The Rule of 72

What is this "Rule of 72", that you run across in investing sooner or later (or right now as you read this)?

It is a fast, simple and reasonably accurate way to estimate how fast your money doubles.

Common Use 1: If your money grows by a consistent G% every year, then it will double after 72/G years.
Example 1: your savings account offers 4% a year. After (72/4) = 18 years, your money will have doubled.

Example 2: Yale's endowment under David Swensen grew at a truly remarkable16.1% a year for many, many years. The endowment was doubling in value every (72/16.1) = 4.47 ~ 4.5 years (!).

Being an approximation, the rule of 72 can't be used indiscriminately, but it is useful for typical investment returns.

• It is very accurate for G% between 5% to 12%
• It is reasonably accurate for G% between 2% to 16%.
• For large returns above 30%, it is not that accurate.

Or using colors where green is accurate and red is inaccurate, the rule of 72 works this well

0.5, 1, 2, 3 4, 5, 6, 7, 8, 9, 10 12,, 14, 15, 16, 18, 20, 25, 30,35, 40, ... .

Less common use: If you sum your returns over several years, even if they are not the same, your money has double when you hit 72.

Example: if you have annual returns (in percent) of 9, 12, -3, 5, 7, 18, 2, 4, 12, 15, this sums to 81. So you would have doubled your money and more in the last year wtih the 15% returns.

Mathematical underpinnings.
If I have time later I'll explain the math behind the rule of 72. For now see the Wikipedia entry.

Keeping it simple in investing

Part of me remains baffled at how many people resist investing. Many highly intelligent, go get'em and otherwise rational people just stick their heads in the sand when it comes to investing. Yet shockingly, it does not take excessive amounts of effort to invest well. One of my mottos of the last few years is:

You can do an B+/A- job investing with very minimal work and relatively little anxiety.

Note that many people do a C- or worse job of investing, so an B+/A- job is pretty darn good. I think one of the problems is paralysis in making investing choices because there are so many bloody choices. And there are numerous tales of how making the wrong choice means losing your shirt, but pretty much all these cases of shirtlessness involve getting too greedy or trusting your money to someone inept or unethical. I present two choices: super-ultra simple and simple.

1) I want to keep my head in the sand:

If you want the absolute simplest plan of action, buy one of the "target lifecycle/retirement" mutual funds which automatically adjust the asset mix as you near retirement or cash withdrawal. Choose the fund with the target date close to your planned retirement. E.g Vanguard offers funds with target dates of 2010, 2015, 2020, etc. As the target date gets nearer, the fund mix gets more conservative.

Recommendation: Vanguard Target 20XX funds. For 20+ year horizons, they keep very little cash, have very low fees. E.g. for their 2035 fund, their mix of domestic/foreign/bonds is a reasonable 72/14/10 . I prefer more foreign, but that's just me.

But if at your brokerage is Fidelity or Schwab, just buy their in house target funds instead and avoid paying the mutual fund transaction fee. At least, I know buying Vanguard funds from a Schwab account has a fee but buying Schwab funds have no fee.

2) I want a simple plan where I am involved:

But if you're in the camp of just not being sure where to start, take the consistent and nearly unanimous advice of the big names (Malkiel, Bogle, Swensen) and the big boys (many pension funds, including TIAA-CREF) and put your money in 2 to 4 low cost index funds each covering a different asset class. I give some baseline weightings for your assets but you can tweak the weightings as you wish. The good news is that your returns are not very sensitive to 5% or even 10% adjustments in weighting. Put the rest in a money market fund.

Recommendations:

If you have less than $6K to invest, use a complete US and a complete foreign fund:

• 60% Total US index (VTI)
• 40% Foreign including some emerging markets (VGTSX or FSIIX, but if you don't have enough money, buy EFA)

If you have less than $20K to invest, put the money in the following categories:

• 55% US stocks (say VTI or VFINX)
• 35% International developed countries (say EFA, DODFX)
• 10% Emerging markets (EEM or VWO)

If you have more than $20K you can also add some real estate or US bonds/Treasury bills:

• 40% US stocks (say VTI or VFINX)
• 25% International developed countries (say EFA, DODFX)
• 5% Emerging markets (EEM or VWO)
• 15% REIT index (VNQ or VGSIX)

And remember, rebalance once every 6 to 18 months to your desired weightings. It turns out your returns are not too sensitive to how frequently you rebalance. But you must rebalance. I recommend every 12 months to minimize the work and to ensure you'll get long term gains.

In short: don't over think how to invest. Just do it and keep it simple. And if you follow the above guidelines, it's hard to mess up much. It's a lot like exercise: the biggest mistake is not doing it; and if you do something, heck anything, reasonable, you'll be fine.

Choosing brokerage firm(s)

The short summary is:
- once you have considerable assets (IRAs, Roths, regular), consolidate into one place
- avoid high cost brokerages, which are the old time big names (Smith Barney, JP Morgan, Merrill, etc).
- Among the discount full-service places (Fidelity, Vanguard, Schwab), I don't think there is too much difference righ now. Among the ultra-value places (E-trade, Ameritrade, etc), I don't think there is much difference. What type of firm you choose is up to you and the relative costs on how you intend to trade.
- once you consolidate, you probably won't want to move assets very often (at most once a decade)
- you can compare costs now but remember the brokerages change their costs and fees over time, so it is important to choose a brokerage that has historically treated their customers well, since you won't likely switch.
- In trades, keep commissions below 0.3% of the trade, preferably below 0.1% of the trade. Your firms fees can influence this if you're making small trades of $2K or less.

My personal preference is for places that started out with a customer focus, offering a unique benefit. I like Schwab as they were the first big discount brokerage with many services. I also like Vanguard which has consistently kept its costs very low, though they have grown from largely handling their own excellent mutual funds to a full service brokerage. I'm a bit leary of Fidelity as they originally were a mutual fund house with many good funds but they charged significant loads (3% entry fee back in the 80's). While they have become a pretty good low-cost firm, it is mainly because they were forced to do so. They scoffed at index funds for a long time but back in the late 90's (?) started offering a few very low cost Spartan index offerings.

I like the bigger companies once you get significant assets, because once you start doing other transactions like buying a house or giving assets away as gifts or charity, you need other services like wiring or DTC. And it is nice to be able to drop in to an office once in a while.

If you have a more modest pool of assets (say less than $50K) and intend to do some trading for fun and loss (I mean profit) and you have the time to monitor all this, then choose a low-cost firm that minimizes your type of trading costs. Namely if you're intending to trade stocks, keep stock commissions low. My office mate opened an account at zecco.com because they have free stock trades and he intends to trade small amounts so even a $10 commision would be significant; of course there are several restrictions to this account. There appear to be other ultra-low cost brokerages if you are so inclined. But remember if you insist on trading individual stocks, make sure that it is less either less than 5% of your holdings or less than $2K; invest the bulk of your money in diversified or safer holdings such as mutual funds, ETFs, T-bills or safe bonds.

Benefits of a Roth versus a regular after-tax IRA

Someone asked if they should recharacterize an after-tax IRA to a Roth. Basically was it worth the trouble to do so.

Here's two, no make it, three, lines of reasoning on the benefits of recharacterizing, from which you can decide yourself.

1) Tax savings.
Let's figure out how much you'll save on taxes.
1a) Let's assume for simplicity you have 40 years for this money to grow, say you are 30 and won't withdraw this until you're 70.
For a somewhat conservative estimate, assume your money doubles every 10 years (a 7.2% return -- using the rule of 72),
so your money has grown to 16X of the current value of 4K => 64K. The taxable portion is the gain, which is 64K - 4K = 60K.

Non-roth tax-deferred distributions are taxed as ordinary income and I'll assume you'll be in a mid-high bracket at the age of 70, due
to your accumulated wealth. Again, I'll assume incremental tax rates of today, so say you pay 30% of %60K, which is $18K.

1b) If your return were slightly better, say 9% a year, you would double every 8 years and your IRA would be 32X, and then you'd save roughly double of (1a) in taxes, say $36K.

2) Tax simplicity.
A Roth frees you from all the paperwork of calculating taxes on that IRA, since you're not taxed again. Ever.
If it remains a non-Roth IRA, when you get distributions, you're forced to assume you're getting a proportional amount
from your basis (the 4K on which you've paid taxes) and the gains (for which you owe taxes).

3) Flexibility.
If it is a Roth, you're not subject to mandatory distributions (I think), so you can pass it along after your death, possibly
having the recipient get a stepped up basis.

It's anybody's guess if the 2010 law letting anyone recharacterize a traditional IRA to a Roth will stand until then.

Were it me, I'd recharacterize.