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.

It’s true. And you will probably never hear this from any other wealth-building “expert.” Unless you have more than $25,000 to invest, you probably shouldn’t be investing in individual stocks—and you definitely shouldn’t be trading options and futures.

The reason is simple: You want to get wealthy in 7 to 15 years— preferably in less than 7. There is no way that $25,000 can turn into something that even sounds like wealth in that amount of time— hough there are a lot of professional investment gurus who will tell you otherwise. In fact, there is a huge, multi-billion-dollar business that is determined to snow you on this issue.

So now you know how I feel about stocks, small business, and real estate. Bonds? I love bonds. Especially if you invest in them the way I do: Buy them. Be happy with the guaranteed return. And forget about them.

With this perspective made clear, you will see some sense in the following four model portfolios, each based on a stage of wealth building.

• Stage One: Your investable net worth is less than $25,000.
• Stage Two: Your investable net worth is between $25,000 and $100,000.
• Stage Three: Your investable net worth is more than $100,000 but less than you need to be financially independent.
• Stage Four: You are financially independent.

Muni funds can also play with the value of your shares to your disadvantage. Muni issues are rarely traded. Muni managers can use any reasonable value for fund assets. Though credit quality may have deteriorated, managers often refrain from writing down asset values for fear of losing shareholders. However, at some point asset values must be marked to market to avoid outright fraud and jail time for the fund managers. If you buy fund shares at a high valuation of assets and later have to redeem when assets are written down to realistic levels, you will justifiably feel betrayed.

Fund managers can also turn tax-free munis into taxable bonds. Capital gains from selling appreciated muni bonds are taxable. Individual savers typically hold munis until maturity so there are no capital gains. Muni fund managers trade bonds. This creates capital gains, often short-term capital gains, which are taxed at the highest rate. Muni funds are outside the comfort zone of most savers.

Occasionally, bond investors experience complete powerlessness. When interest rates and inflation rise dramatically, the value of bonds declines dramatically. If prospects are for continued high interest rates and inflation, bond interest will never compensate for lost purchasing power. In the 1960s, government bonds paid 5 percent or less in interest. During the 1970s, inflation averaged better than 8 percent. Bond investors who bought in the 1960s sat by powerless as the purchasing power of their principal and interest dwindled.

On the other hand, treasuries are the best asset class during extended periods of deflation. In the 1930s, treasury savers had to guard against grandiosity rather than inferiority. Treasuries were the best asset class.

Selling government bonds before maturity brings up feelings of regret if interest rates have risen and the bonds must be sold for less than face value. Commissions, as well as spreads, must also be paid.

Letting bonds mature eliminates both commissions and spreads. Still, when bonds mature, the saver is faced with the dilemma of what to do with the principal. For some, the answer is simple. Others experience anxiety.

Savers who fret over what to buy may be more comfortable in bond funds where the money manager makes all the buy decisions.