Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform market?

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Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform market?

Post by Anon9001 »

I am referring to Robert Hagstrom 1999 study (Page 54-58) that he done as part of his book Warren Buffet Portfolio. He showed that random 15 stock equal weighted portfolios had 27% chance of beating market and random 250 stock equal weighted portfolios had 2% chance of beating market for 1987 to 1996. How is this possible if stock returns are having high positive skew? Shouldn't it be the opposite? Shouldn't having more stocks increase your chance of beating market if stock returns were highly positive skewed?
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by msw1 »

The idea that owning more stocks increases your chances of beating the market does not make sense. In the limit that you own every stock in the market, you have a 0% chance of beating the market because you own the market.

I have not looked at the data but my guess is that a portfolio's standard deviation goes down as you randomly add stocks to it, so that your odds of under or overperforming the market decrease.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by Anon9001 »

You know I am also wondering if skewness is really a issue why aren't equal weighted indexes able to more easily out-perform cap-weighted indexes considering they are betting equally on lots of companies where-as cap-weighted indexes tend to own majority of money in small amount of companies ie S&P 500 is actually S&P 50 as 52.69% of S&P 500 is invested in 50 companies. For more extreme example Nifty 500 local stock Index is 40% invested in 10 companies so actually Nifty 10. If stock returns are highly skewed you should see cap-weighted indexes under-perform equal weighted index heavily due to them being more concentrated but they don't.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by vineviz »

Anon9001 wrote: Tue May 11, 2021 2:20 am I am referring to Robert Hagstrom 1999 study (Page 54-58) that he done as part of his book Warren Buffet Portfolio. He showed that random 15 stock equal weighted portfolios had 27% chance of beating market and random 250 stock equal weighted portfolios had 2% chance of beating market for 1987 to 1996. How is this possible if stock returns are having high positive skew? Shouldn't it be the opposite? Shouldn't having more stocks increase your chance of beating market if stock returns were highly positive skewed?
Just to clarify the premise, stock returns are generally negatively skewed (i.e. skewed to the left).

Anyway, the methodology Hagstrom used leads to results which are peculiar to his study and can't be generalized. For one thing it's pretty clear he didn't properly control for survivorship bias (he only included stocks with financial data for the whole period, so he had zero chance of randomly selecting any of the worst stocks from the database).

More importantly, the stocks we was using in the the experiment had (from 1987-1996, the period he discusses on p. 58) lower average returns than the S&P 500. The more stocks you include in a portfolio, the narrower the dispersion of terminal values: if the average stock underperforms the "market", only small portfolios have much chance of outpeforming the market.

But if Hagstrom had reported the data from the 18-year period (when the average stock in his dataset beat the S&P 500), the pattern at the top of page 58 would be reversed: a higher percentage of 250-stock portfolios would beat the market than of 15-stock portfolios.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by Anon9001 »

vineviz wrote: Tue May 11, 2021 7:26 am Just to clarify the premise, stock returns are generally negatively skewed (i.e. skewed to the left).
Wait according to S&P the stock returns are positive or skewed to the right for S&P 500. Where you are getting data that is skewed to the left or negative? Lots of people here keep mentioning this skewness issue as a reason to avoid concentrated portfolios/active management but what they don't understand is that if this is true than everyone should own a equal weight index as a cap-weighted index is very concentrated in small amount of companies in the comparison to the former and hence the former should massively out-perform cap-weighted index if this is true.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by grok87 »

vineviz wrote: Tue May 11, 2021 7:26 am
Anon9001 wrote: Tue May 11, 2021 2:20 am I am referring to Robert Hagstrom 1999 study (Page 54-58) that he done as part of his book Warren Buffet Portfolio. He showed that random 15 stock equal weighted portfolios had 27% chance of beating market and random 250 stock equal weighted portfolios had 2% chance of beating market for 1987 to 1996. How is this possible if stock returns are having high positive skew? Shouldn't it be the opposite? Shouldn't having more stocks increase your chance of beating market if stock returns were highly positive skewed?
Just to clarify the premise, stock returns are generally negatively skewed (i.e. skewed to the left).

Anyway, the methodology Hagstrom used leads to results which are peculiar to his study and can't be generalized. For one thing it's pretty clear he didn't properly control for survivorship bias (he only included stocks with financial data for the whole period, so he had zero chance of randomly selecting any of the worst stocks from the database).

survivorship bias comes up in almost every study i've seen claiming outperformance. that and reporting bias are big issues for hedge fund data.
also by doing equal weighting he was biasing toward small caps. and with the survivorship bias that means small caps that survived. not surprising such a group would outperform the market.

now if we all could just find a way to invest in small caps that are guaranteed not to go bankrupt or be delisted.
/s

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grok
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by Anon9001 »

grok87 wrote: Tue May 11, 2021 7:40 am survivorship bias comes up in almost every study i've seen claiming outperformance. that and reporting bias are big issues for hedge fund data.
also by doing equal weighting he was biasing toward small caps. and with the survivorship bias that means small caps that survived. not surprising such a group would outperform the market.

now if we all could just find a way to invest in small caps that are guaranteed not to go bankrupt or be delisted.
/s

cheers,
grok
Except the time period he chosen was one in which small-caps under-performed large-caps. If you read his book than you would already know this.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by qwertyjazz »

Beating or not beating is binary
Most of his portfolios you mention do not beat (only 27 and 2%)
The larger the random portfolio the tighter the average
In his book, how did the 98% do vs the 73% do that did not beat the market?
What was the total returns of the smaller portfolios compared to the larger portfolios in total?
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by vineviz »

There's a difference in the distribution of firm-level returns (to which the S&P blog refers) and aggregate market or portfolio returns.

Firm-level returns tend to be positively skewed but portfolio returns tend to be negatively skewed, with the difference due to coskewness among the firm returns.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by Anon9001 »

vineviz wrote: Tue May 11, 2021 7:26 am More importantly, the stocks we was using in the the experiment had (from 1987-1996, the period he discusses on p. 58) lower average returns than the S&P 500. The more stocks you include in a portfolio, the narrower the dispersion of terminal values: if the average stock underperforms the "market", only small portfolios have much chance of outpeforming the market.

But if Hagstrom had reported the data from the 18-year period (when the average stock in his dataset beat the S&P 500), the pattern at the top of page 58 would be reversed: a higher percentage of 250-stock portfolios would beat the market than of 15-stock portfolios.
So what you are saying concentrated portfolios tend to do well when average stock under-performs market but when average stock out-performs market it tends to not do well? So they are better investment than Diversified portfolios if we assume that most of the time average stock under-preforms market?
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by Anon9001 »

Robert Hagstrom study makes some sense to me as if you reduce the number of stocks in a portfolio it becomes much less like a Index in terms of tracking error so probably of out-performance increases relative to a 250 stock portfolio which should have low tracking error relative to Index. The catch is you have to be extremely patient as 97% of the 808 15 stock portfolios experienced periods of under-performance of three, four, five, six even seven years out of 10 years of out-performance.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by HootingSloth »

Anon9001 wrote: Tue May 11, 2021 2:20 am I am referring to Robert Hagstrom 1999 study (Page 54-58) that he done as part of his book Warren Buffet Portfolio. He showed that random 15 stock equal weighted portfolios had 27% chance of beating market and random 250 stock equal weighted portfolios had 2% chance of beating market for 1987 to 1996. How is this possible if stock returns are having high positive skew? Shouldn't it be the opposite? Shouldn't having more stocks increase your chance of beating market if stock returns were highly positive skewed?
I thought that returns for individual stocks typically have been positively skewed but that aggregate returns for diversified portfolios of stocks typically have been negatively skewed. (And, moreover, that skewness also depends on the length of your horizon, which you have not really specified). I think you need to be more precise about what distribution you are talking about.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by grok87 »

Anon9001 wrote: Tue May 11, 2021 7:45 am
grok87 wrote: Tue May 11, 2021 7:40 am survivorship bias comes up in almost every study i've seen claiming outperformance. that and reporting bias are big issues for hedge fund data.
also by doing equal weighting he was biasing toward small caps. and with the survivorship bias that means small caps that survived. not surprising such a group would outperform the market.

now if we all could just find a way to invest in small caps that are guaranteed not to go bankrupt or be delisted.
/s

cheers,
grok
Except the time period he chosen was one in which small-caps under-performed large-caps. If you read his book than you would already know this.
right but that underperformance includes the small caps that went bust and/or delisted
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by Anon9001 »

HootingSloth wrote: Tue May 11, 2021 9:14 am I thought that returns for individual stocks typically have been positively skewed but that aggregate returns for diversified portfolios of stocks typically have been negatively skewed. (And, moreover, that skewness also depends on the length of your horizon, which you have not really specified). I think you need to be more precise about what distribution you are talking about.
The skewness of individual stock returns is what I am talking about in the title. Not market returns. If we assume most individual stocks are losers and few are winners than equal weighted indexes should out-perform market-cap weighted indexes heavily because they are more diversified but that is not happened.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

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Anon9001 wrote: Tue May 11, 2021 9:21 am If we assume most individual stocks are losers and few are winners than equal weighted indexes should out-perform market-cap weighted indexes heavily because they are more diversified but that is not happened.
Please provide a bit more of a mathematical argument about why this must be true. You likely are making unfounded statistical assumptions. As you note, empirically it is not true.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by quantAndHold »

250 stocks is a large enough basket of stocks that you’re getting market returns, more or less. Your particular basket of 250 stocks might do better or worse than the market, but it won’t be by very much.

A basket of 15 stocks is small enough that you’re introducing tracking error. The probability that one or two or three of the stocks in the portfolio is going to pull your overall return away from what the broader market does is much greater than with the more diversified portfolio. Note that in the study you’re referencing, this only went the right direction 27% of the time. The other 3/4 of the time, it went the wrong way.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by Anon9001 »

HootingSloth wrote: Tue May 11, 2021 9:25 am Please provide a bit more of a mathematical argument about why this must be true. You likely are making unfounded statistical assumptions. As you note, empirically it is not true.
Here you go to Page 15. The equal weight index owns more of the stocks with above average returns except Apple. I think the reason why it has not massively out-performing cap-weight index is probably due to trading costs associated with equal weighting along with the fact that large-caps tend to be exhibit much less skewness in comparison to small-caps for instance.
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by vineviz »

Anon9001 wrote: Tue May 11, 2021 8:01 am So what you are saying concentrated portfolios tend to do well when average stock under-performs market but when average stock out-performs market it tends to not do well? So they are better investment than Diversified portfolios if we assume that most of the time average stock under-preforms market?
I'd argue the the concentrated portfolio is, all else equal, an inferior choice: the more diversified portfolios will have lower standard deviations and therefore higher geometric mean returns (CAGR).
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by MarkRoulo »

Anon9001 wrote: Tue May 11, 2021 2:20 am I am referring to Robert Hagstrom 1999 study (Page 54-58) that he done as part of his book Warren Buffet Portfolio. He showed that random 15 stock equal weighted portfolios had 27% chance of beating market and random 250 stock equal weighted portfolios had 2% chance of beating market for 1987 to 1996. How is this possible if stock returns are having high positive skew? Shouldn't it be the opposite? Shouldn't having more stocks increase your chance of beating market if stock returns were highly positive skewed?
One way to think about this is to consider the most concentrated possible portfolio: A portfolio consisting of only one stock.

If 20% of the stocks in some market "beat the market" then a portfolio of one randomly selected stock has a 20% chance of beating the market.

How do you expect that adding a second stock would make the odds of outperforming the market better than 20%?
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by HootingSloth »

Anon9001 wrote: Tue May 11, 2021 9:40 am
HootingSloth wrote: Tue May 11, 2021 9:25 am Please provide a bit more of a mathematical argument about why this must be true. You likely are making unfounded statistical assumptions. As you note, empirically it is not true.
Here you go to Page 15. The equal weight index owns more of the stocks with above average returns except Apple. I think the reason why it has not massively out-performing cap-weight index is probably due to trading costs associated with equal weighting along with the fact that large-caps tend to be exhibit much less skewness in comparison to small-caps for instance.
That appears to be an empirical argument about a different question (why did an equal-weighted S&P500 index outperform a market-cap-weighted S&P500 index during one particular time period?), not a mathematical argument about your previous assertion (unless I misunderstood it) that positive skewness in individual stocks implies that an equal-weighted index on those stocks will always have a higher expected return than the market-cap-weighted index on those stocks. I believe that the latter statement is not true generically and that it depends on assumptions about the "coskewness" of the returns, which is a bit like covariance but for the higher moment. I think this paper goes into some of the relevant math, but would take some work (or someone better at statistics than I am) to tease this out: https://papers.ssrn.com/sol3/papers.cfm ... id=1622343
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Re: Explain if stock returns are skewed to the right than why are concentrated portfolios more likely to out-perform mar

Post by Anon9001 »

Looking at another paper regarding this skewness issue. Hendrik Bessinder paper show that 50 stock portfolio value-weighted returns 47% of the time out-performed value-weighted market returns for 10 Year Horizon and 41% of the time for 90 Year Horizon. It is interesting that 100 stock portfolio value-weighted only has slightly higher possibility of out-performing market at 47% for 10 Year Horizon and 43% for 90 Year Horizon. This shows most of the benefits of diversification for active strategy in terms of probability of out-performing market if one is choosing stocks randomly can be had at 50 stocks and more are not necessary.
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