Portfolio Concentration or Deconcentration

**lzhang** Sun Oct 01, 2006 5:31 am

Portfolio Concentration or Deconcentration
The article "Portfolio Concentration http://value-investing-forum.com/viewtopic.php?t=1029 " by teenvestor criticized an article "Why Diversification is Key in a Portfolio http://www.fool.com/community/pod/2006/060516.htm", which as its title showed, claimed diversification is a key in portfolio. Even I do not agree with the author of the latter article why diversification is a key, I do agree with him on that diversification is a key.

teenvestor quoted Mr. Buffett several times to support his arguments. But from what Mr. Buffett said, I can only see that diversification, if not practiced properly, makes very little sense for anyone who knows what they're doing. When he was talking about risk, he said in his 2005 Chairman's Letter (http://www.berkshirehathaway.com/letters/2005ltr.pdf on pg. 20), "Over the years, a number of very smart people have learned the hard way that a long string of impressive numbers multiplied by a single zero always equals zero..." Although he was talking about debt and risk, I think it is also true for over concentrated portfolio, to the extreme case where people put all into one bet and he can be successful many times but can go to ground zero by just one failed bet.

Joel Greenblatt's statement as quoted is kind of misleading. Yes, the expected return is still 10% whether or not you diversify, but the uncertainty on the expected return drops a lot with diversification.

As a scientific researcher, I want to do (simulated) experiments to prove instead of plain talk. In the experiment we showed earlier in article "Risk, Volatility, Investment Return, and Risk Management", we assume that

1. Initial fund $1
2. Expected return is 20% yearly, which is unbiased and reflects the true value of the business
3. 10 stocks in the portfolio
4. fund equally distributed among them
5. after each year, rebalance the portfolio so that 2, 3, and 4 are true. So, these 10 stocks in the next year are not necessary same as before.
6. final performance after 30 years
7. Repeat 1, 2, 3, 4, 5 and 6 1000 times so that we can see the expected return distributions.

and we have this result for a particular risk model, which we call high risk:

With the largest risk, we have the worst MPV (102.4), the lowest min return of miserable $3.53 for $1 over 30 years, if we compare it with a hypothetical 5% yearly return from T-bond, which will be $1*1.05^30=$4.32, but since the distribution is so spread out that for a very slim chance we do have a return of $2198 for $1 over 30 years, which is extraordinary compared to the nominal return of $237.

So it looks like we are doomed to lose if we assume the riskiest ones as majority will underperform. Hey, the expected return is still 20% per year! What can we do? What if we can find 100 such high risk stocks and diversify more? Let's try again:

1. Initial fund $1
2. Expected return is 20% yearly, which is unbiased and reflects the true value of the business
3. 100 stocks in the portfolio
4. fund equally distributed among them
5. after each year, rebalance the portfolio so that 2, 3, and 4 are true. So, these 100 stocks in the next year are not necessary same as before.
6. final performance after 30 years
7. Repeat 1, 2, 3, 4, 5 and 6 1000 times so that we can see the expected return distributions.

We can pretty much say the same thing for the high risk one, but now the numbers have changed (and the tone):

With the largest risk, we have the worst MPV (197.3, so not too bad), the lowest min return of (pretty decent) $86.28 for $1 over 30 years, if we compare it with a hypothetical 5% yearly return from T-bond, which will be $1*1.05^30=$4.32, but the distribution is not as spread out as less diversified one, we do not have a return of $2198 for $1 over 30 years, which is extraordinary compared to the nominal return of $237.

We also see other effects with high diversification, the distributions are less asymmetric for high risk one compared to low diversification, so we are pretty comfortable that the majority will be in a better position than those with low diversification.

For comparison purposes only, let's study the case with 5 stocks:

1. Initial fund $1
2. Expected return is 20% yearly, which is unbiased and reflects the true value of the business
3. 5 stocks in the portfolio
4. fund equally distributed among them
5. after each year, rebalance the portfolio so that 2, 3, and 4 are true. So, these 5 stocks in the next year are not necessary same as before.
6. final performance after 30 years
7. Repeat 1, 2, 3, 4, 5 and 6 1000 times so that we can see the expected return distributions.

One can see the results are worse over all risk profiles compared to more diversified models. To the high risk profile, we see a very large chance that the model will be wiped out so you never see expected return of 20% per year!

So diversification is the key for risky business. With high business risk, we can still achieve the same level of safe expected return (measured by min return or MPV of return distribution) if we diversify enough. Diversification is not as important if the business risk is fair low as the spread on the final return is not affected that much (because it is low already).

In this sense, to understand the business, to find low risk business, might be better than diversification into high risk business. That is what Mr. Buffett emphasizes always, he invests into business only when he understands it. Excessive diversification runs into the risk that one might diworsify. In real world, there might not be 10 stocks with low risk and high expected return, not even mention 100 such stocks. Try to understand the business with 10 stocks is better than having 100 stocks with no business understanding.

If you do not understand the business, you have to say that the risk (ie, uncertainty) is very very large, so you need to be very very diversified. I think in this respect, EMH kind of makes sense to a layman. By definition, a layman does not understand the business, so what he can do is to assume that the market is right in pricing that business. Since he does not understand what is going on, the best he can do is either do nothing, or maximize diversification. The cheapest, best, and most efficient way to diversify is to dollar-averagely buy index funds.

When we quote Mr. Buffett on diversification, we must understand that there is something he can do, but public Joe can not do. He is a great business man, public Joe is not. He understands deeply into the business he owns, public Joe does not. As value-oriented investor, we are neither Buffett, nor public Joe. In principle, Buffett's way is a very simple way, business like, hunting for value. In reality, it is hard to say, especially as we learn and grow, what we find is the true value that the underlying business should have. So our business view tends to have large uncertainties. So large margin of safety, large diversification, serves better. As we get experienced, those principles are still valid, but our own view might be a little bit less fuzzy. As I believe, even now there are businesses that Mr. Buffett does not understand, so he does not touch them as he assign infinite uncertainties to those businesses. He is a hard-working guy so I think he is trying to understand whatever possible to him.

Ref links:

http://value-investing-forum.com/viewtopic.php?t=1029

http://www.fool.com/community/pod/2006/060516.htm

http://hepinvestor.blogspot.com/2006/09/risk-volatility-investment-return.html

Original post @ http://hepinvestor.blogspot.com/2006/10/portfolio-concentration-or.html

**blast_investor** Sun Oct 01, 2006 7:32 pm

The photo link is not working. Maybe URL is not correct.

**blast_investor** Sun Oct 01, 2006 7:34 pm

Adding a reply, the photo works.

**blast_investor** Sun Oct 01, 2006 7:44 pm

Excellent modeling work on risk profile verses diversification.

Actually, Joel Greenblatt did similar argument for his Magic Formula approach. Mr. Greenblatt argued for 20 stocks in a portfolio because magic formula stock picks tend to be risky without understanding business. Magic fumula is just a formula with number, of course the risk is high. 20 stock picks make each position less than 5%, any total loss of one position will not affect portfolio that much.

Ultimately, in my opinion, the key strategy in value investing to obtain Buffett like performance is 2 part, first is to lower the pick risk to very low level with margin of safety. This typically requires understanding of business. Then concentrate portfolio into picks of 10 and a few sectors. However, without knowing business, only using a formular like Magic formula, or a simple PE, PB, etc, investors should have more diversification such as 20 stocks in a portfolio.

Mutual fund managers in Wall Street have poor performance, they do not understand business as Buffett or Greenblatt could do. Therefore, you never see them to have concentrated portfolio. They do not dare, because they do not understand business or value. The risk of each pick will kill the performance in the long run if they dare to do concentrated investing.

**lzhang** Sun Oct 01, 2006 7:58 pm

well said. totally agreed

the problem with the img is temp due to blogger.com's own problem. Should not be an issue.

blast_investor wrote: Excellent modeling work on risk profile verses diversification.

Actually, Joel Greenblatt did similar argument for his Magic Formula approach. Mr. Greenblatt argued for 20 stocks in a portfolio because magic formula stock picks tend to be risky without understanding business. Magic fumula is just a formula with number, of course the risk is high. 20 stock picks make each position less than 5%, any total loss of one position will not affect portfolio that much.

Ultimately, in my opinion, the key strategy in value investing to obtain Buffett like performance is 2 part, first is to lower the pick risk to very low level with margin of safety. This typically requires understanding of business. Then concentrate portfolio into picks of 10 and a few sectors. However, without knowing business, only using a formular like Magic formula, or a simple PE, PB, etc, investors should have more diversification such as 20 stocks in a portfolio.

Mutual fund managers in Wall Street have poor performance, they do not understand business as Buffett or Greenblatt could do. Therefore, you never see them to have concentrated portfolio. They do not dare, because they do not understand business or value. The risk of each pick will kill the performance in the long run if they dare to do concentrated investing.