Earning 97% of your lifetime 'total money made' in one day

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
Post Reply
User avatar
Topic Author
Robert T
Posts: 2803
Joined: Tue Feb 27, 2007 8:40 pm
Location: 1, 0.2, 0.4, 0.5
Contact:

Earning 97% of your lifetime 'total money made' in one day

Post by Robert T »

.
Nassim Taleb: At least this seems to be what Nassim Taleb (author of the Black Swan) did in October 1987 (according to this interview). No wonder he has been so focused on writing and speaking about Black Swans (events with ‘small probabilities but huge repercussions’). He earned most of his income from an event stuck way out in the distribution tail – lucky it was a positive Black Swan for him and not a negative one, which it was for many others.

He suggests minimizing exposure to negative Black Swans (including through insurance) and maximizing exposure to positive Black Swans. He regards Banks and Reinsurance companies as being susceptible to negative Black Swan – giving examples of the 1982 banking crisis – where banks lost more than they had made in all previous years (from the article “The eight biggest banks in America had $ 22 bn in capital, and $ 60 bn in loans to South and Central America. They lost everything in one incident.”) On reinsurance companies he gives the example of Lloyd of London. He regards biotech to be susceptible to positive Black Swans – unexpected breakthroughs leading to dramatic increases in company revenue. His current approach to investing (as I understand it) is keep 80 to 90% in t-bills and the remaining 10-20% in the riskiest investments (focusing on those which are more susceptibile to positive Black Swans than negative ones).

Sampling error and broad exposure. He also highlights the risk of sampling error highlighting that in finance, ‘outliers’ (or a few observations) often dominate the mean. He gives the example that about 170 stocks (out of 5000+) account for about 60% of total market capitalization. Some other examples, which I think are useful: 33 stocks accounted for 75% of the return of the S&P500 in 1998. Only a few stocks migrating from a small value portfolio account for most of its return. The point he makes (more eloquently than the above) is that using a small sample of stocks in a portfolio risks missing the few that make the difference (sampling error). He suggests broad diversification (for more detail see Taleb on Black Swans).

Implications for finances and investing (at least my take):
  • 1. More stock diversification is better than less in each asset class used in a portfolio (to reduce the sampling error risk of missing those stocks that make the difference).

    2. Minimize negative Black Swans through insurance (disability, life, auto, home, umbrella), and through diversification into asset classes that do well when negative Black Swan’s show up (US treasuries seem to do well when Banks collapse, and CCFs seem to do well during other unpredictable events – climatic shocks and wars [although I don’t currently own CCFs]). IMO this will likely reduce the impact of negative Black Swan’s while retaining broad diversification (as in 1 above) .

    3. Don’t expect to make 97% of lifetime ''total money made" in one day…[in my, perhaps biased, view this is less replicable than the more incremental approach taken by many of today's successful retirees (many who post here)].
His book "The Black Swan: The Impact of the Highly Improbable" is an interesting read.

Robert
.
rich
Posts: 933
Joined: Fri Mar 16, 2007 6:51 pm

Post by rich »

Excellent summary Robert! Thank you!
Best regards, | Rich
edge
Posts: 3833
Joined: Mon Feb 19, 2007 6:44 pm
Location: NY

Post by edge »

Thanks Robert, great summary.
User avatar
stratton
Posts: 11085
Joined: Sun Mar 04, 2007 4:05 pm
Location: Puget Sound

Post by stratton »

Robert,

On diversification: Taleb was the Keynote speaker at the 2008 CFA Institute conference and notes from his presentation::
Sharpe ratios (dividing a poprtfolio’s excess return over a risk-free rate by the standard deviation of the portfolio’s return) are a trap, because they do not predict future Sharpe ratios. So abandon them.

Don’t use standard deviations, and instead use mean variation.

Diversification doesn’t work. You might need as many as 12,000 companies before it truly works. Another example he uses is profits from the drug industry, which are concentrated in a tiny proportion of successful drugs - so you would need to buy a lot of drugs stocks to be truly diversified.

As for derivatives: “Take a walk and see if you can rid yourself of the desire to use derivatives. It’s amazing how little people who claim to know derivatives really know derivatives.”
...
So on his argument, risk managers should penalise exposure to “tail risks” or extreme “black swan” events. They should not be worried about minimising volatility, as this is not a problem. But, he said in exasperated tones, “we seem to go the other way”.
DFA investors are probably the closest to having 12,000 companies. The problem is a lot of funds are a little too representative of their indexes. For example Intl developed SC funds such as GWX have about 500 stocks while their index has 2800+ stocks. Another example is Vangaurd's FTSE ex-US fund (VEU) actually has about 2200 stocks as its index. Yet the iShares equivalent only has 600 stocks. Same with VWO vs EEM with 900 and ~550 stocks. The funds with more stocks should allow for more positive black swans.

For us to truly get this many investible companies we'll probably need to wait for some of the international index reconstituations. EM is moving to around 900 companies in the MSCI large/mid index and ~1200 in the small portion. Right now we don't have any funds other than DFA which go to that depth in the international small area.

Paul
User avatar
AzRunner
Posts: 999
Joined: Mon Feb 19, 2007 5:18 pm
Location: Phoenix

Post by AzRunner »

Taleb is a very entertaining author and his message that the markets are riskier than most perceive is well documented. That said, I think it is difficult to plan for retirement based on his advice.

Someone my age (late 50s) who has been investing since the late 1970s has lived through many market conditions. Using index funds to the extent possible I've been able to have my portfolio grow over the years doing nothing extraordinary, just by following basic Diehard principles (before they were documented as such).

I'm more inclined to follow the William Bernstein dictum that the markets are relatively efficient but now and then they go totally bonkers. Without risk there is no reward. As Diehards we try to diversify as much as possible. I'm not convinced that I need 12,000 stocks to achieve adequate diversification. It would seem that Vg Total Stock Mkt + Vg Total Intl Stock Mkt + various funds to provideone's desired tilt is good enough for practical purposes.

Taleb's example of drug companies and their profits doesn't seem to prove his point. Yes drug companies make most of their profits from a few drugs. But an investor can easily invest in the vast majority of drug companies by owning the TSM + Total Int'l Stock Market index.

Norm
User avatar
craigr
Posts: 2696
Joined: Tue Mar 13, 2007 6:54 pm

Post by craigr »

Nice write-up, Robert. I think you encapsulated a lot of Taleb's advice well.

As for the 12,000 stocks I agree with AzRunner. At some point you just need to acknowledge you have enough and just let things go. Even assuming you miss the next Google, chances are that your index wouldn't have held enough of it anyway to make that much of a difference. By the time the company gets big enough the index probably will have added it anyway.

Also if I recall from the EconTalk interview, Taleb takes a lot of his risk on venture capital plays and other investments that are generally out of reach of most investors. I know from my own experience with Venture Capitalists that the funds you want to be in probably don't want/need your money. The funds you should probably avoid will be happy to take your money and gamble with it.

I really like Taleb's ideas, however in some respects I think he underestimates the difficulty and extreme risk involved in trying to find positive black swan investments.

My advice is a little different than his. If you want to hit it big with a positive black swan you should look for it on your career side. Start your own business, work for a start-up with a good equity compensation, etc. Being an entrepreneur is all about going out and looking for Black Swans actively. But if you try long enough, work hard enough, pick yourself up after the failures and perhaps with some good luck, you may find that things work out OK.
User avatar
gummy
Posts: 340
Joined: Mon Mar 12, 2007 2:34 pm
Location: Burlington, Ontari-ari-ari-O
Contact:

Post by gummy »

Don’t use standard deviations, and instead use mean variation.
And what is "mean variation"? Anybuddy know?

Elsewhere, Taleb has written:
"... options are not priced off a mean-square variation in the underlying, but off a mean variation in the underlying".

Interesting.
diasurfer
Posts: 1855
Joined: Fri Jul 06, 2007 8:33 pm
Location: miami-dade

what am I missing here?

Post by diasurfer »

I don't get this "need 12000 stocks" business or "DFA is better because it holds more stocks" (leave aside screens, filters, block buying, etc, this is not about DFA per se).

Let's say a small value fund gets its high returns from 0.1% of small value stocks. If I buy 1000 SV stocks in a fund, then I have 1 winner and 999 stocks dragging the returns of my winner down. If I buy 10000 SV stocks in another fund, then I should have 10 winners and 9990 duds. I have 10 times as many of the gems but also 10 times as much drag (not to mention possibly higher expenses). There may be something else going on here to explain it, but it sure isn't the law of averages.
User avatar
Topic Author
Robert T
Posts: 2803
Joined: Tue Feb 27, 2007 8:40 pm
Location: 1, 0.2, 0.4, 0.5
Contact:

Post by Robert T »

.
A few more from Nassim Taleb on the Sharpe Ratio, diversification, and risk

On the Sharpe Ratio: Sharpe ratio, key hedge fund risk gauge is 'flawed' (perhaps the impact of 'outliers' on hedge fund returns is amplified by their use of leverage).

On diversification (and risk): How the Finance Guru’s Get Risk All Wrong
First, diversify as broadly as you can—far more than the supposed experts tell you now. This isn’t just a matter of avoiding losses: Long-run market returns are dominated by a small number of investments, hence the risk of missing them must be mitigated by investing as broadly as possible. Passive indexing is far more effective than active selection—but you need to go well beyond an S&P 500 fund to do yourself much good. And wherever you put your money, understand that conventional measures of risk severely underestimate potential losses —and gains. For better or worse, your exposure is larger than you think.
On risk ('stress testing'):A focus on the exceptions that prove the rule. Taleb suggests using a fractal approach (described in the linked article) for ‘stress testing’ rather than the normal distribution (I will try to do this for my portfolio sometime).
Indeed, this fractal approach can prove to be an extremely robust method to identify a portfolio’s vulnerability to severe risks. Traditional “stress testing” is usually done by selecting an arbitrary number of “worst-case scenarios” from past data. It assumes that whenever one has seen in the past a large move of, say, 10 per cent, one can conclude that a fluctuation of this magnitude would be the worst one can expect for the future. This method forgets that crashes happen without antecedents. Before the crash of 1987, stress testing would not have allowed for a 22 per cent move.
Robert
.
PS: Grantham also provides some interesting views on outliers like the crash of 1987 suggesting that unit of observation (1-day, 1-year, 5-years, 30-years) can make a significant different to what a return distribution looks like ( an attempted summary provided in this earlier thread)
.
User avatar
stratton
Posts: 11085
Joined: Sun Mar 04, 2007 4:05 pm
Location: Puget Sound

Post by stratton »

Robert T wrote:On the Sharpe Ratio: Sharpe ratio, key hedge fund risk gauge is 'flawed' (perhaps the impact of 'outliers' on hedge fund returns is amplified by their use of leverage).
He mentioned in the interview from the OP low volatility markets are the most dangerous. This I assume is from hedge funds needing to crank up the leverage to have any effect. We know where that got us with the detonating hedge funds in August 2007.

Paul
Wagnerjb
Posts: 7213
Joined: Mon Feb 19, 2007 7:44 pm
Location: Houston, Texas

Post by Wagnerjb »

First, diversify as broadly as you can—far more than the supposed experts tell you now. This isn’t just a matter of avoiding losses: Long-run market returns are dominated by a small number of investments, hence the risk of missing them must be mitigated by investing as broadly as possible. Passive indexing is far more effective than active selection—but you need to go well beyond an S&P 500 fund to do yourself much good. And wherever you put your money, understand that conventional measures of risk severely underestimate potential losses —and gains. For better or worse, your exposure is larger than you think.
If Taleb is simply saying to diversify well beyond the S&P500, nobody here would disagree with him. Until I see more on his problem with "diversification", I will assume (based on this passage) that he is talking to the naive investors out there, not to Bogleheads.

Best wishes.
Andy
User avatar
craigr
Posts: 2696
Joined: Tue Mar 13, 2007 6:54 pm

Post by craigr »

stratton wrote:
Robert T wrote:On the Sharpe Ratio: Sharpe ratio, key hedge fund risk gauge is 'flawed' (perhaps the impact of 'outliers' on hedge fund returns is amplified by their use of leverage).
He mentioned in the interview from the OP low volatility markets are the most dangerous. This I assume is from hedge funds needing to crank up the leverage to have any effect. We know where that got us with the detonating hedge funds in August 2007.
I interpreted his statements more along the lines of awareness of risk.

When you think things are going to be calm perhaps you take on more risk. However when you know what you're doing is risky you tend to be more cautious and diversified.

In the venture capital world things are extremely volatile. For instance perhaps 90% of their investments are going to fail or won't go anywhere fast enough. So they invest as if this were reality and stay diversified, get other firms to pool into investments and limit their exposure to single companies until they show they are moving ahead in a good direction. They are hoping for that 1 in 10 investment to hit it so big that it wipes out their other losses.

We can then contrast that with investments that people think are safer and less volatile, such as mortgages or money market funds holding them. They concentrate their bets thinking nothing will happen and then one day they wake up to see that something completely unexpected has wiped them out.

It's probably best to assume anything you invest in has risk even if you can't think of what it could be right now. If anything, it may convince you not to concentrate 100% of your wealth in any particular asset, even if people are saying the investment is "riskless".
User avatar
House Blend
Posts: 4877
Joined: Fri May 04, 2007 1:02 pm

Post by House Blend »

gummy wrote:
Don’t use standard deviations, and instead use mean variation.
And what is "mean variation"? Anybuddy know?

Elsewhere, Taleb has written:
"... options are not priced off a mean-square variation in the underlying, but off a mean variation in the underlying".
It's pretty clear from the "elsewhere" article that he's talking about replacing the L^2 norm with an L^1 norm: instead of averaging (X - E[X])^2, which you would use for computing variance/standard deviation, he's averaging |X - E[X]|.

But this is in a context of pricing options, and I can only claim a vague understanding of why L^1 norms are more appropriate there: prices should tend to be proportional to perceived differences in values, whereas an L^2 norm would assign more value to larger differences.

Also, I would bet that the first quote ("Don't use standard deviations...") is out of context. Given Taleb's reputation as Mr. Black Swan, I seriously doubt that he is advocating that investors should replace the L^2 norm with the L^1 norm as a measure of risk. That gives less weight to outliers, not more.
User avatar
gummy
Posts: 340
Joined: Mon Mar 12, 2007 2:34 pm
Location: Burlington, Ontari-ari-ari-O
Contact:

Post by gummy »

Sharpe ratios (dividing a portfolio’s excess return over a risk-free rate by the standard deviation of the portfolio’s return) are a trap, because they do not predict future Sharpe ratios.
Perhaps Taleb is saying to use the "mean absolute deviation" since a mean is typically used to describe an "Expected (future) Value", not the "Standard Deviation".

Hmmm ... sounds like an interesting study ...
User avatar
Topic Author
Robert T
Posts: 2803
Joined: Tue Feb 27, 2007 8:40 pm
Location: 1, 0.2, 0.4, 0.5
Contact:

Post by Robert T »

.
Using a portfolio with:

Expected return = 7%
Expected standard deviation = 12%

(Similar to a 75:25 equity:fixed income portfolio with a small cap and value tilt).

Code: Select all

Expected portfolio return ‘stress-test’ (approximation):

Expected
Annual       Gaussian method               Fractile method
Return      ‘normal distribution’   ‘Tail exponent=2”    ‘Tail exponent=1”

 -5%            every 6 yrs            every 6 yrs           every 6 yrs    
-15%            every 44 yrs           every 48 yrs          every 24 yrs
-30%            every 720 yrs          every 192 yrs         every 96 yrs

So the extreme event (-30% annual return) is expected to occur more frequently using Taleb and Mandelbrot’s fractile method (almost 4 time more frequently with a tail exponent of 2, and 7 times more frequently with a tail exponent of 1). Either way – the extreme event of a 30% loss in one year is expected to occur fairly infrequently). This of course assumes I have done the above approximate calculations correctly. (Not sure – corrections welcome. The normal distribution numbers are approximations, the more accurate expected return numbers are -5%, -17%, and -29%).

Robert
.
ETFnerd
Posts: 320
Joined: Mon Mar 03, 2008 10:01 am

Post by ETFnerd »

I sometimes bet on deep out-of-the-money options with less than 2 weeks to expiry based on this thesis. The bets are small (say $1K) but highly concentrated. Then I do the fundamental analysis to find a situation that is mispriced. Options markets are not that liquid at the out-of-the-money extrema.
User avatar
gummy
Posts: 340
Joined: Mon Mar 12, 2007 2:34 pm
Location: Burlington, Ontari-ari-ari-O
Contact:

Post by gummy »

I looked at using Taleb's Mean Variation over a 10-year period to see how well it predicted the Mean Variation for the following year.

Then I compared to using the reg'lar, garden variety Standard Deviation.

I did this for several stocks, like GE, MSFT, XOM etc..
The latter does a better job in that "next year's" SD is closer to the "historical" SD.

Conclusion?
I have no idea what Taleb is talking about.
I'm often in that state. :?
ETFnerd
Posts: 320
Joined: Mon Mar 03, 2008 10:01 am

Post by ETFnerd »

I don't understand what the fascination with calculating a more accurate number is. These are all approximations based on restrictive assumptions. The market gives you a perfect hedge because you can purchase the put option for the underlying indeces at a 75:25 ratio. You choose the strike protection and the market sets the price. Your analysis may give you an indication of whether you're paying a fair price for the protection but this is generally useful only if you are speculating on the value of the protection. From the POV of the portfolio holder, you just want to hedge against the black swan event, and the market sets the clearing price for this right.

Also you should clarify for those not mathematically inclined that the tails calculate the probability of a return of -5% or less, -15% or less and -30% or less. The probability of a return of -30% is zero.
Robert T wrote:.
Using a portfolio with:

Expected return = 7%
Expected standard deviation = 12%

(Similar to a 75:25 equity:fixed income portfolio with a small cap and value tilt).

Code: Select all

Expected portfolio return ‘stress-test’ (approximation):

Expected
Annual       Gaussian method               Fractile method
Return      ‘normal distribution’   ‘Tail exponent=2”    ‘Tail exponent=1”

 -5%            every 6 yrs            every 6 yrs           every 6 yrs    
-15%            every 44 yrs           every 48 yrs          every 24 yrs
-30%            every 720 yrs          every 192 yrs         every 96 yrs

So the extreme event (-30% annual return) is expected to occur more frequently using Taleb and Mandelbrot’s fractile method (almost 4 time more frequently with a tail exponent of 2, and 7 times more frequently with a tail exponent of 1). Either way – the extreme event of a 30% loss in one year is expected to occur fairly infrequently). This of course assumes I have done the above approximate calculations correctly. (Not sure – corrections welcome. The normal distribution numbers are approximations, the more accurate expected return numbers are -5%, -17%, and -29%).

Robert
.
peter71
Posts: 3769
Joined: Tue Jul 24, 2007 8:28 pm

Post by peter71 »

Hi All,

My two cents is that Taleb is obviously /profoundly/ gifted. I've followed some of the discussions of him over on the Wilmott board (which is largely populated by math PhD's) and I've never seen anyone question the fact that he knows his math . . . beyond that, there's also a profundity to his thinking that I suspect is pretty rare among other quants . . . BUT, he's still a human being and I personally think that either his megalomania obscures his cognitive functioning or his desire to promote himself clouds his common sense . . . he definitely sounds some helpful cautionary notes for quants making highly leveraged bets on "sure things," and insofar as he also wants to remind us that skewness and kurtosis exist even at the index level that's of course true to an extent . . . for Bogleheads though, I think the bottom line is that the stock market as a whole just isn't /that/ non-normal over any period of time a Boglehead should care about. Even if we set the time period to just one year, for example, the below calculator suggests that there's only been one > 3 sigma left tail event in 137 years (back in 1931) and to me that's just not all /that/ surprising. Particularly if we begin to think about factors exogenous to the math model (e.g., all the institutional changes that have occurred since 1931) I guess I'm just not all that worried that, say, a six sigma 1-year drop for the TSM could be just around the corner . . . at a minimum, I think it would have to be in the form of a /true/ black swan like a US civil war or an alien attack . . .

http://www.moneychimp.com/articles/rand ... orizon.htm


All best,
Pete
avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

Post by avalpert »

peter71 wrote:Hi All,

My two cents is that Taleb is obviously /profoundly/ gifted. I've followed some of the discussions of him over on the Wilmott board (which is largely populated by math PhD's) and I've never seen anyone question the fact that he knows his math . . . beyond that, there's also a profundity to his thinking that I suspect is pretty rare among other quants . . . BUT, he's still a human being and I personally think that either his megalomania obscures his cognitive functioning or his desire to promote himself clouds his common sense . . . he definitely sounds some helpful cautionary notes for quants making highly leveraged bets on "sure things," and insofar as he also wants to remind us that skewness and kurtosis exist even at the index level that's of course true to an extent . . . for Bogleheads though, I think the bottom line is that the stock market as a whole just isn't /that/ non-normal over any period of time a Boglehead should care about. Even if we set the time period to just one year, for example, the below calculator suggests that there's only been one > 3 sigma left tail event in 137 years (back in 1931) and to me that's just not all /that/ surprising. Particularly if we begin to think about factors exogenous to the math model (e.g., all the institutional changes that have occurred since 1931) I guess I'm just not all that worried that, say, a six sigma 1-year drop for the TSM could be just around the corner . . . at a minimum, I think it would have to be in the form of a /true/ black swan like a US civil war or an alien attack . . .

http://www.moneychimp.com/articles/rand ... orizon.htm


All best,
Pete
But the real problem, and here Taleb is right, is that that true black swan can happen any time and may happen with zero warning - in which case all the portfolio planning in the world gets thrown out the window.

The problem is, and I haven't seen Taleb solve this, as humans with limited time spans and limited option we can't possibly plan for all or even many possible black swans. So we have to do the best we can with the knowledge we have and see how it all plays out. The example I often use is predicting how long I need to drive through DC traffic to make a 9 am meeting - if I were planning for true black swan possiblities I probably would have to have left yesterday - its just not practical and therefor should not be allowed to paralyze us from actually living our lives.
peter71
Posts: 3769
Joined: Tue Jul 24, 2007 8:28 pm

Post by peter71 »

avalpert wrote:
peter71 wrote:Hi All,

My two cents is that Taleb is obviously /profoundly/ gifted. I've followed some of the discussions of him over on the Wilmott board (which is largely populated by math PhD's) and I've never seen anyone question the fact that he knows his math . . . beyond that, there's also a profundity to his thinking that I suspect is pretty rare among other quants . . . BUT, he's still a human being and I personally think that either his megalomania obscures his cognitive functioning or his desire to promote himself clouds his common sense . . . he definitely sounds some helpful cautionary notes for quants making highly leveraged bets on "sure things," and insofar as he also wants to remind us that skewness and kurtosis exist even at the index level that's of course true to an extent . . . for Bogleheads though, I think the bottom line is that the stock market as a whole just isn't /that/ non-normal over any period of time a Boglehead should care about. Even if we set the time period to just one year, for example, the below calculator suggests that there's only been one > 3 sigma left tail event in 137 years (back in 1931) and to me that's just not all /that/ surprising. Particularly if we begin to think about factors exogenous to the math model (e.g., all the institutional changes that have occurred since 1931) I guess I'm just not all that worried that, say, a six sigma 1-year drop for the TSM could be just around the corner . . . at a minimum, I think it would have to be in the form of a /true/ black swan like a US civil war or an alien attack . . .

http://www.moneychimp.com/articles/rand ... orizon.htm


All best,
Pete
But the real problem, and here Taleb is right, is that that true black swan can happen any time and may happen with zero warning - in which case all the portfolio planning in the world gets thrown out the window.

The problem is, and I haven't seen Taleb solve this, as humans with limited time spans and limited option we can't possibly plan for all or even many possible black swans. So we have to do the best we can with the knowledge we have and see how it all plays out. The example I often use is predicting how long I need to drive through DC traffic to make a 9 am meeting - if I were planning for true black swan possiblities I probably would have to have left yesterday - its just not practical and therefor should not be allowed to paralyze us from actually living our lives.
I agree. I trust he'd say that what you should do is buy 90% conservative stuff and 10% way out of the money options, etc., and insofar as someone actually offers a simple low fee product that does that for ordinary investors I think it'd be interesting, but AFAIK his hedge fund failed and even though Bodie seems to want a similar product too I've got to think there's a reason no one's offering it.

All best,
Pete
avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

Post by avalpert »

peter71 wrote:

I agree. I trust he'd say that what you should do is buy 90% conservative stuff and 10% way out of the money options, etc., and insofar as someone actually offers a simple low fee product that does that for ordinary investors I think it'd be interesting, but AFAIK his hedge fund failed and even though Bodie seems to want a similar product too I've got to think there's a reason no one's offering it.

All best,
Pete
Yeah, I have hard time seeing profitability in a product for retail investors that is designed to payoff big at some, unknown, future moment and otherwise maybe track inflation. To the extent it is profitable we already have such a low cost prodcut - the lottery.
ETFnerd
Posts: 320
Joined: Mon Mar 03, 2008 10:01 am

Post by ETFnerd »

The lottery is not low cost.
dumbmoney
Posts: 2419
Joined: Sun Mar 16, 2008 8:58 pm

Post by dumbmoney »

Taleb is another overconfident hedge fund guru, just overconfident in a different way than most. He's overconfident in another people's supposed overconfidence.

But maybe I'm being overconfident in my assessment of the overconfidence of Taleb's overconfidence assessment.

----

In the end, it doesn't matter what might have happened - only what actually does. Since we aren't immortal, we shouldn't worry too much about low probability events. We'll all be dead before anything bad can happen to us.
diasurfer
Posts: 1855
Joined: Fri Jul 06, 2007 8:33 pm
Location: miami-dade

Re: what am I missing here?

Post by diasurfer »

diasurfer wrote:I don't get this "need 12000 stocks" business or "DFA is better because it holds more stocks" (leave aside screens, filters, block buying, etc, this is not about DFA per se).

Let's say a small value fund gets its high returns from 0.1% of small value stocks. If I buy 1000 SV stocks in a fund, then I have 1 winner and 999 stocks dragging the returns of my winner down. If I buy 10000 SV stocks in another fund, then I should have 10 winners and 9990 duds. I have 10 times as many of the gems but also 10 times as much drag (not to mention possibly higher expenses). There may be something else going on here to explain it, but it sure isn't the law of averages.
Anybody care to take a crack at this? I don't see how the size of the tails in the distribution would change this at all. Buying more stocks in your mutual fund gives you more of those out on the tails of the distribution, and more of everything else. No improvement in net return. Wrong?
FinanceGeek
Posts: 989
Joined: Sun Jul 01, 2007 5:27 pm

Post by FinanceGeek »

One thing I found interesting about Taleb's book is the idea of a barbell portfolio. 90% of your assets in T-bills and shoot the moon with the other 10% in uncorrelated high risk bets like VC, commodities, etc. Limits your max drawdown to 10%, while leaving open the potential for significant upside. He claims such a portfolio is better immunized against Black Swans that will trash the supposedly-well-diversified portfolio that most of us pursue. Maybe deep out of the money puts and calls on the major indices, mixed with leveraged bets on emerging markets?

Whaddya all think of doing that? I worry about the availability of the positions that would make up that 10%, but otherwise (to use MythBusters terminology), it seems "plausible".
User avatar
market timer
Posts: 6535
Joined: Tue Aug 21, 2007 1:42 am

Re: what am I missing here?

Post by market timer »

diasurfer wrote:Anybody care to take a crack at this? I don't see how the size of the tails in the distribution would change this at all. Buying more stocks in your mutual fund gives you more of those out on the tails of the distribution, and more of everything else. No improvement in net return. Wrong?
He's probably just talking about return per unit of risk. While the expected return won't change with sample size, the variance will. Moreoever, many people, especially around here, worship at the altar of annual geometric returns, which will increase in sample size.
peter71
Posts: 3769
Joined: Tue Jul 24, 2007 8:28 pm

Re: what am I missing here?

Post by peter71 »

diasurfer wrote:
diasurfer wrote:I don't get this "need 12000 stocks" business or "DFA is better because it holds more stocks" (leave aside screens, filters, block buying, etc, this is not about DFA per se).

Let's say a small value fund gets its high returns from 0.1% of small value stocks. If I buy 1000 SV stocks in a fund, then I have 1 winner and 999 stocks dragging the returns of my winner down. If I buy 10000 SV stocks in another fund, then I should have 10 winners and 9990 duds. I have 10 times as many of the gems but also 10 times as much drag (not to mention possibly higher expenses). There may be something else going on here to explain it, but it sure isn't the law of averages.
Anybody care to take a crack at this? I don't see how the size of the tails in the distribution would change this at all. Buying more stocks in your mutual fund gives you more of those out on the tails of the distribution, and more of everything else. No improvement in net return. Wrong?
This part I actually agree with, as I think he's just talking about positive skewness or what others sometimes call the "Dell effect" . . .

http://www.theskilledinvestor.com/ss.it ... ation.html

I've posted about how skewness might make equal-weighting (RSP) superior to cap-weighting (VFINX) before aside from issues of tilting, and you can see the difference between equal weight and cap weight returns in the tables in the following paper (but it's in any case a small effect overall and I believe it approaches zero at 150 stocks owned in equal weights)

http://mba.tuck.dartmouth.edu/pages/fac ... ewness.pdf

All best,
Pete
User avatar
Topic Author
Robert T
Posts: 2803
Joined: Tue Feb 27, 2007 8:40 pm
Location: 1, 0.2, 0.4, 0.5
Contact:

Post by Robert T »

.
diasurfer wrote:
I don't get this "need 12000 stocks" business or "DFA is better because it holds more stocks" (leave aside screens, filters, block buying, etc, this is not about DFA per se). Let's say a small value fund gets its high returns from 0.1% of small value stocks. If I buy 1000 SV stocks in a fund, then I have 1 winner and 999 stocks dragging the returns of my winner down. If I buy 10000 SV stocks in another fund, then I should have 10 winners and 9990 duds. I have 10 times as many of the gems but also 10 times as much drag (not to mention possibly higher expenses). There may be something else going on here to explain it, but it sure isn't the law of averages.

Anybody care to take a crack at this? I don't see how the size of the tails in the distribution would change this at all. Buying more stocks in your mutual fund gives you more of those out on the tails of the distribution, and more of everything else. No improvement in net return. Wrong?
Let me try. This assumes your sample of 1,000 SV stocks is fully representative of the universe of SV stocks (lets assume the universe is 10,000 stocks following your example).

In the universe of 10,000 SV stocks (assuming this is all the listed SV stocks) 10 stocks account for all the return and 9990 have zero return (following the example for illustration). If your sample of 1,000 SV stocks are all from the 9990 stocks with zero return, then the 1,000 SV stock portfolio will have significantly lower returns from the 10,000 SV stock portfolio. It could of course work the other way – that your 1,000 SV stock portfolio includes all 10 of the ‘winning’ stocks in which case the 1,000 SV stock performance will be significantly higher than the 10,000 SV stock portfolio.

The sampling error risk (as I understand it) is the risk that the sample (of 1,000 SV stocks in this case) is not representative of the universe of SV stocks which may lead to missing out on the ‘winning stocks’.

Hope this helps.

Robert
.
SmallHi
Posts: 1718
Joined: Wed Feb 21, 2007 5:11 pm

Post by SmallHi »

Robert,

You are exactly right. And, to make matters worse, normally we choose asset class (or portfolio tilts :wink: ) understanding that capturing the asset class return will allow us to achieve our results.

Failing to capture the asset class return will likely impair our ability to achieve our goals without further capital inflows...but we will still take all of the risk as if we had captured the return. Because any sample basket of securities is expected to have at least as much return as the population, if not more! The guarantee of all the risk without the certainty of a fair return (relative to the total universe of securities you are choosing from) -- now thats a raw deal!

sh
diasurfer
Posts: 1855
Joined: Fri Jul 06, 2007 8:33 pm
Location: miami-dade

okay

Post by diasurfer »

I think market timer's explanation about risk-adjusted return is the clearest, but not sure if that's the issue.

Peter71's first paper and Robert's explanation makes sense too. It's not that your more diversified portfolio has a higher expected return, it's that your more diversified portfolio is less likely to have lower return.

Thanks for you input. I think I'll run a simulation and test some of these ideas.
diasurfer
Posts: 1855
Joined: Fri Jul 06, 2007 8:33 pm
Location: miami-dade

simulation

Post by diasurfer »

I ran a simulation of these ideas in Matlab.

I created a universe of 1000 stocks. The return of these stocks was chosen from a normal distribution with mean 0 and standard deviation 1. To produce mean positive returns (stocks tend to go up over long times!) I added 1 to each return. Thus the mean return of these 1000 stocks is 1 and the std is 1. Thus there are winners and losers but on average the universe is going up. [I realize the std presented here of my universe is not the same as the std/volatility of a stock over time].

I then altered my 1000 stock universe by chosing Stock #1 to have return 100. Thus the mean return of my 1000 stock universe is now 1.0990.

I created two portfolios, Portfolio #1 and Portfolio #2. Portfolio #1 holds 500 randomly selectedstocks from the 1000 stock universe. Portfolio #2 holds 100 randomly selected stocks. For each portfolio I calculated the mean return and the std of the returns. Then, I randomly reselected the portfolios 999 more times for 1000 different versions of Portfolio #1 and #2 per universe. For each portfolio, I calculated the number of times the mean return was greater than or equal to the mean universe return of 1.0990.

I repeated the entire process above 10,000 times (10,000 universes) and averaged the results.

RESULTS:
Portfolio #1 Mean Return: 1.0988
Portfolio #2 Mean Return: 1.0988

Portfolio #1 Mean Std: 2.75
Portfolio #1 Mean Std: 2.02

Average number of times per 1000 portfolios in which portfolio exceeded Universe Average of 1.0990:

Portfolio #1: 499.87
Portfolio #2: 244.17

Mean return / Mean Std
Portfolio #1: 0.39
Portfolio #2: 0.58

CONCLUSIONS

I believe the results are for the most part consistent with the posts above.

1. Average return is the same for small and large portfolios

2. Higher probability for underperforming the full universe of stocks with a smaller portfolio.

3. Unexpected: lower mean standard deviation for the smaller portfolio. I believe this is because you are less likely to have the outperformer Stock #1 in your portfolio.

4. Unexpected: portfolio #2 looks better on "risk adjusted" basis. I use quotes because I'm not sure that the standard deviation I have calculated is same as the "volatility" standard deviation. I think you would need some sort of ergodicity assumption for equivalence.
Rodc
Posts: 13601
Joined: Tue Jun 26, 2007 9:46 am

Re: simulation

Post by Rodc »

diasurfer wrote:I ran a simulation of these ideas in Matlab.

I created a universe of 1000 stocks. The return of these stocks was chosen from a normal distribution with mean 0 and standard deviation 1. To produce mean positive returns (stocks tend to go up over long times!) I added 1 to each return. Thus the mean return of these 1000 stocks is 1 and the std is 1. Thus there are winners and losers but on average the universe is going up. [I realize the std presented here of my universe is not the same as the std/volatility of a stock over time].

I then altered my 1000 stock universe by chosing Stock #1 to have return 100. Thus the mean return of my 1000 stock universe is now 1.0990.

I created two portfolios, Portfolio #1 and Portfolio #2. Portfolio #1 holds 500 randomly selectedstocks from the 1000 stock universe. Portfolio #2 holds 100 randomly selected stocks. For each portfolio I calculated the mean return and the std of the returns. Then, I randomly reselected the portfolios 999 more times for 1000 different versions of Portfolio #1 and #2 per universe. For each portfolio, I calculated the number of times the mean return was greater than or equal to the mean universe return of 1.0990.

I repeated the entire process above 10,000 times (10,000 universes) and averaged the results.

RESULTS:
Portfolio #1 Mean Return: 1.0988
Portfolio #2 Mean Return: 1.0988

Portfolio #1 Mean Std: 2.75
Portfolio #1 Mean Std: 2.02

Average number of times per 1000 portfolios in which portfolio exceeded Universe Average of 1.0990:

Portfolio #1: 499.87
Portfolio #2: 244.17

Mean return / Mean Std
Portfolio #1: 0.39
Portfolio #2: 0.58

CONCLUSIONS

I believe the results are for the most part consistent with the posts above.

1. Average return is the same for small and large portfolios

2. Higher probability for underperforming the full universe of stocks with a smaller portfolio.

3. Unexpected: lower mean standard deviation for the smaller portfolio. I believe this is because you are less likely to have the outperformer Stock #1 in your portfolio.

4. Unexpected: portfolio #2 looks better on "risk adjusted" basis. I use quotes because I'm not sure that the standard deviation I have calculated is same as the "volatility" standard deviation. I think you would need some sort of ergodicity assumption for equivalence.
Interesting exercise. Your risk adjusted is not quite a sharpe ratio as there is no risk free asset involved, but including a risk free asset would only change the numbers, not the sense of the result, so the conclusion holds. I would argue all four results are as expected, but it is interesting to see numbers put to it. It would be interesting to see this redone with more realistic values for input, although I'm not entire sure just what those inputs would be.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
diasurfer
Posts: 1855
Joined: Fri Jul 06, 2007 8:33 pm
Location: miami-dade

Post by diasurfer »

Glad you found it interesting. As someone currently considering small value ETFs for an SV tilt, it was nice to be convinced of the need to hold many stocks by my own numbers.

As far as Sharpe ratio, besides the fact that I haven't calculated return above risk free, I don't believe I have calculated "volatility". As I understand it (the only thing I know about investment is what I have read on this board!), volatility is the standard deviation of a time series. I've read lots of back and forth about differences in monthly, quarterly, yearly time series, etc.

My std is essentially a snapshot - a single point in time. If you asserted that my 10000 universes was instead 10000 days, then both portfolios would have the same volatility because they're from the same distribution, except for inclusion of Stock #1, which randomly appears and disappears in a portfolio on a daily basis. Conclusions 3 and 4 above would still hold, but I'm not sure how realistic or insightful that is.

I recall you're a Matlab user. There are other built-in distributions to generate the universe of stocks from, but I don't believe that would really prove any more insightful. [By central limit theoreom, any random combination of variables is normally distributed regardless of their underlying distribution, right?]. I can post/PM the matlab code if you're interested.
Rodc
Posts: 13601
Joined: Tue Jun 26, 2007 9:46 am

Post by Rodc »

diasurfer wrote:Glad you found it interesting. As someone currently considering small value ETFs for an SV tilt, it was nice to be convinced of the need to hold many stocks by my own numbers.

As far as Sharpe ratio, besides the fact that I haven't calculated return above risk free, I don't believe I have calculated "volatility". As I understand it (the only thing I know about investment is what I have read on this board!), volatility is the standard deviation of a time series. I've read lots of back and forth about differences in monthly, quarterly, yearly time series, etc.

My std is essentially a snapshot - a single point in time. If you asserted that my 10000 universes was instead 10000 days, then both portfolios would have the same volatility because they're from the same distribution, except for inclusion of Stock #1, which randomly appears and disappears in a portfolio on a daily basis. Conclusions 3 and 4 above would still hold, but I'm not sure how realistic or insightful that is.

I recall you're a Matlab user. There are other built-in distributions to generate the universe of stocks from, but I don't believe that would really prove any more insightful. [By central limit theoreom, any random combination of variables is normally distributed regardless of their underlying distribution, right?]. I can post/PM the matlab code if you're interested.
I missed that about which SD you listed. But I think you'd get similar numbers of you did a time series.

For a combination of variables that are added yes, but if you multiply them, as in computing returns over the years (1+r1)*(1+r2)*...*(1+rn) the multiplicative central limit theorem says the results are lognormal, which is good as that distribution has a smaller left tail and a larger right tail.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
diasurfer
Posts: 1855
Joined: Fri Jul 06, 2007 8:33 pm
Location: miami-dade

Post by diasurfer »

Rodc wrote:
For a combination of variables that are added yes, but if you multiply them, as in computing returns over the years (1+r1)*(1+r2)*...*(1+rn) the multiplicative central limit theorem says the results are lognormal, which is good as that distribution has a smaller left tail and a larger right tail.
Hardly a day goes by that I don't learn something on this board!
User avatar
Topic Author
Robert T
Posts: 2803
Joined: Tue Feb 27, 2007 8:40 pm
Location: 1, 0.2, 0.4, 0.5
Contact:

Post by Robert T »

.
On sampling error

FWIW - this is my summary from the Fama-French Migration Paper: (Financial Analysts Journal. Vol 63, No. 3. 2007), with 2005 stock number data from Ken French’s website.

Code: Select all

FF SMALL VALUE portfolio: 922 stocks at the end of 2005.

                                                                 1927-2005

                                                        Average Contribution to
                                                        Portfolio’s Av. Excess 
On average:                                                      Return
 
74% of SV stocks remained as SV                                    -0.5%
18% of SV stocks moved to growth + 2% were acquired                 4.2% 
3% of SV stocks became big                                          5.4%
Remainder return due to stocks moving to SV, delists               -0.2%

Total SV Portfolio Average Annual Excess Return above Market        9.2%


FF LARGE VALUE portfolio: 173 stocks at the end of 2005.

                                                       Average Contribution to
                                                       Portfolio’s Av. Excess 
On average:                                                      Return
 
69% of LV stocks remained as LV                                     2.3%
21% of LV stocks moved to growth + 2% were acquired                 3.3% 
3% of LV stocks became small                                       -0.7%
Remainder return due to stocks moving to LV & delists               0.0%

Total LV Portfolio Average Annual Excess Return above Market        4.8%

Source: Fama-French Migration paper

What I get from the above?
  • 1. For the SV portfolio, 3% of stocks accounted for close to 60% of excess returns, and 23% of stocks accounted for all the excess return.
    2. For the LV portfolio, 23% of stocks accounted for over 60% of excess returns, and 92% of stocks accounted for all the excess return.
Most of the return of the SV portfolio was from small stocks getting big (rather than from value moving to growth – although both are important). Interestingly for a small blend portfolio (SG+SN+SV), about 5% of stocks move from small to big annually, accounting most of the return.

Implications? (at least my take)
  • 1. The probability of sampling error is higher for small value stock portfolios than for large value stock portfolios (and arguably small cap blend portfolios).
    2. Gaining small cap and value exposure through a combination of a large value and a small cap blend portfolio may lower sampling error relative to a small value portfolio. Obviously no guarantees.
Robert
.
edge
Posts: 3833
Joined: Mon Feb 19, 2007 6:44 pm
Location: NY

Post by edge »

It seems Vanguard has also figured this out. Their products tend to have WAY more holdings than comparable iShares products.

Robert et al - thanks for the discussion
User avatar
sperry8
Posts: 3065
Joined: Sat Mar 29, 2008 9:25 pm
Location: Miami FL

Re:

Post by sperry8 »

Robert T wrote:.
On sampling error

FWIW - this is my summary from the Fama-French Migration Paper: (Financial Analysts Journal. Vol 63, No. 3. 2007), with 2005 stock number data from Ken French’s website.

Code: Select all

FF SMALL VALUE portfolio: 922 stocks at the end of 2005.

                                                                 1927-2005

                                                        Average Contribution to
                                                        Portfolio’s Av. Excess 
On average:                                                      Return
 
74% of SV stocks remained as SV                                    -0.5%
18% of SV stocks moved to growth + 2% were acquired                 4.2% 
3% of SV stocks became big                                          5.4%
Remainder return due to stocks moving to SV, delists               -0.2%

Total SV Portfolio Average Annual Excess Return above Market        9.2%


FF LARGE VALUE portfolio: 173 stocks at the end of 2005.

                                                       Average Contribution to
                                                       Portfolio’s Av. Excess 
On average:                                                      Return
 
69% of LV stocks remained as LV                                     2.3%
21% of LV stocks moved to growth + 2% were acquired                 3.3% 
3% of LV stocks became small                                       -0.7%
Remainder return due to stocks moving to LV & delists               0.0%

Total LV Portfolio Average Annual Excess Return above Market        4.8%

Source: Fama-French Migration paper

What I get from the above?
  • 1. For the SV portfolio, 3% of stocks accounted for close to 60% of excess returns, and 23% of stocks accounted for all the excess return.
    2. For the LV portfolio, 23% of stocks accounted for over 60% of excess returns, and 92% of stocks accounted for all the excess return.
Most of the return of the SV portfolio was from small stocks getting big (rather than from value moving to growth – although both are important). Interestingly for a small blend portfolio (SG+SN+SV), about 5% of stocks move from small to big annually, accounting most of the return.

Implications? (at least my take)
  • 1. The probability of sampling error is higher for small value stock portfolios than for large value stock portfolios (and arguably small cap blend portfolios).
    2. Gaining small cap and value exposure through a combination of a large value and a small cap blend portfolio may lower sampling error relative to a small value portfolio. Obviously no guarantees.
Robert
.
That 3% number is interesting. I wonder if the SV premium will shrink now that IPOs are down. Perhaps there are now less small lottery tickets coming into the market - making this number harder to achieve going forward. I wonder if there is any correlation regarding those 3%... are they from IPOs? or from companies that have been public for >10 years, etc.
BH Contests: 23 #89 of 607 | 22 #512 of 674 | 21 #66 of 636 |20 #253/664 |19 #233/645 |18 #150/493 |17 #516/647 |16 #121/610 |15 #18/552 |14 #225/503 |13 #383/433 |12 #366/410 |11 #113/369 |10 #53/282
Post Reply