Reference

The number of debt-adjusted shares is defined as follows:

debt adjusted share count represents average debt divided by average share price plus average shares outstanding

In other words, this treats both sources of company capital equally, as if debt-holders held “debt shares” priced the same as equity shares.

[The quote is from a Pioneer Natural Resources presentation.]

A diffusion index measures the prevalence of change in a particular direction. Examples include

- The share of companies that are increasing their staff levels
- The share of ports that are recording an increase in traffic
- The share of stocks that are above their 50-day moving average
- The share of banks that are tightening their lending standars

The way “share” is defined varies somewhat. The two most common definitions are

- Net percentage: The percentage decreasing is subtracted from the percentage increasing (with the percentage unchanged being ignored)
- Weighted average index: Each possible outcome (e.g. “strongly increasing”, “increasing”, “unchanged”, “decreasing”, “strongly decreasing”) is assigned a numerical value, and the values are added to give an index running from 0 to 100

Note that diffusion indices are intended to show direction; quantitative implications are generally not too reliable.

From the Canadian Economic Observer:

Measuring how widespread, or diffuse, an economic phenomenon has become is a basic analytic tool. It is important to know whether growth or recession is widespread or confined to certain sectors. …

A diffusion index measures the share of industries experiencing an increase in activity … over a given time span. Developed by the National Bureau of Economic Research (NBER), diffusion indices look only at the direction, not the rate of change. …

They are also used to isolate drops in output due to irregular or industry-specific factors (such as strikes or bad weather) from the incremental factors normally associated with cyclical fluctuations … These extraordinary events can cause output in an industry to abruptly drop towards zero, a change in amplitude that the diffusion index helps analysts to ignore. …

Like all summary measures of the economy, diffusion indices also hide important information. One cannot tell from their aggregate values the industries that are driving the overall change, their relative importance, their recent trend, or how fast they are changing.

From the OECD Glossary of Statistical Terms:

Definition:

A term proposed by Burns (1950) and Moore (1950) to denote the proportion of a set of time series in a given collection of series which are increasing at a given point of time.

Source Publication:

A Dictionary of Statistical Terms, 5th edition, prepared for the International Statistical Institute by F.H.C. Marriott. Published for the International Statistical Institute by Longman Scientific and Technical.

From a Bank of Tokyo-Mitsubishi report, a clear example of the weighted sum calculation:

Each survey participant response is assigned a weight from 1 to 0:

1.00 = Substantially Higher 0.75 = Higher 0.50 = Same 0.25 = Lower 0.00 = Substantially LowerThe diffusion index is simply a weighted average:

Diffusion Index = 100 x [1.00 x (% reporting substantially higher) + 0.75 x (% reporting higher) + 0.50 x (% reporting same) + 0.25 x (% reporting lower) + 0.00 x (% reporting substantially lower)]

By definition, the diffusion index, since it is multiplied by 100, is bounded by 0 and 100%. At 0%, it would imply every participant answered “substantially lower”; at 100%, it would imply every participant answered “substantially higher” …

For example, if the reporting distribution was as follows:

Substantially Higher = 5% Higher = 15% Same = 65% Lower = 10% Substantially Lower = 5% Total = 100%The diffusion index would be calculated as follows:

Diffusion Index = 100 x [(1.00 x 5%) + (0.75 x 15%) + (0.50 x 65%) + (0.25 x 10%) + (0.00 x 5%)] = 51.25%

This is a subset of GDP measuring what households and businesses are spending. It excludes changes in inventories, net exports, and the entire government sector.

For more background and a link to a formal definition from an economist, see 09-private_demand_suggests_sustainable_recovery_proceeding_slowly.

The duration of a bond is the number of years a bond holder has to wait, on average, for each of the dollars he will eventually receive. Dollars in the average include both interest and principal, so duration is shorter for high-coupon bonds.

Technically, let

- p
_{i}be the ith payment (principal, interest, or both), expressed as a present value - fp
_{i}the same, expressed as a fraction of the total - t
_{i}the time from the present to the receipt of p_{i}, in years

Then the sum over i of fp_{i}*t_{i} is the duration.

A rule of thumb is that a 1% change in interest rates changes the price of the bond by (duration)%. (Intuitively, this is a consequence of the fact that the nth power of 1.01 is about 1 + n*.01.)

From InvestorWords:

“Duration is a weighted measure of the length of time the bond will pay out. Unlike maturity, duration takes into account interest payments that occur throughout the course of holding the bond. Basically, duration is a weighted average of the maturity of all the income streams from a bond or portfolio of bonds. … Notice that the duration on any bond that pays coupons will be less than the maturity because there is some amount of the payments that are going to come before the maturity date.”

From Wikipedia:

“In finance, the duration of a financial asset, specifically a bond, is a measure of the sensitivity of the asset's price to interest rate movements. It broadly corresponds to the length of time before the asset is due to be repaid. …

The units of duration are years, and duration is generally between 0 years and the time to maturity of the bond. It is equal to the time to maturity if and only if the bond is a zero-coupon bond.”

From Investopedia:

“Advanced Bond Concepts: Duration. The term duration has a special meaning in the context of bonds. It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations. ”