How allocated do you need to be?

Water Cooler
#1

I posted this in the Bogleheads forum, and it didn’t get a lot of attention, maybe because Jack Bogle hadn’t already written in four different books. Hopefully somebody here can comment.

I’m looking for some kind of academic or professional research that shows how increasing your exposure to different assets actually explains the volatility of a portfolio. Particularly, I wonder what the excess benefits are to diversifying beyond a basic stock mutual fund and a bond mutual fund.

In other words, Investor A is invested simply in two different mutual funds–an S&P 500 index fund and a LBAB (or whatever it’s called) bond index fund. He has a return of X and stdev of Y.

Investor B invests in both of those funds but also in an international stock index fund. We would assume his return would be higher than X and his stdev would be lower than Y.

Investor C invests in the three mentioned above, but also in an emerging markets index fund.

Investor D invests in all of the above,and also invests in REITs.

Eventually, if you keep going down this path, eventually you’ll find somebody who has large cap value stocks, large cap growth stocks, mid cap value, small cap value, mid cap growth, small cap growth, micro-cap, emerging markets (large and small), foreign (large and small) and “frontier” stocks. They’ll also have ST government bonds, medium-term gov’t bonds, LT gov’t bonds, ST investment-grade corporates, MT investment-grade corporates, LT investment-grade corporates, ST hi-yield corporates, LT hi-yield corporates, investment grade munis (long and short), high yield munis (long and short), TIPS, STRIPS, government zeroes, corporate zeroes, high-yield floating rate corporate debt, commodities, MLP’s, BCP’s, REITS of all shapes and sizes, distressed debt, callable convertible corporates, preferred shares, inverse floaters, CMO’s, CDO’s, LYONs, TIGRs, and bear funds. Oh my!!!

At some point, this becomes a little ridiculous. I can understand diversifying into stocks and bonds, and also into foreign funds. But at what point is there no real benefit to further diversification? (among the asset classes, that is) Does an investor really need exposure to emerging market high yield floating rate callable municipal bonds? What good does that do for them?

#2

You tend to get diminishing returns as you diversify the portfolio, because it tends to get harder and harder to find uncorrelated yet positive-long-term-expected-return assets. Ultimately, you get to a point where either transaction costs or unquantifiable risks (generally, the idea that you don’t understand that particular market very well) tells you that your allocation is going to be so small and not substantially different from each other that it’s not worth the cost of rebalancing the thing in order to take advantage of diversification.

#3

^I understand. Hence the question. Do you need just two mutual funds–a diversified stock fund and a diversified bond fund (US, of course)? Or do you need 28 different funds?

Do we know of any research done on the subject?

(Please note–I’m not talking about how many stocks a person needs to be diversified within an asset class. I’m talking about exposure to different asset classes.)

#4

This is discussed in the CAIA surrounding FoF.

#5

I’ve heard that investing in 10 stocks gets you approximately 90% of the diversification benefits of holding an S&P 500 index fund.

Most fund of funds pay 2-3% management fees plus incentive fees in exchange for exposure to the broad stock market. In my opinion, equity funds should be fairly concentrated, as in 15-50 holdings tops.

#6

^Edupristine? Is that you?

#7

Large cap and small cap are already pretty correlated, at least when compared to stocks and bonds, or even US and EM.

It also depends on how large your fund is. An institutional-sized fund can get lower transaction costs.

My sense is that standard stock diversifcation tends to have large cap, small cap, value growth, foreign developed, and emerging market funds. Then there may be allocations to real estate, and then maybe 3 bond types (LT Treasurys, TIPS, High Yield). Possibly some commodity exposure, but that’s less common now. So that’s maybe 10-12 asset classes and sub asset classes. This would be something like a 500k portfolio.

An institutional portfolio might break emerging markets down further by region or country, might do developed markets in segments like value and growth, might have more exposure to investment grade corporates, sovereign risk, specific hedge fund strategies like CTAs and currency strategies (if they believe in them), as well as more illiquid stuff like private equity and private real estate management.

#8

There are many different ways to look at this. The easiest thing to do is to just get the covariance matrix with some different weights and show that the portfolio variance/standard deviation is different with different weights. (or on an efficient frontier with different options plotted)

Academics will sometimes use a utility function to express how much investors would be willing to pay to add something to a portfolio. This is kind of like finding out how much you would be willing to pay above cash to take some kind of risk. I’m kind of skeptical of this idea becuase people don’t buy funds that way, but I see it a lot in papers.

More generally, if you care about the change in volatility for a change in weights, then that’s a derivative. If you have the covariance matrix of the assets in the fund, (call it S) and portfolio weights (w), then w’Sw is the portfolio variance, the derivative wrt w is then Sw.

If you want to know how much each individual asset contributes to the overall portfolio variance, then its something like w .* Sw/(w’Sw)^0.5 where .* is the element-by-element multiplication. This can be used for risk parity when assets are allowed to be correlated.

It’s also possible to get some kind of measure of the diversification of the portfolio, like the effective number of bets. This involves PCA, which means you’d need an add-in to do it in excel. It’s similar to above, but you do it for the orthogonal portfolios to isolate independent bets. Then you consider it an entropy and take -exp(sum(p.*ln§)) to get the effective number of bets (where p is basically the result from above applied to the orthogonal version). The general idea of this is that if you buy a U.S. all market index and a U.S. large cap index, you’re really not taking different bets. This approach corrects for that by essentially converting your portfolio into a large cap position and a portfolio long the all market and short the large cap (effectively long small cap), or something like that. It then figures out how much of these contributes to risk and produces a number representing the effective number of bets you’ve taken.

#9

Basically, you can diversify to gold, commodities, hog futures, beenie babies, Babe Ruth rookie cards, 67 Mustangs, and illegal dog fight betting. At some point, you’ll be di-worse-icating your portfolio.

I talked to the Chief Market Strategist at RBC years ago whom told me to keep it G with 50% stocks (domestic/international), 20% bonds, 20% real estate/REITS, and 5% commodities, 5% cash. Getting crazier than this can lead to trouble. Other BSDs I’ve talked to agreed. I’m a EMH dude because I’ve accepted the fact I’m not smart enough to outperform by stock picking, market timing, and so forth.

This is the dummy allocation I’ve been using for some time and like my man Warren B, I don’t know my beta, standard deviation, nor sortino ratio.

#10

My sincerest apologies for not fully reading your overly wordy first post, then not fully reading your additional wordy post 2 posts down. Clearly I am an idiot.

I think my point was clear enough. The more assets with correlation below 1 you add to a portfolio, the smaller the incremental diversification benefit. I can’t point you to any studies to quantify this, but it can be demonstrated with math, as done in the CFA curriculum. Calculate the expected variance of a 3 asset portfolio. Add an asset and calculate again. Calculate the percent change.

#11

You need to be really allocated. Like SO allocated.

#12

If you’re investing for 30+ years, Bogle doesn’t believe in diversifying among different equity markets. After currency fluctuations, the 30 year returns of US, European and Japanese markets are similar.

#13

As for small vs large cap, small tends to outperform during rebounds and underperform at market peaks vs large. So what I do is overallocate to small during corrections and vice versa while keeping my equity exposure allocation the same in the total portfolio.

#14

I don’t want “expected return” or “expected variance”. I want empirical results from an empirical study using “real” data.

And I don’t want to do the research myself. If I did, I would go get a PhD. Or do Level 3, which is the same thing.

#15

The danger of dismissing expected return and expected variance is that you end up performance chasing, buying what did well recently. You have to invest based on future expectations, not past delivery.

Of course, that begs the question of how do you develop sensible future expectations other than by looking at past performance. Basically it comes down to looking at past performance and then asking if there’s anything about the present and the future that marks a material difference between the present and the past, and adjust expectations accordingly. So (as a possible example) when valuations seem higher than the past, maybe future returns won’t be quite as good as past returns; when they are lower.

Obvioiusly, you can end up performance chasing if you just compute past returns and past volatilites and correlations and do nothing else, particularly if your window of returns is short, but that doesn’t mean you shouldn’t be investing based on expected returns and expected variances. It just means that it’s more than simply extrapolating the past.

#16

at these rates, I wouldnt even touch bonds. Any type of growth in the economy occurs and your ****ed. I’ll take the potential downside in equities. Junk bonds have higher yields, but are historically overpriced.

#17

I was helping my brother select his 401K allocation after a job change recently and this topic came up. Basically, his 401K offers about 10 different target date funds, an SP500 index fund, a handful of large cap, mid cap, small cap funds, 1 real estat fund, a foreign equity fund, a short term/cash fund and a bond fund. It sure seems like 70% of those are going to be very highly correlated. You want to diversify, but the target date funds are basically just specific allocations of the other offered funds, so if you throw money at a target date fund, and the SP500 fund and a bond fund, you’re sort of defeating the purpose of the target date fund. Although, the purpose of the target date funds appear to be fee collections for 401k administrators, so in that case simply selecting one is fulfilling the purpose.

#18

Agree, most 401k plans do employees an injustice regarding plan investment options and constructing a reasonable portfolio.

#19

Well, DFA has done a ton of research on the subject, but it’s not published - as far as I know. Basically they found you should have a tilt toward small and value vs just buying the market. I’m not sure if they started it, but they’re really running with this whole “smart beta” thing. It’s a fad and will soon be corrected.

If small and value are constantly undervalued, investors will recognize this and bid them up to fair value. There goes the smart beta…

#20

This whole smart beta thing makes Bill Sharpe sick.

Short read here