Portfolio fraction averaging

In the last couple of days, Michael James has been exploring variations of the 4% rule, and has proposed his own modified version, which simply states that you should spend 4% of your portfolio per year, and allow the resulting income to fluctuate.

Though this strategy as stated leaves some important questions unanswered, it does have a fundamental advantage over William Bengen's original 4% rule, which advises a constant withdrawal (in real terms) in dollars every year.

Bengen's advice amounts to dollar cost averaging in reverse: rather than periodically buying a fixed dollar value of assets, you periodically sell a fixed dollar value of assets.

The name "dollar cost averaging" refers to the fact that the average price you're paying for assets is determined by spending a fixed dollar cost for each purchase. The average price paid for the assets equals the total paid divided by the total units purchased, and in the case of dollar cost averaging, this works out to the harmonic mean of the purchase prices (though I'll spare you the mathematical details). This kind of mean makes DCA attractive while buying, and much less attractive while selling.

For example, consider just two purchases using dollar cost averaging, buying $1 of assets each time. For the first purchase, the asset cost 20 cents per unit, and for the second purchase, it cost 5 cents per unit. The first purchase gets 5 units, and the second gets 20, for a total of 25 units costing $2, which is 8 cents each.

Michael's plan, on the other hand, advises you to sell a fixed fraction of your portfolio each time period. This "portfolio fraction averaging" is, to a first approximation, much like selling a fixed number of asset units each time. (The diminishing number of units held is offset by new units purchased by reinvested dividends, so let's ignore both of these things for now.) The average price for each unit in such a scheme is the arithmetic mean of the individual sale prices.

Using the same example asset as before, consider just two sales using portfolio fraction averaging, where 4% of your portfolio amounts to one unit. The first sale would earn 20 cents, and the second sale would earn 5 cents. The two units together netted 25 cents, for an average of 12.5 cents each. Note that this is more than the 8 cent average we paid for these units. The arithmetic mean is always greater than the harmonic mean!

So, when you sell your assets, would you prefer to earn an average of 8 cents per unit, or 12.5 cents?

I thought so.

Is the 4% rule good advice?

If you've spent any time reading personal finance blogs, you must have come across the "4% rule". It is quoted with impressive regularity, yet it is rarely explained, and even more rarely questioned.

What is the 4% rule?

Many would summarize the 4% rule as follows:

You can safely withdraw 4% of your retirement savings each year in retirement without risk of running out of money.

This statement is not only vague; it's inaccurate. It doesn't say anything about how the retirement savings is invested, or how to cope with inflation, or just how much risk there is of running out of money.

The 4% rule was first developed in a paper by William Bengen. Here is the 4% rule from the horse's mouth:

For a client just beginning retirement, determine first the "safe" withdrawal rate. … For a client of age 60–65, this will usually be about 4 percent. The withdrawal dollar amount for the first year (calculated as the withdrawal percentage times the starting value of the portfolio), will be adjusted up or down for inflation every succeeding year. After the first year, the withdrawal rate is no longer used for computing the amount withdrawn; that will be computed instead from last year's withdrawal, plus an inflation factor.

So this is not a withdrawal rate of 4% per year. It's a withdrawal rate of 4% in the first year, adjusted for inflation thereafter.

What is Bengen's advice for asset allocation?

Despite advice you may have heard to the contrary, the historical record supports an allocation of between 50-percent and 75-percent stocks as the best starting allocation for a client. For most clients, it can be maintained throughout retirement, or until their investing goals change. Stock allocations below 50 percent and above 75 percent are counterproductive.

And just how safe is this strategy? Bengen back-tests the strategy using market performance and inflation numbers between 1926 and 1992. With a 50/50 split between stocks and bonds, Bengen concludes:

Assuming a minimum requirement of 30 years of portfolio longevity, a first-year withdrawal of 4 percent, followed by inflation-adjusted withdrawals in subsequent years, should be safe. In no past case has it caused a portfolio to be exhausted before 33 years, and in most cases it will lead to portfolio lives of 50 years or longer.

Of course, the merits of conclusions based on back-testing can be questionable, but at least we know exactly where the 4% rule comes from.

Does this make sense?

The main problem I have with this advice is that it breaks what I consider a very reasonable soundness test: two people in identical situations should be given the same advice. However, consider Allan and Barney, both 65 years old with $1M in 50/50 stocks and bonds, and both with the same actuarial risks (both married, non-smokers, living in the same part of the country, etc.). Suppose inflation is 3%.

Allan is retiring in March 2009. Barney retired in March 2008. At the time, Barney's nest egg was $1.3M. He dutifully withdrew $52k for the year.

What advice do we give these two men in March 2009?

We advise Allan to withdraw $40,000 (which is 4% of his portfolio), but we advise Barney to withdraw $53,500 (the previous withdrawal adjusted for inflation) despite being in precisely the same financial situation. To me, this is inherently irrational, but it's hard to offer better advice to poor Barney, who would be understandably upset at the prospect of decreasing his annual income by 20%.

Can we do better?

A subsequent paper by Scott, Sharpe, and Watson addresses the question of whether Bengen's strategy is the most cost-efficient way to ensure you get a reliable cash flow during retirement. They identify two sources of inefficiency: one is a relatively minor one that they address using option trading; I find that one fairly uninteresting because it only amounts to 2-4% of your savings, and recouping that requires some fairly esoteric financial maneuvering. However, the more interesting inefficiency is fairly straightforward and accounts for 10-20% of the portfolio's value.

To understand this inefficiency, first consider that if you kept your nest egg as cash under your mattress, you could safely withdraw 4% per year for 25 years with zero risk of running out of money during that time. Suddenly, investing in a mix of stocks and bonds to achieve a probable 33 years of withdrawals is not so impressive anymore.

Of course, your mattress doesn't compensate you for inflation, but this is easily fixed using inflation-protected government bonds. With a typical real return of 2%, Scott et al argue that the retiree could finance 30 years of guaranteed inflation-adjusted withdrawals for the price of just 22.4 years. This amounts to a withdrawal rate of 1/22.4 = 4.46%!

What gives? How could stogy old inflation-protected bonds offer a withdrawal rate 11% higher than that of the stocks-and-bonds portfolio?

The answer is that choosing the bonds over the market portfolio gives up both the potential upside and downside of the market. Because the market generally increases over time, the upside over a 30-year time frame is much higher than the downside risk, and the market values this at approximately 11% of the withdrawals per year.

The bond investor has also accepted the certainty that his money will be gone after year 30. The stocks-and-bonds investor likely still has money left to continue his withdrawals indefinitely, and extremely likely still has enough at least for years 31-33.

This is what the inflation-protected bond investor has given up in exchange for a 11% higher withdrawal rate and zero risk.

So what should we do?

The best course of action may be a combination of the two. Buy inflation-protected bonds to fund 30 years of living expenses based on your budget, and use the remainder of your portfolio to invest in stocks and bonds, which could improve your standard of living, fund your expenses after 30 years, and leave an inheritance for your family.

Time-tested financial advice

I've been a bit preoccupied lately, so it has been a while since my last blog post. It will probably be another couple of weeks before I'm back in the swing of things.

In the mean time, check out this financial advice from fellow blogger Nicholas. This is one that deserves to be in everyone's blogroll. He boils investing down to three basic steps, and discusses some common investing misconceptions.

Securities lending: the next bubble?

So it goes something like this: you buy units of an ETF, which holds securities on your behalf. Then the fun begins: the ETF lends your securities to someone who wants to short-sell them, and the ETF charges interest. More money for the unitholder and for the ETF management. Everyone wins, right? Not so fast...

There have been several sobering posts lately regarding this practice of security lending by ETFs. By way of background reading, here are a few good articles by Larry McDonald:

• Securities Lending Wake-up Call
• Two related blog posts here and here
  

Finally, as of a couple of years ago, someone has done the obvious, offering an ETF with a nominal expense ratio of 0%, with management making all their money from security lending.

While this is an obvious triumph of marketing, it scares me. Now, I am not an expert here; I don't know the ins and outs of the regulations surrounding these investment practices. But having said that, the main problem I see is that this scheme doesn't align the interests of the shareholder and management. Management's entire profit comes from security lending, and the profit of security lending can be boosted a few ways, such as, I dunno, lending at higher interest to those with a lower credit rating, or investing the collateral aggressively. Worst of all, while all the potential for profit goes to management, all the risk of loss is borne by the fund investor.

This is a scary situation. You've got a scheme that offers money for nothing with a plausible, if esoteric, explanation ("hey, we're not angels; we make our money from security lending, but don't worry your pretty little head about complicated details like that"); and it does so with a scheme that puts management's interest at odds with the interests of investors. Worse, the kinds of abuses that this scheme invites seem to be the same kind of aggressive lending and investing practices that led to this financial meltdown that some of of you may remember from a few months back.

As usual, Vanguard seems to have their act together on this one. They make their money from an explicit MER, and give all profits from the security lending to the unitholders. This way, the risks of profit and loss go to the same party--the unitholders--and investors know exactly how much they are paying management. I gather Vanguard's seemingly unwavering ethical behaviour stems from the fact that they are actually owned by their unitholders.

Next time you buy an ETF, you might want to consider what they do with the profits and collateral from their security lending operations.

(Please keep in mind that these are just the opinions of a relatively uninformed amateur. Also, I have no financial stake in Vanguard, nor any funds invested with them.)

"Nothing goes up forever"

I heard a market prognosticator on the radio at the start of June, claiming that the market was going to drop soon. Well, good for him; people make such predictions all the time, and they're right roughly half the time.

The interesting thing about this prediction was that this fellow made the argument that we're due for a big correction because "nothing goes up forever". I agree completely that the chance of having no down-days on the market approaches zero as your time horizon extends farther into the future, but that general argument, based on the law of large numbers, most certainly does not support his conclusion that the beginning of June was a good time to sell stocks.

It doesn't even matter that the stock market is down 3.8% from the day he made his call. He was still wrong.

If I toss a coin and get 10 heads in a row, I could make the statement "you can't get heads forever" and I would be entirely correct. If I went on to make the prediction that the next coin toss is now more likely than before to come up tails, I would be dead wrong, even if the next coin toss did in fact come up tails. You can't credit your pet theory for your own lucky guess.

Waiting until the market "calms down"

Michael James has updated his Market Timer Breakeven Date. This is an amusing way to measure the futility of selling the TSX index and trying to buy it later at a lower price. For anyone who did their selling later than October 6, their decision to sell has lost them money compared with staying invested. October 6 was fairly early in the Great Recession, so this kind of market timing would have required substantial clairvoyance foresight just to break even.

This is a concrete example of a case where market timing failed to produce any improvement over buy-and-hold. But, after all, it is only a single example. Isn't it usually a good idea to to sell stocks when they're crashing, and wait for the market to "calm down" before buying back in?

The answer is definitely no. This does not make sense, and if you feel the need to do this, you are either acting irrationally, or you have a poor asset allocation that does not match your financial needs or appetite for risk. The reason for this has to do with the concept of Risk Premium.

The risk premium means that, quite rationally, an investor will demand a better return from an investment with higher risk. If two investments have the same expected return, and one has lower risk, nobody buys the other.

Of course, the stock market as a whole will naturally seem riskier whenever stock prices drop. Therefore, we can expect stock prices during a crash to drop more than the fundamental value of those stocks. If economic conditions make it likely for a company's earnings to drop by 20%, we should expect the stock price to drop more than 20%: specifically, 20%+X, where X is the additional risk premium.

The risk premium makes it a particularly bad idea for investors to wait until the markets "calm down". If "calm down" means lower risk, then these investors are specifically waiting until the risk premium disappears! Combine this with the fact that the market's estimation of risk subsides only when stock prices rise, and you will find that waiting for markets to "calm down" is an ideal way to sell low and buy high.

So am I saying that people should not sell stocks while the market is crashing? On the contrary: if they need the money soon, and it's tied up in stocks, people most certainly should be selling them. The sooner, the better. What I'm saying is that, if they needed the money soon, that money shouldn't have been in stocks in the first place.

How does one avoid getting into such a mess? My own answer is, of course, more advice from Michael James. People who have several years' worth of expenses saved up in low-risk (and hence low-return) investments should find their paper losses in stocks inconvenient, but not alarming. Inconvenient, because of reduced liquidity: you don't want to sell stocks while they're cheap, so now you're stuck with them. But not alarming, because it has no impact on your standard of living, since you're not basing your standard of living on your stocks.

I've used an approach (which I christened bottom-up asset allocation) based largely on Michael James's advice. When the market crashed, I was not overly concerned with my deep paper losses; in fact, I bought more stocks. Why would I worry about a drop in the price of a commodity I hadn't planned to sell anyway?

Put money you need for anticipated expenses into stable investments and cash. The rest goes into investments with the highest expected chance of meeting your financial goals, which generally means a diverse basket of stocks. This approach should help you sleep at night while your stocks lose half their value, secure in the knowledge that your paper losses are unlikely ever to be realized.

The Future Value Paradox

When planning your future, it seems self-evident that you should use the most accurate possible predictions. However, consider this:

When I consider a large purchase, sometimes it helps for me to think along the following lines:

I'm about three decades from retirement. The stock market roughly doubles every decade, so a dollar I spend now is worth $8 at retirement. Therefore, I shouldn't buy that $12k car because I'll be costing myself almost $100k at retirement!

This factor of eight multiplier really helps me build a visceral aversion to spending my money.

Now, if I'm careful enough with my money, my retirement could come much sooner than three decades. Suppose my frugal nature affords me a retirement in one decade. When planning for my future, I should strive to be as accurate as possible, so naturally I should frame my thinking in terms of a one-decade timeline:

I'm about one decade from retirement, so that $12k car will cost me $24k at retirement. Well, that's not so bad, so I should buy the car.

However, switching to this line of thinking would make me much less thrifty, and would greatly postpone my retirement. This leads me to what I'm calling the Future Value Paradox:

The longer the timeline I assume for my retirement planning, the more frugal I become, and thus the sooner I will retire.

So, the less accurate my prediction, the better my results!

Pessimism and the Risk Premium

The Dividend Guy has posted an article discussing market rebounds after downturns. This effect could be explained statistically by reversion to the mean, but this doesn't give any insights to the causes of the phenomenon, which I think is quite easily explained.

An investment with higher risk must, if fairly priced, give a higher expected return. This phenomenon is referred to as the risk premium. Now, in an efficient market, when some bad news comes to light, investors adjust their expectations for future earnings, and stock prices drop to maintain a fair P/E ratio. However, investors also conclude that risk has increased, causing them to demand a higher return, which implies a lower P/E ratio, so prices drop further.

When the bad news ends and good news starts to roll in, prices will initially grow along with higher expected future earnings; and then the perception of risk drops, causing the P/E ratio to grow again.

So, for example, suppose we learn that company ABC's expected earnings will be half what they were thought to be. For a fixed P/E ratio, this means that the stock price should be half what it was. However, this bad news also leads to increased perception of risk, so the P/E ratio drops, and the stock price can end up much lower than half of what it was.

Conversely, when the bad news ends and the expected earnings double, the stock price would merely double if not for the risk premium; but when the risk premium disappears, the P/E ratio increases, and the stock price can end up much higher than it was.

Without the risk premium, P/E ratios would remain fixed. Thanks to the risk premium, P/E ratios fluctuate with the market mood. This is a good thing for those with longer investment horizons: they are less risk-averse, and can pick up some good bargains during times of pessimism.

Lower P/E ratios during times of pessimism explain why returns would be higher during those times, causing overall stock performance to revert to the mean. This explains one small part of why Warren Buffet has had so much success being greedy when others are fearful.

Still renting?

A year ago, I posted my most popular article yet: Save money by renting your home. A lot has changed in the last year, but one thing that's the same as ever is that I'm perfectly content renting for the foreseeable future.

The the article hinged on a calculation of the largest mortgage I could carry and still save money every month:

I pay $1200 per month in rent, including my parking space. That rent includes a number of items that would come out of my own pocket if I owned a home, such as property tax, repairs, maintenance, and some utilities. All told, I get about $500 in value every month included in my rent. That leaves $700 that is truly "thrown away" just like mortgage interest.

How large a mortgage would cost $700 per month in interest? Today's variable-rate mortgages are going for about 4.6% per year. At that rate, a mortgage of $182k would have interest charges of $700 per month. That means if I could stop renting and move into a house with a mortgage of $182k or less, I would save money every month.

Here's what has changed:

• My rent has increased by $50/mth. That brings my "thrown away" money up to $750/mth.
• Variable-rate mortgages can now be had for 3.05% interest.

With these new figures, we find that the magic mortgage number is now about $295k. If I can find a buy a home with a mortgage of $295k or less, I would save money every month.

Here's what hasn't changed:

• Homes in my area still don't go for $295k. They're still up around $480k.
• Condos can be had for $295k, but the condo fees move the break-even point below $295k, so they're still not better financially.
• I still don't particularly want to own a home.

I'd like to leave you with one final thought. It is being claimed that now is the time to buy a home because of increasingly favourable interest rates and home prices. To my mind, the best time to make any investment is when the price is low and increasing. Right now, real estate prices are high and decreasing. As far as price is concerned, you could hardly choose a worse time to buy a home than right now (except perhaps six months ago).

The worst has happened. The sky has fallen. I've lost a gut-wrenching amount of money on paper in the stock market since September. But I'm as satisfied as I ever was in my asset allocation, my risk tolerance, and my decision to rent rather than buy.

Update, Apr 21: As of this week, you can get mortgage rates as low as 3.05%, so I have adjusted my calculations above to use this number instead of 3.3%.

Update, July 15: Looking at the same link given above, we see now that variable mortgage rates are as low 2.85%, so the break-even mortgage is up to $315k. This means I probably could buy a house in my neighborhood and, ignoring the buying and moving costs, I might save a few bucks every month starting on day one. But I still have no interest in buying a house just yet. For one thing, the moment the mortgages return to more historically normal rates, the mortgage's advantage over renting disappears, and I would be back to losing money every month relative to renting. I consider it unwise to bet against this happening in, say, the next five years. There are also non-financial considerations, like the freedom to change homes with just 60 days' notice at no cost, or my nearly complete protection from risk in the real estate market. A house would need to cost substantially less than my rent for me to take on the extra risk and responsibility of house ownership.

Update, November 3: Now rates are down to 2.25%, so the break-even mortgage is up to $400k. If I were convinced mortgage rates would stay this low indefinitely, and I liked the idea of skewing my asset allocation heavily toward residential real estate, and I didn't mind mowing my own lawn and fixing my own roof/furnace/toilet/whatever, and I was ok with losing the freedom to move with 60 days' notice, I'd buy a house right away!

Update, November 24: The neighbors just sold their house for $650k. It was a decent-sized 5-bedroom house, but it just goes to show that I wasn't being overly pessimistic by estimating $480k.

Protectionist frenzy over 22 cars?

Is protectionism ok when we do it?

Please, everyone, get a grip. We buy their cars; they buy our lumber, machinery, and energy (and cars!); and everyone wins. That's how international trade works.

It's not the job of Ontario Lottery and Gaming to stimulate the auto industry, and I think Smitherman is way out of line in his criticisms.

Update: The protectionism isn't over yet. Apparently MPs are now supposed to drive Ontaio-made cars only. Given the outrage we all heard over American protectionism so very recently, this hypocrisy is almost unbelievable.

Update 2: I'm glad I'm not the only one who feels this way.

Update 3: Here we go again. They're closing the barn door after the horse has left. They ought to ask themselves why Canada's manufacturing sector can't out-compete China in the first place.

The auto bailout: wrong in so many ways

Michael James hit the nail on the head today in his comments regarding the auto bailouts. I've made the same point about boosting EI rather than writing a vast cheque to a mismanaged company that makes inferior products.

It's importat to realize that the Canadian government is indebted to the EI system (at least morally, if not fiscally) to the tune of $51 billion anyway, so it seems perfectly fair for them to pay out an extra few billion in EI benefits to auto workers to tide them over until new jobs arise. It would also seem reasonable to fund re-training for the auto workers, and tax incentives for successful manufacturing companies (say, Japanese auto makers) to set up plants in Ontario.

All of this would seem more likely to succeed than to deliver billions of buckets to the crew of the Titanic.

I'd like to add that the way the Canadian bailout was determined also shows a startling lack of leadership. Queen's park decided ahead of time that they would pay 20% of whatever figure the US government arrived at, thereby abdicating our nation's fiscal sovereignty on one of its largest expenditures. This is just the latest in a string of actions since parliament was prorogued against all logic in December, all of which show that the current federal government is a rudderless ship.

ETrade's inactivity fees

I'm not happy with ETrade. I opened trading accounts there a couple of years ago, but until recently I only used the self-directed RRSP account. The regular trading account that you get along with the RRSP account sat idle.

Then, in October, Pizza Pizza (PZA.UN) shares dropped to the point that the distribution yield hit 14%. Now, the percentage yield is only interesting if it's a percentage of a large number, or if it's compounding; but at 14%, it meant I could buy 100 shares (for $640, which I had lying around) and the monthly distribution would be more than enough to buy one additional share every month. I transferred the cash, put in the order, activated the synthetic DRIP, and by the end of the year, the three distributions I had received had already covered the (rather pricey) $20 trading commission.

When I checked the account in January, I was in for a surprise: they had charged the account a $25 "inactivity fee". I thought at first there was some sort of mistake, but it turns out they charge regular accounts (not registered accounts) $25 each quarter in which you make fewer than two trades. There is an incredible irony in charging me an inactivity fee the very first time I used this account.

I was not impressed. At this point, I think my letters to ETrade speak for themselves:

Hello,

You have charged my cash trading account a $25 "low-activity admin fee". I would like it to be refunded immediately please. My account ID is XXXXXX.

I find it absurd and infuriating that you charge me $25 specifically for providing me with no service. Your trading fees and currency exchange rates are already among the costliest in the industry, and they are only tolerable because I don't trade frequently. If you insist on charging me $25 per quarter to do nothing for me, I will be closing my accounts, transferring my holdings to a brokerage with a sane fee structure, and publicizing my displeasure as widely as possible.

I don't mind paying for service, but I refuse to pay for a lack of service, and I suggest you take a moment to reflect on the wisdom of surprising your customers with this mean-spirited, punitive fee.

Out of respect to the service agent, I won't name him or post his reply, but perhaps you can infer what was said from my response:

Dear Xxx,

Thank you for your reply, but I'm afraid it doesn't stand to reason. Why does ETrade need to charge this fee if I make one trade, but not if I make two? Why does ETrade encounter these back-office expenses if I have $4999 in my account, but not if I have $5000? It is absurd. I think the real explanation is that ETrade wants to guarantee themselves a minimum revenue stream from each customer regardless of the level of service provided. This is what happens when you let accountants run your business.

More to the point, other discount brokerages don't charge this fee. I would rather part with $125 for closing my account than get hit with this infuriating fee every quarter, or pay $160 every year for trades I don't want to do.

I think ETrade needs to consider carefully whether they want to lose people like me as customers. Certainly, my account balance is tiny now, since most of my assets are elsewhere, and I am at the start of my investing career; but I'm looking for a broker to use for the next three decades until my retirement, and I'm not going to choose one who charges me for nothing.

I will not pay this fee again. It is up to you whether that is because you have waived it, or because I have closed my account.

As expected, they did not waive the fee, and the service agent seemed to become somewhat personally affronted by my emails, which prompted me to say this:

Dear Xxx,

I didn't mean to accuse you personally of setting the policy. I made an effort to refer specifically to "ETrade" separately from yourself, but if I wasn't clear enough, I apologize.

Nonetheless, the inactivity fee is unacceptable to me. I am aware of a number of discount brokerages that have no such fee, so charging me a fee for no service is not only unethical: it also puts ETrade at a disadvantage relative to its competitors. I will be exploring my options before the time comes that ETrade can charge me that fee again.

I do not want to switch brokerages (partly because I don't want to pay the $125 ransom to get my assets back) so I would sincerely appreciate it if you could find a way to help me get this "fee for nothing" waived.

Naturally they were unable to waive the fee. What I have done is open a TFSA at ETrade and move my shares there. The TFSA is a registered account and is not subject to the inactivity fee. With any luck, that $25 fee is the last money I'll be paying ETrade for a very long time.

What do you think? Am I being unreasonable?

Thanks, Larry!

On October 27, Larry McDonald posted an article on saving money by defending yourself against traffic tickets, rather than paying an agent several hundred dollars to represent you.

The following evening, I was pulled over by a policeman and given a number of tickets for administrative matters. I can't be too specific, but it was a pretty expensive evening. Worst of all, the convictions would disqualify me for my current hallowed status with my car insurance provider, and would lead to increased premiums for years to come. This seemed manifestly unfair to me, since I believe my poor administrative skills have no bearing whatsoever on my actuarial risk.

My first thought was not to take chances: to hire an agent to represent me and get the convictions dropped; but after reading Larry's article, I decided to go it alone.

Early in January, I attended my appointment with the prosecutor, and with a wave of her pen, my life got a whole lot easier.

I saved myself four convictions, three demerit points, and over $500 in fines, all at no cost besides my time.

Thanks, Larry!