Sampling the S&P 500 to Minimize Spreads

From prior work, we know that stocks’ bid-ask spreads tend to widen as their value traded falls. The same is basically true as market cap falls, too, as larger stocks tend to trade more (in dollars, not shares). 

For someone looking to invest an index cashflow or hedge an index future, that creates an interesting trade-off: 

• Add more stocks to your portfolio, and you reduce the risk of a missing stock reducing your profits.
• Reduce stocks in your portfolio, and you might save on spread and per-ticket settlement costs.

Today, we’re looking at how that trade-off looks as you add more stocks to the portfolio.

Spreads increase as you add more stocks to the S&P basket

In the chart below, we start on the left with the largest stock in the S&P 500. We then add each stock by (declining) index weight until we have a portfolio of all 500 stocks at the right of the chart. The curves show how spread and index coverage increase as the portfolio grows and how the trade-offs between the two work:

1. The circle heights show portfolio spread costs as each additional stock is added to the portfolio (left axis). It generally increases with added diversification.
2. The circle size shows how much value that newly added stock trades (on its own). Traded value tends to shrink as stocks get smaller (circles on the right are generally smaller).
3. The circle color shows the spread of the newly added stock (on its own). Spreads for smaller stocks are often, but not always, wider – as the color variation across the arc shows.
4. The grey area shows the proportion of the whole S&P 500 index weights that are covered as each additional stock is added to the portfolio at its proportional index weights (right axis).

Chart 1: S&P 500 index spreads and weights as you build up to a 500 stock fully replicating index portfolio 

Spreads and completeness increase at a similar rate

Interestingly, the curve of the circles (for cumulative spreads) and the grey area (cumulative index coverage) track very closely.

At the bottom left of the chart, MSFT and AAPL both have spreads around 1 basis point (bps). But as we move deeper into the “Magnificent 7” stocks, we start to see spreads widen (as the color darkens). TSLA, which can be volatile and harder to make markets in, stands out (and is red).

By the time we have a 10-largest-stocks portfolio (first vertical line):

• The portfolio spread is close to 2.5 bps.
• The portfolio already represents around 35% of the S&P 500’s weights despite being just 2% of all companies in the index.

Adding the next 90 largest stocks gets us to the 100-largest-stocks portfolio (second vertical line), then:

• The average spread cost has increased to around 3.7bps
• Index coverage increased to over 70% of the market cap despite only holding just 20% of all companies in the index.

In contrast, trading the whole S&P 500 incurs spread costs of just over 4.5 bps. Interestingly, many of the smaller stocks have higher spreads (red circles), but because they also have smaller index weights, adding them to the portfolio at index weight doesn’t increase the portfolio’s spread costs or coverage very much at all. That’s why the curve flattens as the portfolio moves from the 300th to 500th stock.

We also see that the value traded (circle size) typically falls – as we move right – and the market cap falls. In fact, the circles for most of the last 200 stocks in the S&P 500 have become dots. 

Importantly, though, a lower value of trading for small stocks is not actually a liquidity problem for index traders. That’s because index funds buy in proportion to the size of each company in the index, so they invest a lot less dollars in the smaller companies, too. That’s also why we’ve previously looked at turnover as a better measure of relative liquidity.

Traders can trade off completeness for costs

This data shows a trade-off between the costs of trading and the index coverage you obtain as you broaden your portfolio.

For investors where fixed (per stock) trading costs are important, a relatively small basket can cover a large proportion of the index weights while reducing the spread (and maybe settlement) costs being paid. 

Although that leaves you unexposed to stocks you didn’t buy, sometimes that’s a trade-off that might be worth making.