present value

Present value is the worth today of a promised payment that will be made in the future.

There are, of course, lots of risks in any contract like this–the borrower might go in to bankruptcy, or simply refuse to pay… Let’s take the case of a Treasury security, where, in theory anyway, none of the typical commercial risks apply. To make this simpler, we’ll assume that the security we hold is a Treasury principal strip. This is a zero-coupon instrument, that is, one it makes no interest payments. It consists of a lump sum payment of the face value of $1000 at maturity, which we’ll say is five years hence.

If we were buying today, what should we pay, given that interest rates–what we’ll use to discount the future $1000 back to today’s value, are, let’s say, 2%? The answer is

1000/ (1.02)(1.02)(1.02)(1.02)(1.02), or $905.73.

Suppose rates rise to 4% immediately after we buy. What is our security worth now? The new present value is 1000/(1.04)(1.04)(1.04)(1.04)(1.04), or $821.93. If rates rise to 6%, the value would be $747.26.

Were rates to fall to 1% instead, the value would jump to slightly more than $951.

Three points:

–this is the simplest and most volatile case. There are no periodic interest payments, which tend to act as stabilizers of the security’s value

–the US government is assumed to be a totally creditworthy borrower, something that hasn’t always been true (think: the Carter administration issue of D-mark and Swiss franc bonds), and

–we’re not taking into account possible effects the business cycle might have on valuation, a factor that’s in theory not relevant for Treasuries but something that could have a significant impact on some corporate bonds (think: junk).

duration

“Duration” is the name for a family of related concepts, the first of which was introduced by Frederick Macaulay. They all use a weighted average of the present values of the cash flows from a bond–interest payments and return of principal–as a way of assessing its sensitivity to changes in interest rates. The basic result is a more muted version of the Treasury strip behavior illustrated above: the farther in the future the preponderance of the cash flows (i.e., the closer it is to a zero-coupon bond), the more the bond moves down as interest rates rise and rises as rates fall.

stocks vs. bonds

The main thrust of the academic financial theory of stocks, as I see it anyway, is to describe them as a peculiar type of bond. This idea has the advantages of simplicity and of piggybacking on the well-developed, present value-based structure of bond analysis and applying it to equities. It also has the disadvantage of not working particularly well, and of functioning increasingly less well as time has passed.

It did work well in the 1950s, when it was developed. The dominant publicly-listed firms back then were ATT, the big integrated oils, miners, steels, automakers, chemicals, stores like Sears and Woolworth… These are the kinds of entities you’d expect to see trading in an emerging market today. Companies had relatively easily forecastable cash flows, dividend yields were high, dividends were perhaps the major investor focus. Also, my sense, which may be incorrect since this is before my time, is that stock market participants back then were mostly very wealthy entities looking for quasi-bonds. Said a different way, lots of value-type stocks were on offer and/because buyers were relatively risk averse and had no stomach for stocks that didn’t look/act like bonds.

Today, we’re in a far different world. Many investors are mainly interested in capital gains, not dividends, for one thing. Many companies (as a result of this change in preference? …or is it vice versa?) are prized for their intellectual property, their brand names, their distribution networks, none of which appear on the balance sheet, but all of which give them a chance at superior future earnings growth. These firms, and their shareholders tend to think of dividend payments as a sign of weakness–that high dividends imply management has no better ideas about how to invest their money–rather than strength.

The academic world really has nothing meaningful to say about large parts of today’s stock market, in my view. There are consequences of the party line that stocks can be reduced to a funny kind of bond, however. If nothing else, this is because no one has come up with a comprehensive, simple-to-teach alternative to the present value discount models.

more tomorrow