# Size Analysis

Last week there was an article by Bloomberg, that stated the following:

“(…) The SPDR S&P MidCap 400 ETF Trust, or MDY, is the largest mid-cap ETF. Despite **grossly outperforming its large-cap and small-cap** fund competitors, it has the least amount of assets among the three (…)”

When I see this type of article I immediately think about two things:

- If this is true, it will cease to be in the short-term future, because the market will find out and over-allocate resources that will make that asset expensive;
- Or, someone is ‘cherry picking’ the dates to support this conclusion.

## Inefficiencies in the Stock Market

The return of one asset, among other things, can be broken down into one of three things:

**Holding a riskier asset**. Thus you are compensated with a higher return. Think historically stocks and bonds. From 1915 to 2014, 100 years, the**real returns**were**8.1%**and**1.1%**respectively. (Source)**Taking advantage of an inefficiency in the market**. Think historically in value investing, where you invest in stocks when they’re cheaper and then enjoy the profit when the value goes up.**Finding the next big thing**. Such as investing in 1980 all you’ve got on Apple. By the way, if you invested in Apple in**1980 $1000 ($0.50 per share)**, today that investment would be worth**+$361’000 ($188 per share)**.

If you keep holding a riskier asset or the next big thing keeps innovating you will keep on being compensated. The problem with number 2 (inefficiency) is once everyone knows it, there will be a flow of allocation of capital leading to a point of **equilibrium**. When you reach this point you have to find another inefficiency or you will not be further compensated.

## Cherry Picking

Cherry picking, also known as the **fallacy of incomplete evidence** is the act of pointing to individual cases or data that seem to confirm a particular position while ignoring a significant portion of related cases or data that may contradict that position.

Today let’s find out if the statement ‘**mid-cap outperformance**‘ holds up.

So in terms of ETFs I used:

**Small Cap**: iShares Core S&P SmallCap 600 Index (IJR) – An ETF that holds/invests in 600 small companies.

**Mid Cap**: iShares Core S&P MidCap 400 Index (IJH) – An ETF that holds/invests in 400 medium companies.

**Large Cap**: SPDR S&P 500 Index (SPY) – An ETF that holds/invests in 500 large companies.

## Theory

So theory says that if you’re holding smaller companies, you’re holding a riskier asset when compared with larger and well-established companies. Thus you should be compensated with a higher (expected) return and a higher (expected) volatility.

This got me suspicious about that article. Maybe ‘real life’ is different from theory. Or maybe if you choose (torture) the dates long enough, you eventually could reach any conclusion that you wish for. Let’s find out.

## Last 3 Years

As we can see in the images below, there’s clearly a small cap premium in the last 36 months. You would have a superior return (**about 8% more**) but with a catch: **more volatility**. Just as theory predicted. More expected risk, more expected return.

The problem is with mid-cap. Here we saw the exact opposite: **less return and more volatility**. Therefore, the theory not always holds up in “real life”.

**IJR vs SPY**

**IJH vs SPY**

## Last 10 Years

If we go back 10 years, the theory holds up perfectly. Small-cap did deliver a **premium return of 50%**, that’s 5% per year more when compared with large-cap. And with more volatility, just as expected.

Mid-cap delivered **more than** large-cap, but **less than** small-cap. Also, volatility was precisely in the middle of the volatility experienced in large and small-cap. Exactly as the theory should have guessed.

**IJR vs SPY**

**IJH vs SPY**

## Since the end of 2002

Now I tried to simulate the maximum possible total return and volatility. I went back more than 15 years. Again the theory was spot on. The small cap premium was much (really much!) higher, with a total return of **537%**. The SPY had a 326% total return. Investors who hold the **riskier asset** – an ETF with small companies – did get to profit a lot more. With **more volatility** just as expected.

Like the example before (10 years), mid-cap did more than large-cap, but less than small-cap. Again the volatility was exactly in the middle of the large and small-cap.

**IJR vs SPY**

**IJH vs SPY**

# Conclusion

As you probably know, past performance doesn’t guarantee future results. Also, this is not financial advice or any kind of advice. But what we can conclude from this data is that there is clearly a ‘**size premium**‘ and comes together with additional volatility.

Going forward we don’t know what will happen, but we do know that past data proves the theory right: if you expose yourself to smaller companies through an ETF you could **expect more return with more volatility**. If you want less volatility, hence less expected return you could invest in mid or large-cap companies.

**History** tells us that **size does matter**.

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