Oldest known version of this page was edited on 2005-10-03 18:29:24 by RichardBerg []
(originally posted here∞)


The risk of ruin formula, maybe?

Regardless, there is no "optimum" level of risk when dealing with humans. All the formulas in the world won't help if dropping 90% (but with a huge upside!) causes you lose sleep, let alone lose your shirt by quitting the market.

I agree. They "should." My faith in the human spirit wants to believe it. Unfortunately, the facts reveal that the vast majority of high-priced "investment professionals" have the same impact as fancy masseuses, chaffeurs, or concierges -- most of them will get you what you need and make you feel dignified in the process, but they constitute are a net drag on your finances. And for an unlucky percentage, there's added risk they'll lead you in the completely wrong direction.

The vast majority of pension funds, universities, charity trusts, etc. use indexed security instruments these days. I doubt the wealthy people you know have as much money as the Yale Endowment -- and more to the point, the latter have a lot more willingness to avoid the costly Wall Street gimmick of the day.

As we probably agree, a highly successful person's best chance of beating the market is to be an entrepreneur. That doesn't mean it's a good chance, but at least it puts fate in his own hands, presumably in an area where he's shown competence if not excellence. And numerically speaking, it's the only way to acquire serious wealth.

Now to finally answer the OP...
Two reasons. Most importantly, "diversification" to an average U.S. investor -- who conceives of "the market" as the Dow figure shown on TV -- means exposure to asset classes with larger risk premia: small, value, international, etc. Since this can be done while maintaining or reducing the portfolio's total risk exposure, it's a free lunch.

The second piece is the so-called rebalancing bonus referred to in the other thread. Basically: go into Excel, create two independent normal distributions with μ = 10% and σ = 50%. Pretend these are the annual returns of an idealized, uncorrelated asset pair. Now pick an initial value, multiply it by each year's return, rebalance, and send the result to the next row, etc. At the end of the day you'll get an annualized return greater than 10% most (but not all) of the time. The net EV is in the neighborhood of 0.3%. Not enough to recommend slice & dice to the average investor (to whom the switch to passive management is a big enough hurdle), but with exponential compounding, it adds up.

If you want more reading, AltruistFA maintains an awesome link library: http://www.altruistfa.com/readingroomarticles.htm#Diversification∞

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That may be true, but it depends on two things:
(1) implementation -- many advocates of diversification also advocate non-market weightings, in which case direct comparisons to "the market" become nonsensical
(2) definition -- what is "market average"? The Dow? S&P 500? Wilshire 5000? Wilshire + EAFE? Even if you're talking about all of the above, then what about privately held companies, commodity futures, newly emerging markets, etc. etc.? Unless you're way more diversified than the average investor, there is plenty of room to reap the benefits.

I agree with you about the last two points, but may as well raise the other side of the coin so long as we have an investment discussion thread...

You know this, but worth repeating: The hard part isn't finding excellent businesses. It's finding excellent businesses that other people haven't found first.

Not sure why you bring up derivatives, but it seem to me you're more likely to find mispriced securities in the derivatives market than anywhere else. Graham & Dodd is like 70 years old, while options weren't given rigorous treatment until 30 years ago or so (Black-Scholes pricing theory and its, err, derivatives). Even now, options markets stray from theory a lot more often -- partly due to limitations in theory, no doubt, but that doesn't mean a correct theory that might be exploited doesn't exist. On a more practical level, options tend to originate from sources known to be less efficient than the ordinary market: employer benefits, individuals making leveraged gambles, institutions who need to move large positions for cashflow reasons. Inefficiencies, of course, draw sharks -- even VFINX, stalwart idol of the passive investor, has occasionally overcome its expense ratio to beat its index by trading short-term S&P futures when its managers saw an opportunity for arbitrage.

So yeah, I like studying derivatives...it reminds me of utility theory, another sliver of the academic economics literature that explicitly disregards real-world units of measure yet implicates your every action if you think [way too] hard about it. At least I'm not crazy, because other people∞ are starting to think so too.

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KalTorak:


Let me say that back, to make sure I've got it right:

Start with X dollars.

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Divide into 2 (well, N, but let's set N=2 for now) pieces.

Multiply each piece by a value independently chosen from a normal distribution, with μ=1.1 and σ=50%. [Note that I'm a little different from your instructions here; I'm modeling the value of the investment+return, so a value <1 means you lost some principal. Also, a value <0 can't exist... which means this isn't REALLY a normal distribution. You can't lose more than the invested principal; what's the right way to model that without screwing with the real μ?]

Add the two results together; that's your total in year 1. Iterate over Y years.

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If I understand the steps the same way you meant them, I think we still disagree. I claim that for n_0 ideally-diversified investments, and any y_0 years' time, there's no difference in the mean result whether N=1 or N=n_0.

I suspect I can prove it, too, if my model's the same thing you're describing, either theoretically by multiplying the distributions out, or experimentally by running lots of trials on that model.

Are we talking about the same experiment?

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That experiment corresponds to my earlier description, yes. I've only seen the effect demonstrated in spreadsheets, so I'm interested in pursuing a more rigorous analysis to see whether those observations merely reflected luck or +EV.

Now that I think about it with your (our) phrasing, I think you're correct; in our model, identical means at every point follows directly from independence.

This leads to an immediate criticism: a normal distribution of annual returns won't actually tend toward a long-term annualized return of μ -- you can't take an arithmetic average over an exponential rate. Intuitively, one expects reversion to the mean rate from our model, but not the mean return. I think a proper distribution function will provide this intuitive RTM without actually making the Yth-year return depend (in the probability sense) on Y-1.

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KalTorak:


Man, you stumbled onto the answer here, but I'm not sure you recognized it.

A mean annual growth rate is NOT enough information to determine the return.

The obvious examples for a 10% mean annual growth rate:
1) 10% growth in year 1, 10% growth in year 2 (with simple compounding, but the result doesn't change): 21% total return at the end of year 2

2) 120% growth in year 1, -100% growth in year 2: -100% total return at the end of year 2

(It's always true, in fact; 8% in yr1, 12% in yr2, or reversed, gives a total return of 20.96%.)

The broader rule ("duh" to prove, now that RB's got me asking the right question) is that, because of the compounding effect, the best return for an investment with a mean annual growth rate of N% is achieved when every year's exactly N%. Broader still, the tighter the distribution of annual growth rates, the better the total return.

And it follows that diversifying really DOES get you both. Damn, but I did NOT see that coming.

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Yup, those are decent rates for a personal financial planner (including insurance, tax strategies, trusts, inheritance, etc.). Unfortunately, most of the industry will charge you a lot more than that and/or direct you to investments that actually cost more than what's available to ordinary joes.

OTOH, if you can find an honest one, having someone to personally explain the benefits of low-cost diversified investing and take care of its details is nice. And if that education keeps you from taking a hot stock tip from a friend or broker, it's priceless. It sounds pathetic, but every planner I've met has horror stories of clients who build themselves a comfortable nest egg only to lose 70% on a one-time mistake...and even that's nothing compared with how bad the average portfolio looks before they came in for advice. Wall Street marketing is insidious enough to infect otherwise brilliant people.

Nope, totally backwards. Endowments have a theoretical investment horizon of "infinite". Which is why you are correct when you later say that they invest in very risky sectors like private equity. (The other reason is, of course, diversification.)

Now we're just smoking crack. Swenson, the undisputed hero of institutional investing, the guy who got Yale (and the rest of the industry) to diversify into hedge funds and timber et al. in the first place, has made a little over 16% in his career. Having combined his rare skill with two decades of falling interest rates and skyrocketing equity valuations, I expect that record to stand a generation longer than Roger Marris' (so long as the SEC keeps "steroids" at bay). As I noted in another thread, Buffett -- easily the best stockpicker of the 20th century, and one of the more arrogant -- doesn't expect much more than 6% out of himself going forward. Peter Lynch stomped the market for >20%, but since he only worked for 13 years it was impossible to statistically establish∞ his skill until it was too late.

Meanwhile, one thing all 3 of these giants have in common is that they recommend index funds to individual investors.

A huge ++ on your take of the American Dream, BTW. I love this forum.

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KalTorak: thanks for filling in the last missing pieces. I'm glad we were able to come to the "right" conclusion on purely theoretical ground -- it's not only more satisfying, but for me anyway, it's more likely I'll actually follow a strategy if I've proved it to myself independently.

With that hurdle overcome, I don't feel bad combing Bernstein's site for more in depth analyses. (Ordinarily, doing so feels like cheating. A smart guy on the Morningstar forums once quipped "there are only two kinds of advice Bill writes: thing you agree with immediately, and things you'll agree with later.") Naturally, he has plenty of fascinating things to say if anyone's still interested and doesn't mind math:

http://www.efficientfrontier.com/ef/996/rebal.htm∞
http://www.efficientfrontier.com/ef/197/rebal197.htm∞
http://www.efficientfrontier.com/ef/100/rebal100.htm∞
http://www.efficientfrontier.com/ef/400/rebal400.htm∞
http://www.efficientfrontier.com/ef/198/gmf.pdf∞

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[defending the Buffett authority-grab]

Here's the other thread∞ (with citation). 5% appreciation, dividends well under 2%, round down for overhead...I don't feel it's unfair to claim Buffett is forecasting long-term U.S. returns in the 6% range. Naturally, he also tells his shareholders that he aims for BRK's underlying value to edge out the broader market's rate of return. However, it's unfair to characterize it as a bloated mutual fund. BRK doesn't primarily get its value from holding pieces of Coke et al., but by funneling excess cash & talent from its very stable subsidiaries (e.g. insurance) to those with more growth potential. Nevertheless, the continuing reliance on said core operations implies that Buffett is not expecting to beat the market rate via stockpicking but via business acumen.

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note: the "other thread" is PayOffOrInvest