The measures of the spread discussed above require observations on transaction prices and bid–ask quotes. Very often, however, quoted prices are either unavailable, unreliable or difficult to handle. As noted, quotes may not be binding or the spread may vary in the course of the trading day, so estimation of the spread based on transaction prices is usually preferred. Roll (1984) offers a very parsimonious model for estimating spread, using the time series of the prices at which trades were made. This model shows that when transaction costs consist of order processing costs only, i.e. in the absence of both adverse selection and inventory costs, the quoted spread coincides with the realized spread.

Roll demonstrates that it is possible to estimate spread by computing the autocovariance of transaction prices. Below we show how in the absence of transaction costs this auto-covariance is equal to zero, whereas with transaction costs, it is negative and a function of the spread. This allows us to estimate the spread by using transaction prices alone. This method proves useful when quoted bid and ask prices are not available.

You will notice that in this second stage there are no stocks, options, futures, metals, rare coins, or derivatives in the portfolio. And there is a good reason for that. When you have less than $100,000 to invest and less than a long time to get rich, you should focus on only two things:

1. Continuing to increase your income by continuing to perfect a financially valued skill such as selling, marketing, product development, or profit management

2. Investing the surplus in high-return equity ventures If you focus on this for a few years, chances are that you’ll end up with a surfeit of cash—that is, more cash than you need for your side business and real estate ventures. This extra cash should be kept safe. Extra safe. Remember, this is the beginning of your retirement nest egg. So place this surplus cash in bonds, and reinvest the interest in bonds, too. Make it a primary objective to have this safety reserve grow substantially every year. Once your bond savings become significant, you’ll start to appreciate what a valuable, comforting investment bonds can be.