Small Cap Premium
Small Cap Premium
In literature I have reviewed on the historical small cap premium, the returns are presented using simple averages over time rather than compound returns. Given the higher volatility of returns for small cap stocks, particularly in early periods, the use of an average return rather than a compound return is material. Using compound returns across all market cap deciles (as shown in the below paper) greatly diminishes the small cap premium. Is there any logic behind using an average rather than compound return in the analysis at the below web location?
http://aswathdamodaran.blogspot.com/201 ... nand.html
http://aswathdamodaran.blogspot.com/201 ... nand.html
Re: Small Cap Premium
Interesting article, worth a read.
I like to point to the performance of the S&P 600 though. It vastly outperformed the broad market.
I like to point to the performance of the S&P 600 though. It vastly outperformed the broad market.
Re: Small Cap Premium
The simple answer is that a factor risk premium is defined that way. Factors models are applied versions of CAPM/APT which are singleperiod models.
The full answer requires an understanding of the difference between single and multiperiod returns. Both have applications, but for most practical finance/valuation tasks, a singleperiod/arithmetic return is actually more useful. This paper explores the topic a little:
http://faculty.london.edu/icooper/asset ... metric.pdf
If you are analyzing factor premiums to decide how to allocate a portfolio you may be more interested in backtests, which produce compounded/annualized returns.
Backtests are inconvenient in academia because they are nearly impossible to reproduce and have too many assumptions that can be tweaked. Trading frequency, rebalancing methodology, transaction costs, available volume, etc... will all impact the results.
The full answer requires an understanding of the difference between single and multiperiod returns. Both have applications, but for most practical finance/valuation tasks, a singleperiod/arithmetic return is actually more useful. This paper explores the topic a little:
http://faculty.london.edu/icooper/asset ... metric.pdf
If you are analyzing factor premiums to decide how to allocate a portfolio you may be more interested in backtests, which produce compounded/annualized returns.
Backtests are inconvenient in academia because they are nearly impossible to reproduce and have too many assumptions that can be tweaked. Trading frequency, rebalancing methodology, transaction costs, available volume, etc... will all impact the results.
Re: Small Cap Premium
kosomoto wrote:Interesting article, worth a read.
I like to point to the performance of the S&P 600 though. It vastly outperformed the broad market.
But even the S&P SmallCap 600 was outperformed by the S&P MidCap 400 over the course of it's existence which pokes some holes in the idea that there's a "premium" for smaller.
Morningstar Chart
It is a good article though, and I think he hits the nail on the head with the last paragraph:
"...looking for under valued stocks may be greater with small companies, partly because they are more likely to be overlooked, but it will take more work on your part and it won't be easy! ..."
It falls more in line with other schools of thought that don't follow the modern EMH "Risk Premium" ideas:
Benjamin Graham in The Intelligent Investor wrote: ... there has developed the general notion that the rate of return which the investor should aim for is more or less proportionate to the degree of risk he is ready to run. Our view is different. The rate of return sought should be dependent, rather, on the amount of intelligent effort the investor is willing and able to bring to bear on his task. ...
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks."  Benjamin Graham
Re: Small Cap Premium
Welcome Eric, heck of a first post!
The Q/A following the article was also interesting, and controversial.
Paul
The Q/A following the article was also interesting, and controversial.
Paul
When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.

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Re: Small Cap Premium
JoMoney
Keep in mind that the midcaps avoid buying those blackholes the lottery tickets
But even with that black hole the data historically is almost monotonic with returns rising as you go to smaller deciles
larry
Keep in mind that the midcaps avoid buying those blackholes the lottery tickets
But even with that black hole the data historically is almost monotonic with returns rising as you go to smaller deciles
larry

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Re: Small Cap Premium
larryswedroe wrote:JoMoney
Keep in mind that the midcaps avoid buying those blackholes the lottery tickets
But even with that black hole the data historically is almost monotonic with returns rising as you go to smaller deciles
larry
Would the modern lottery tickets be those penny stocks not within TSM (pink sheets) or even most small growth index funds that do any sort of liquidity screening? So the Vanguard Small Cap Growth and S&P 600 Growth aren't likely to show these "lottery" characteristics, whereas a "midcap IPO" might?
Re: Small Cap Premium
With regard to the small growth "black hole" "junk" stocks, I find the results of this paper very interesting
http://papers.ssrn.com/sol3/papers.cfm? ... id=2394711
Showing that constituency requirements, particularly with regard to liquidity in real world mutual funds and investable index funds screen out a lot of this "junk" already. Also find it interesting that when doing a factor regression on Vanguard Total Stock Market Index , you do see a very small loading on "value / hml" with a 0.00 loading on size and a market beta of 1 (as you'd expect for the "total market").
http://papers.ssrn.com/sol3/papers.cfm? ... id=2394711
Showing that constituency requirements, particularly with regard to liquidity in real world mutual funds and investable index funds screen out a lot of this "junk" already. Also find it interesting that when doing a factor regression on Vanguard Total Stock Market Index , you do see a very small loading on "value / hml" with a 0.00 loading on size and a market beta of 1 (as you'd expect for the "total market").
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks."  Benjamin Graham

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Re: Small Cap Premium
JoMoney wrote:But even the S&P SmallCap 600 was outperformed by the S&P MidCap 400 over the course of it's existence which pokes some holes in the idea that there's a "premium" for smaller.
In the interest of fairness let's add the 500 TR & VG TSM to that chart and observe the results:
S&P 400: 121055.68
S&P 600: 100459.29
VTSMX: 69112.47
S&P 500: 69105.53

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Re: Small Cap Premium
Eric 3232,
You are referring to volatility drag, which I think is a huge issue. But I think volatility drag is relevant at the portfolio level. At the individual asset class level I think the average annual returns ( and SD) are meaningful. It gives you a sense of the expected premium over market. It's how the individual components mix in a portfolio that matters. For example, a volatile component with low correlations to other portfolio components can actually dampen portfolio volatility and bring the compounded return closer to the weighted average annual return of the portfolio components. Sometimes I read references to Sharpe ratios for individual funds. I don't think those are very meaningful either. What's meaningful is what the addition of a component does to the Sharpe ratio of the portfolio.
Dave
You are referring to volatility drag, which I think is a huge issue. But I think volatility drag is relevant at the portfolio level. At the individual asset class level I think the average annual returns ( and SD) are meaningful. It gives you a sense of the expected premium over market. It's how the individual components mix in a portfolio that matters. For example, a volatile component with low correlations to other portfolio components can actually dampen portfolio volatility and bring the compounded return closer to the weighted average annual return of the portfolio components. Sometimes I read references to Sharpe ratios for individual funds. I don't think those are very meaningful either. What's meaningful is what the addition of a component does to the Sharpe ratio of the portfolio.
Dave

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Re: Small Cap Premium
Theoretical
I don't know what each small cap fund does in terms of screening. But any index fund would be buying all the stocks in the index, otherwise not an index fund.
Larry
I don't know what each small cap fund does in terms of screening. But any index fund would be buying all the stocks in the index, otherwise not an index fund.
Larry
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Re: Small Cap Premium
Yes and no. This is a very tricky issue. I don't understand it completely. Let's take the bits I think I understand. I'm going to state them as puzzle pieces. I'm not going to try to put the puzzle together, and don't try to read any conclusion into this. Frankly, beware of attempts to put the puzzle togetherdon't ever be sure the person you're listening to is doing it correctly. Don't ever forget that anyone who works for an investment firm is an interested party. If you're trying to sell something, it's very easy to seize on a few of the puzzle pieces and force them together to support your sales proposition.Eric3232 wrote:...Is there any logic behind using an average rather than compound return in the analysis at the below web location?...
1) Over any given period of time, let's say a year, the return of a portfolio is the weighted arithmetic mean of the returns of its components. For example, if our portfolio is 50% X and 50% Y and X has a return of 6% and Y has a return of 8% then the return of the portfolio is 7%. So you shouldn't automatically tune out arithmetic averages. They have a legitimate use.
2) Over a sequence of years, the returns of a portfolio compound or multiply or parlay or whathaveyou, so the best "average" annual return is the geometric mean or compound return.
3) If a bank account earned exactly 7% every year , then, over a tenyear period, a $10,000 investment will grow to 10,000 * (1.07)^10 = $19,671.
4) If the portfolio fluctuates, a lot or a little, but it has a geometric mean return of 7% per year, then, over a tenyear period, it, too will grow a $10,000 to exactly $19,671, no matter whether the fluctuations are big or small and no matter what order they occur in.
5) If the portfolio fluctuates, a lot or a little, and has an arithmetic mean return of 7% per year, then over a tenyear period it will grow to less than $19,671, possibly a lot less, depending on how big the fluctuations are. This is "volatility drag."
6) I've frequently read that an approximate formula for volatility drag is that geometric mean approximately equals arithmetic mean minus half the square of the standard deviation. I don't know under what situations this is a good approximation.
7) Read this carefully: the CAGR of a portfolio over a ten years a) the geometric mean of ten numbers, each of which b) the weighted arithmetic mean of the return of the constituents, in a single year.
8) A lot of analyses in terms of modern portfolio theory are implicitly analyzing the case where there aren't any patterns in time. The standard "Markowitz bullet" charts are in effect looking at a situation where every year in the future resembles a randomly chosen year out of the past data set. That is, they don't allow for momentum, mean reversion or what have you. To take an obvious example, the premise of "Stocks for the Long Run" by Jeremy Siegel is that stock market returns show a definite tendency to mean reversiondecades of lowerthanaverage returns are likely to be partly compensated by decades of higherthanaverage returnstherefore the standard deviation of compounded returns over, say, thirty years, is lower than you'd expect if they were independence. "The dice have no memory," but the stock market does; it showshe saysactive compensation, not just the law of averages. Fine, but if so, you can't extrapolate average from individual years into expected average compound returns for decades, no matter what kind of averages you are using.
9) I strongly recommend a fantastic book, Fortune's Formula, by William Poundstone. It is not, as I'd assumed, touting a particular point of view. It is instead a really good, thoughtful, critical examination of a number of points of view. I'm afraid it's one of these books that I think I understand while I'm reading it, and the understanding lasts about a month, then it fades. It presents a view of an alternate universe of thinking about compounding returns over time in a situation involving risk. It centers around the "Kelly criterion," which in term actually comes out of thinking about gambling and is, I'm told, actually used by gamblers.
In what might be termed the traditional view, you can use leverage to increase your risk and your return at the same time, and, if you can borrow at no cost, there is no logical limit to how much leverage you should usethe extra return always justifies the extra risk if you wish to take that risk. In the "Kelly criterion view," there are reasons, not related to any "utility function," why you ought to optimize, not the average return, but the log of the average return. This leads to the conclusion thatfor examplethere's a limit to how much leverage you should use because the more leverage you use and the longer your sequence of compounded returns continues, the higher the chances of devastating losses... or... something like that.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.