solid information to help us all run our financial lives well.

Monday, October 1, 2012

Is a Lump Sum or Annual Contributions Better for an RESP?

Nancy Woods at Globe Investor answered a reader question about an RESP for his newborn grandchild: “does it make more sense to contribute a lump sum and forgo the government grant (CESG) or do I make annual contributions and take the government’s free $500? Signed Bill”. Unfortunately, her analysis failed to find the best option.

This question only matters if Bill actually has $50,000 (the maximum total contribution RESP amount) available right now. So, he either throws it all into the RESP now or he puts a certain amount in each year and invests the amount held back in a non-registered account.

The advantage of the lump sum right now is longer tax-free compounding. The advantage of spreading out the contribution is that each year the government will match 20% of the contribution up to a maximum of $500 per year and a lifetime maximum of $7200. (There are also catch-up provisions, but they are not relevant in this case.) Woods concludes that Bill has two options:

1. Make a $50,000 contribution right away and get only one $500 government grant.

2. Maximize the government grants by making a $16,500 contribution in the first year, then $2500 more each year for 13 years, and a final year’s contribution of $1000.

Assuming a 5% annual investment return (tax-free in the RESP and taxed in the non-registered account), option 1 leads to an RESP balance of over $121,000 when the grandchild turns 18, but option 2 only gives $119,000 in total between the RESP and non-registered account.

Woods concludes that tax-free growth trumps the government grants by a small margin. However, she fails to consider the best option, which is somewhere between options 1 and 2. To see what I mean, consider the strategy of making a $47,500 contribution right away and $2500 the next year. This would get $1000 in government grants. Compared to option 1, this strategy loses out on one year of 5% tax-free growth on $2500 but makes 20% on this $2500 with a government grant. This is clearly better than option 1.

Even better would be if Bill makes an initial $45,000 contribution right away and $2500 for 2 years. No doubt you can see where this is going now. The best answer is for Bill to make a sizeable initial contribution and then $2500 for several years until he reaches the maximum $50,000 lifetime maximum. The optimum number of years of smaller contributions depends on the rate of return assumptions and Bill’s marginal tax rate.

If we assume a 5% investment return and a 40% marginal tax rate, Bill’s best option is a $35,000 initial contribution and $2500 more each year for 6 years. This gives Bill’s grandchild a final total of over $124,000 at age 18. The best strategy will vary with the return and tax assumptions, but one thing is certain: contributing an initial lump sum of $50,000 is not optimal under any sensible assumptions.