In our last set of videos, we discussed how robo advisors select an asset allocation for their investors. They use models to estimate expected returns, covariances, and standard deviations. They ask questions online to gauge risk tolerance. They then find the highest expected return portfolio, given the risk that an investor can tolerate. What do these advisors invest in? They invest in what are called exchange-traded funds, or ETFs. An ETF is kind of a fintech in and of itself, and that's why we put together this video, to have a little bit of a detour, discuss how ETFs actually work. They allow you to hold a broad portfolio of a particular asset class. And so if you want to hold equities, they allow you to hold a portfolio of a lot of different equities, as opposed to a single stock. They have low fees because there's very little management associated with them. They simply try to mimic some other portfolio of assets. To think about this, let's think about specific stock indices that are supposed to be broad representations of the overall stock market. And in particular, we'll think about the Standard and Poor's 500 index. The Standard and Poor's 500 index, or S&P 500, is a portfolio of 500 stocks that's meant to represent the largest stocks in the US economy. When we say large, we mean large by virtue of their market capitalization, which is each stock's price multiplied by the number of stock shares that it has outstanding. Each stock in this index is held with what is called a value weight. So for example, the weight of Apple in the index, and Apple is one of the stocks in the S&P 500, is Apple's market capitalization divided by the sum of the market capitalization of all 500 stocks in the index. And as I mentioned before, market capitalization is simply the price per share multiplied by the shares outstanding. To think of how this works, let's consider a much simpler index, an index that's composed just of Microsoft and Apple. At the end of 2018, Microsoft had a bit over 7.6 billion shares outstanding. It had a closing price at the end of 2018 of $101.57. And so if we multiply those two things together, the market capitalization of Microsoft in total was about $779 billion. Apple, in contrast, had about 4.7 billion shares outstanding, had a closing price of $157.74. And so therefore had a market cap, multiplying those two things together, of about $748 billion. If we add up the market cap of Microsoft and Apple, we come up with a number that's $1.528 trillion, which is the total market capitalization of Microsoft and Apple together. If we were to form an index where we held Microsoft and Apple in value weights, what we would do is take the market capitalization of Microsoft, 779 billion, and divide it by the total market capitalization of 1.528 trillion. To come up with the weight that you see on the far right, which is about 51%. Similarly, we would figure out the weight for Apple by taking the market capitalization of Apple of about 748 billion, dividing by the total market cap of 1.528 trillion, and coming up with a weight of about 49%. And as you can see, by construction, these two weights add up to be 100%. Now, if we wanted to hold this particular portfolio, we could closely do it by holding a portfolio of 34 shares of Microsoft and 21 shares of Apple, at a total cost of $6,766. And you could verify for yourself that by investing in 34 shares of Microsoft at $101.57, and 21 shares of Apple at a price of $157.74, we would wind up with a portfolio that costs a total of $6,766. And has about 51% of its value invested in Microsoft, and 49% in Apple. Unfortunately, it's not always that easy to hold an actual index. The example that we constructed before was relatively simple because we were only dealing with two stocks. But as the name implies, the Standard and Poor's 500 actually holds about 500 stocks. As two extreme examples, let's think about Molson-Coors, which has a ticker name of TAP. Its weight as of 12/31 of 2018 in the index was about 0.0000162, so far less than 1% of the index. In contrast, Microsoft, which was the largest stock in the index, had a weight of about 3.7%, 0.037. What does that mean in practice? Well, it means that if we wanted to hold the S&P 500 index, for every single share of Molson-Coors that we bought, we would have to buy 1,433 shares of Microsoft. At a $101.57 per share, that Microsoft holding alone would cost $146,555. So we can see at least intuitively that, if we're trying to hold 500 stocks with different weights, we're going to need to come up with a lot of money to be able to replicate the portfolio fairly precisely. The problem with this situation is that it makes it virtually prohibitive for small investors to hold indices. The cost of holding a diversified index like the S&P 500 is probably not obtainable to most small investors. If we were to invest in just one share of each stock in the S&P 500, it would cost us over $50,000 as of the end of 2018. And as we Illustrated in the previous example, holding one share of each stock is not going to provide us value weights. For each one share of a small stock like Molson-Coors, we need to hold 1,433 shares of a stock like Microsoft. So as one can imagine, the costs of replicating this index quickly add up. On the other hand, finance theory and asset allocation problems, as we discussed before, suggest to us that we should hold diversified portfolios. And so the question at hand is, how can a small investor access a diversified portfolio of one asset class, let alone many? So again, in our asset allocation problems, we've been thinking about situations where investors invest in mixes of stocks and bonds. How is a small investor supposed to access a diversified portfolio of just stocks, let alone a diversified portfolio of stocks and bonds? The answer to this question at least in part comes from exchange-traded funds or ETFs.