Bonds lifted off today, with the 10y rate all the way back to 3.33%, but this time with TIPS underperforming. We really have seen it all recently, with TIPS sometimes outperforming in rallies, sometimes outperforming in selloffs, sometimes underperforming in rallies, sometimes underperforming in selloffs, and sometimes outperforming when nothing else was happening. Nominal rates have been up and down with considerable ranges on no news at all (for example, today) and other times have been quiescent despite important data. Even the one constant these last few months, a rallying stock market, hasn't been constant. On the week, it rallied just a little bit but not exactly in a straight line!

This is all noise, rather than the prelude to a larger move imminently, if the vol markets are any indication. Sure, implied volatilities tend to sag a little bit in December, but not as much as you would think they would - the thin trading conditions make it harder to hedge short-vol positions and the wide ranges make it more costly to do so. But today, the VIX approached three-and-a-half-year lows in the 15 range.

The fact that no one is currently winning the tug-of-war does not necessarily imply that there are no forces pulling on the rope. In my opinion, strong conflicting forces - the possibility that there is some budding economic growth, the significant Fed liquidity provision, tax cuts and associated increased near-term deficits, pressures on the EU periphery (Moody's finally downgraded Ireland today, 5 notches), oil at levels that would have been all-time highs except for the melt-up two years ago...I don't know who wins that tug of war, but my suspicion is that the most-likely outcome isn't "a tie," and that's what is being priced into vols.

But let's take a step back, in what is probably my last comment for the year, and forget about the one-week and one-month swings. The end of the year is a great time for a top-down portfolio allocation exercise.

To do such an exercise right, you need several things. You need to know what your stream of "liabilities" looks like (are your future expenditures fixed in nominal terms, or are they real? How do they grow over time?). You need to specify the asset classes you want to include in the investing universe and the allowable maximum and minimum weights in each asset class. These are all important decisions, and we all would think about these problems in similar ways. But equally important are the assumptions about the expected returns, expected risks, and the correlations between asset classes. And here, we would all come up with different answers. For many years, asset allocation exercises were fond of using historical numbers for asset class returns. This produced recommendations of a very high weighting in equities, because the period of 1930-2000 (for example) produced an exaggerated historical return: from deep in the Depression to the top of the bubble.

Asset allocation specialists, many of whom either worked for Wall Street firms or were effectively in thrall to them, loved an answer that included lots of equities, because the fees for management of equity funds are a lot higher than the fees for management of bond funds.

And then, the 2000-2010 period hit. Asset allocations began to emphasize estimates of future returns, rather than historical inputs. I am not saying that this necessarily had anything to do with the fact that the other method would have implied very low allocations to equities, but whatever the reason the industry seemed to arrive at the right answer. Ironically, while we know very little about what the returns next week will be, we have much greater confidence that we can say something intelligent about the central tendency and the likely range of possible outcomes over the next decade. This is because we have at least a basic idea of what the drivers of long-term returns are, even though we are clueless about the drivers of short-term returns. As the saying goes, in the short-run the market is a voting mechanism; in the long-run it is a weighing mechanism. The vicissitudes of politics versus the confident predictions of physics - and this is why we use long term average returns to drive asset allocation exercises.

I know that some readers at this point will protest "but this is crazy. Surely no one could have seen the equity returns of the 2000s coming! But this is not so.

At the end of December, 1999, the S&P stood at 1469.25. The 10-year "Shiller P/E" stood at 44.20 (the Shiller spreadsheet is here) compared to a long-run average of 15 or 16. If we assume that equity multiples return half-way to the mean, our calculation of expected 10-year return on December 31, 1999 would have looked something like this:

Long-term real growth in earnings: 2.25%/yr (Note: see this commentary for discussion on why this is a solid long-term assumption)

Long-term inflation: 2.11% /yr (difference between 10y nominal bonds and 10y TIPS at the time)

Dividends: 1.15%/yr
Valuation Reversion:= -3.75%/yr

...for a back-of-the-envelope, somewhat-optimistic (for it assumes that only some of the overvaluation is unwound) estimate of 2.25% + 2.11% + 1.15% - 3.75% = 1.76%/year. A full return to average valuations implied more like a -4%/year return (n.b. I'm not being super precise here about compounding; this is just for illustration). So the actual total return of the S&P from 1999-2009 of -0.95%/year was actually right about where we would have expected.

Actually, it's even better than that. The actual Shiller P/E at the end of 2009 was 20.24 and compound inflation was 2.52%. If we had correctly forecast those two numbers, then our overall forecast would have been: 2.25% + 2.52% + 1.15% - 7.51% = -1.59%/year. Not bad!

None of this math is particularly challenging, and none of the numbers hard to come by. And folks like Jeremy Grantham were right out front in telling folks that that was about what we could expect from equities.

So there is some reason to think that we can make some reasonable guesses at long-run return numbers. The better our estimates, the more appropriate our asset allocation will be (even if the estimates don't turn out to be exactly right, our asset allocation will still be a more efficient allocation of risk and reward if our description of the distribution is approximately correct).

With that lengthy preliminary, then, here are my asset-class estimates that I am plugging into my own asset allocation exercise for year-end 2010 (along with a brief explanation). All numbers are annually compounded real returns, except for inflation which is obviously not in real terms!

Chart 1: Moody's A Corporates vs Treasuries - looks about right.

Chart 2: Home prices getting close to fair (these data through Q3).

There are lots of other flavors of assets, of course: I haven't included global equities, emerging market instruments, or hedge funds (just to name several). Coming up with a determination whether Brazilian stocks are overvalued relative to U.S. stocks or vice-versa is very difficult, and also a very important part of the expected return. I have left them out here (partly because this table will provoke enough arguments as it is!)

The chart below shows the expected returns I have explained above, together with the historical volatilities over the last decade - which is what I use as inputs, in most cases. Volatility is generally considered to be strongly mean-reverting (look at the VIX!), so unless you have a good reason to think a market over the long run...and we are talking about 10 years here...is going to have different risk characteristics for some reason, using historical volatilities is a reasonable approach.

Chart 3: Projected 10y Real Returns and Risks

We can take those real returns and risks and, when we incorporate a correlation matrix, produce an "efficient frontier" that shows the best combinations of risks and returns that are available, without leverage, in a portfolio which includes those assets.

Chart 4: Estimated efficient frontier from the points above.

Notice that, like good little Markowitzian portfolio optimizers, we recognize that we can achieve points in a portfolio that are superior to any of the individual points, because the variance of the sum of two assets is less than the sum of the variances due to the covariance between them.

We can also look at the composition of the minimum-variance portfolio for a given target return. Chart 5, below, illustrates this. Notice that even though real yields for TIPS are rotten, they still show up as a crucial element in lower-risk portfolios.

Chart 5: Even with puny real yields, TIPS are an important part of many portfolios.

Indeed, notice that the way you build an efficient portfolio in real space tends to be a barbell of the lowest-risk asset (TIPS) and a higher-risk asset (in this case, commodity indices or stocks). This is contrary to the usual practice of "buying some of everything." That turns out to be inefficient because you are wasting part of your risk budget on assets that are too expensive, in terms of the return for the risk you're taking. Better to spend your risk on the things that give you the best return per unit of risk, and put everything else in something as close to riskless as you can get. (If you expand this exercise to include hedge funds and private equity, allocations to public equities all but disappear!)

Something else you can probably not help but notice is that even the riskiest portfolios have pretty poor expected real returns over the next ten years. That isn't because I am pessimistic; it is because that's what the numbers are. We live in a low-return world. This probably doesn't mean you should take on extra risk to reach your return targets, but it does mean that it is more important than ever to watch fees and expenses on investment products you own, and to try very diligently to stay as close to the efficient frontier as possible. There isn't enough return out there to go wasting it on inefficiency.

So, what does this mean for your asset allocation? Unfortunately, I can't tell you that because I don't know your risk tolerance. And, even more importantly, this analysis is very one-sided. I looked only at the asset side of the balance sheet. I didn't consider what your liabilities might be. Remember how I alluded to that early on in this exercise? You see, if most of your expenses are exposed to inflation (and this is true for most of us), then your optimal portfolio is probably heavier-still in inflation-linked bonds. This is because the real goal of investing for retirement isn't to maximize your return on assets subject to a given level of risk on the assets; it is to maximize your retirement surplus (or minimize the shortfall) while constraining the risk of that surplus. To put it another way, if you have fixed-dollar expenses and invest in fixed-rate bonds, then you are well-hedged. But the same portfolio of fixed-rate bonds will be a total disaster if your expenses rise with inflation, and there is an inflation surprise. It is important to consider your entire life situation not just in the master plan, but in the asset-allocation exercise itself.

And with that thought, I will leave you for 2010. Happy holidays, everyone! See you on the flip side: this comment will return on January 4th.