Rate duration

The ha2ard assessment is to iaclude identification of a worst-case scenario and other more likely scenarios for release of a regulated substance, and analy2e the off-site consequences of such releases. The release and consequence assessment is to iaclude the rate, duration, and quantity of the release, the distances for exposure or damage (usiag atmospheric, called "F" stabiUty and a 1.5-m/s wiad, and most-often-occurriag conditions), populations that could be exposed, and environmental damage that could be expected. 

Decomposition/stabilization rate, duration of composting (immature or mature compost)... 

Modeling of gas transport is also useful for correlating dose-response data obtained under different conditions. Brain suggested that the total dose of an inhaled gas is relate to ventilation rate, duration of exposure, and gas concentration before inhalation. Folinsbee et al. exposed human subjects to ozone at 0.37, 0.5, or 0.75 ppm for 2 h while they were at rest or exerdsing intermittently. The primary response of the subjects was an alteration in the exercise ventilatory pattern. They... 

An exposure assessment is the quantitative or qualitative evaluation of the amount of a substance that humans come into contact with and includes consideration of the intensity, frequency and duration of contact, the route of exposure (e.g., dermal, oral, or respiratory), rates (chemical intake or uptake rates), the resulting amount that actually crosses the boundary (a dose), and the amount absorbed (internal dose). Depending on the purpose of an exposure assessment, the numerical output may be an estimate of the intensity, rate, duration, and frequency of contact exposure or dose (the resulting amount that actually crosses the boundary). For risk assessments of chemical substances based on dose-response relationships, the output usually includes an estimate of dose (WHO/IPCS 1999). 

One of the most profound specifics of polymers is the strong dependence of their mechanical response on the external conditions, especially temperature, strain, strain rate, duration of the loading, etc. A single polymer can show all the features of a glassy brittle soHd or an elastic rubber and, eventually, viscous liq-... 

To quantify the consequences of hazardous events, their flow rate, duration and phase (gas, liquid, solid) must be determined accurately. Flow rate, duration and phase are functions of storage and release conditions, the properties of the chemical or mixture of chemicals, and the nature of the containment failure. 

These data suggest that the optimal regimen for reducing body fat is a combination of diet restriction and aerobic exercise. The components of an exercise program are defined by the parameters intensity, duration, and frequency. Intensity refers to the vigor of the activity and can be defined by heart rate. Duration describes the length of the workout, and frequency indicates the... 

Site Length of Therapy (mo) Rating (Duration) Corticosteroids Rating (Corticosteroids)... 

The primary route of exposure to tetrachloroethylene is inhalation. In humans, tetrachloroethylene is readily absorbed into the blood through the lungs. Pulmonary uptake of tetrachloroethylene is proportional to ventilation rate, duration of exposure, and at lower atmospheric concentrations of tetrachloroethylene, to the concentration of tetrachloroethylene in the inspired air (Hake and Stewart 1977 Stewart et al. 1981). Absorption was measured in male volunteers exposed to concentrations between 72 and 144 ppm for 4 hours (Monster et al. 1979). The data indicated that uptake was influenced more by lean body mass than by ventilation rate or the amount of adipose tissue. In addition, uptake deeieased as a function of exposure time, so that after 4 hours, it was 75% of its initial value. This latter finding may be attributable to a large percentage uptake of tetrachloroethylene during the first few minutes of exposure, or the decreased uptake may result from a decrease in retention of tetrachloroethylene with exposure time. 

Physical Stress Magnitude Repetition rate Duration... 

Code Type of Rating Duration Value Definition... 

After designing the right biodegradable polymers, miCToencapsulation has permitted controUed-release delivery systems. These revolutionary systems allow controlling the rate, duration, and distribution of the active drug. With these systems, miaoparticles sensitive to the biological environment are... 

A portfolio duration of 6.413 means that for a 100 basis point change in the yield for each of the three bonds, the portfolio s market value will change by approximately 6.413%. It is paramount to keep in mind that the yield for each of the three bonds must change by 100 basis points for this duration measure to be useful. This is a critical assumption and its importance cannot be overemphasized. Portfolio managers will find it necessary to be able to measure a portfolio s exposure to a reshaping of the yield curve. We will examine methods for doing later in the chapter when we discuss key rate duration. 

The most popular version of this approach was developed by Thomas Ho in 1992. This approach examines how changes in US Treasury yields at different points on the spot curve affect the value of a bond portfolio. Ho s methodology has three basic steps. The first step is to select several key maturities or key rates of the spot rate curve. Ho s approach focuses on 11 key maturities on the spot rate curve. These rate durations are called key rate durations. The specific maturities on the spot rate curve for which a key rate duration is measured are 3 months, 1 year, 2 years, 3 years, 5 years, 7 years, 10 years, 15 years, 20 years, 25 years, and 30 years. However, in order to illustrate Ho s methodology, we will select only three key rates 1 year, 10 years, and 30 years. 

Thomas S. Y. Ho, Key Rate Durations Measures of Interest Rate Risk, Journal of Fixed Income (September 1992), pp. 29-44. 

The third and final step is to calculate the percentage change in the bond s portfolio value when each key rate and neighboring spot rates are changed. There will be as many key rate durations as there are preselected key rates. Let s illustrate this process by calculating the key rate duration for a coupon bond. Our hypothetical 6% coupon bond has a maturity value of 100 and matures in five years. The bond delivers coupon payments semiannually. Valuation is accomplished by discounting each cash flow using the appropriate spot rate. The bond s current value is 107.32 and the process is illustrated in Exhibit 4.27. The initial hypothetical (and short) spot curve is contained in column (3). The present values of each of the bond s cash flows is presented in the last column. 

To compute the key rate duration of the 5-year bond, we must select some key rates. We assume the key rates are 0.5, 3, and 5 years. To compute the 0.5-year key rate duration, we shift the 0.5-year rate upwards by 20 basis points and adjust the neighboring spot rates between 0.5 and 3 years as described earlier. (The choice of 20 basis points is arbitrary.) Exhibit 4.28 is a graph of the initial spot curve and the spot curve after the 0.5-year key rate and neighboring rates are shifted. The next step is to compute the bond s new value as a result of the shift. This calculation is shown in Exhibit 4.29. The bond s value subsequent to the shift is 107.30. To... 

Substituting in numbers from our illustration presented above, we can compute the 0.5-year key rate duration as follows ... 

Exhibit 4.32 presents a graph of the initial spot curve and the spot curve after the 5-year key rate and neighboring rates are shifted. The bond s postshift value is 106.48 and the calculation appears in Exhibit 4.33. Accordingly, the 5 year key rate duration is computed as follows ... 

What information can be gleaned from these key rate durations Each key rate duration by itself means relatively little. However, the distribution of the bond s key rate durations helps us assess its exposure to yield curve risk. Intuitively, the sum of the key rate durations is approximately equal to a bond s duration. As a result, it is useful to think of a set of key rate durations as a decomposition of duration into sensitivities to various portions of the yield curve. In our illustration, it is not surprising that the lion s share of the yield curve risk exposure of the... 

The reason it is only approximate is because modified duration assumes a flat yield curve whereas key rate duration takes the spot curve as given. 

Key rate durations are most useful when comparing two (or more) bond portfolios that have approximately the same duration. If the spot curve is flat and experiences a parallel shift, these two bond portfolios can be expected to experience approximately the same percentage change in value. However, the performance of the two portfolios will generally not be the same for a nonparallel shift in the spot curve. The key rate duration profile of each portfolio will give the portfolio manager some clues about the relative performance of the two portfolios when the yield curve changes shape and slope. 

Golub, B. W., and L. M. Tilman, Measuring Yield Curve Risk Using Principal Components Analysis, Value at Risk, and Key Rate Durations, Journal of Portfolio Management (Summer 1997), pp. 72-84. RiskMetrics-09/30/96—Spot ZC 3M-30Y 3 92.8/4.8/1.27... 

Purging efficiency (the percentage of analytes removed from the sample) depends upon the properties of the analytes, purge temperature, flow rate, duration of the purging, and sample matrix. Purging is most efficient for VOCs that are insoluble or... 

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