Day count basis

The accrued interest calculation for a bond is dependent on the day-count basis specified for the bond in question. We have already seen that when bonds are traded in the market the actual consideration that changes hands is made up of the clean price of the bond together with the accrued that has accumulated on the bond since the last coupon payment these two components make up the dirty price of the bond. When calculating the accrued interest, the market will use the appropriate day-count convention for that bond. A particular market will apply one of five different methods to calculate accrued interest these are ... 

Market Coupon Frequency Day Count Basis Ex-dividend Period... 

Exhibit 1.8 shows the conventions (coupon frequency, Day count basis, and ex-dividend period) for the the government bond market of major European countries. 

Note coupon Day-count basis Index Current LIBOR rate Rate fixing Initial coupon Minimum coupon 15.75% - (2 X LIBOR) actual/365 6-month LIBOR 5.15% Semiannual 5.45% 0% ... 

Maturity Date 6/20/11 Payment Frequency Q Quarterly Day Count Basis ACT/360 Business Days EUR Business Day Adj 1 Follouiing Issue Spread 40.0 bps Par Amount o.og)... 

FIGURE 17.2 shows the spreadsheet used to calculate price, yield, and duration for a hypothetical bond traded forsetdement on December 10, 2005-It has a 5 percent coupon and matures in July 2012. Given the price, we can calculate yield, and given yield, we can calculate price and duration. We need to also set the coupon frequency, in this case semiannual, and the accrued interest day-count basis, in this case act/act, in order for the formulae to work. 

We will illustrate this process using a hypothetical 4-year floater that deliver cash flows quarterly with a coupon formula equal to 3-month LIBOR plus 15 basis points and does not possess a cap or a floor. The coupon reset and payment dates are assumed to be the same. For ease of exposition, we will invoke some simplifying assumptions. First, the issue will be priced on a coupon reset date. Second, although floaters typically use an ACT/360 day-count convention, for simplicity we will assume that each quarter has 91 days. Third, we will assume initially that the LIBOR yield curve is flat such that all implied 3-month LIBOR forward rates are the same. (We will relax this assumption shortly.) Note the same principles apply with equal force when these assumptions are relaxed. 

Normally, the fixed interest payments are paid on the basis of a 30/ 360 day count floating-rate payments are paid on the basis of an actual/ 360 day count. Accordingly, the fixed interest payments will differ slightly owing to the differences in the lengths of successive coupon periods. The floating payments will differ owing to day counts as well as movements in the reference rate. 

The swap s value will change by approximately the same amount, but in the opposite direction, as the bond s value. The match will not be exact. It is very difficult to establish a precise hedge for a number of reasons, including differences in day count and in maturity, and basis risk. To minimize the mismatch, the swap s maturity should be as close as possible to... 

The U.S. Treasury interest basis is semiannual, and the market uses an actual/actual day count. So, the value of n for the 90-day T-bill whose yield analysis as of March 25, 2004, is shown in figure 16.1 would be 90/183, where 183 represents the number of days in half a year, given that 2004, as a leap year, had 366 days. The bill was priced... 

Our confirmation is shown at Figure 17.4. It is important to get the day-count fraction for the first coupon payment correct, and the confirmation of this is shown at FIGURE 17.6, which is Bloomberg page DCX with the relevant dates entered. We see that on the 30/360 basis the number of days accrued for the Ford bond for value January 6, 2006 is 39-The spreadsheet cell formulae are shown at FIGURE 17.7. 

Therapy is perfectly adequate with simple iron salts (Table 2). In adults ferrous gluconate, fumarate or sulphate are all of proven equal efficiency. Approximately 50 mg of iron is present in each tablet with the remaining 300 mg made up with an inert filler. These are given on an empty stomach at least twice a day but should nausea prevail they can be taken with food. Absorption of slow release preparations is not recommended since iron is detached from the carrier beyond the main areas of absorption in the duodenum or jejunum. Stools turn black in all cases and this is a useful index of patient compliance. In 25% of individuals gastrointestinal tract side effects are encountered in the form of diarrhoea or constipation and patients will often spontaneously discontinue medication. It is therefore essential that a tablet-count be carried out on a regular basis with a substitute being provided when this first-line medication is intolerable. In children the same preparations are favoured as syrups these are given twice... 

Animal studies support the observations made in humans and show that benzene affects humoral and cellular immunity. A decrease in spleen weight was observed in mice after acute-duration exposure to benzene at 25 ppm, 6 hours per day for 5 days, the same dose levels at which a decrease in circulating leukocytes was observed (Wells and Nerland 1991). Benzene decreases the formation of the B-lymphocytes that produce the serum immunoglobulins or antibodies. Exposure to benzene at 10 ppm and above for 6 days decreased the ability of bone marrow cells to produce mature B-lymphocytes in C57BL/6 mice (Rozen et al. 1984). The spleen was also inhibited from forming mature T-lymphocytes at exposure levels of 31 ppm and above. Mitogen-induced blastogenesis of B- and T-lymphocytes was depressed at 10 ppm and above. Peripheral lymphocyte counts were depressed at all levels, whereas erythrocyte counts were depressed only at 100 and 300 ppm. This study is the basis for the acute inhalation MRL of 0.05 ppm (see footnote to Table 2-1 and Appendix A). 

Benzene also affects functional immune responses, as indicated by decreased resistance to infectious agents. Pre-exposure to benzene at >30 ppm for 5-12 days increased the bacterial counts in mice on day 4 of infection with Listeria monocytogenes (Rosenthal and Snyder 1985). Recovery of the immune system was noted on day 7. The effects did not occur at 10 ppm. In addition, a concentration-dependent statistically significant depression was noted in T- and B-lymphocyte populations from day 1 through day 7 at 30 ppm and above. B-cells were more sensitive to benzene than were T-cells on a percentage-of-control basis. This indicates a benzene-induced delay in immune response to L. monocytogenes. Concentrations of 200 or 400 ppm for 4-5 weeks (5 days per week) suppressed the primary antibody response to tetanus toxin in mice, but there was no effect at 50 ppm (Stoner et al. 1981). In another intermediate-duration exposure study, no changes were noted in the numbers of splenic B-cells, T-cells, or... 

A summary of airborne radioactivity measurements in Monthldry, France is presented in the report by Milles-Lacroix et al. (1994). Radioactive aerosols particles are collected in surface air, using cellulose filters and high output pumps (110 m%). Equipment operates on a permanent, 24-hour a day basis, and filters are replaced daily throughout the year. The volume of filtered air is 2600 m per day. After removal, individual filters are subjected to alpha counting, using a ZnS counter, and to beta... 

Inspect the plate each day and score the formation of syncytia, either on a semiquantitative basis (+++++/+++/+/-) or by counting individual syncytia (see Note 6). 

Tire Anderson and Molhave (1983) study identified an apparent effect level (0.2 ppm), based on subjective reports of irritation that is lower than the effect levels (0.35-0.4 ppm) in the studies by Pazdrak et al. (1993), Krakowiak et al. (1998), and Bender et al. (1993), which used more objective measures of acute irritation (eosinophil counts and protein concentrations in nasal lavage fluid or time to first reporting of irritation see section 2.2.1.2 Systemic Effects - Respiratory Effects Acute Controlled Exposure Human Studies.) Because of the use of objective measures of toxicity and the general weight of the available data indicating that some people will not experience eye or upper respiratoiy tract irritation from formaldehyde even at 1 ppm (see Day et al. 1984 Kulle et al. 1987, Weber Tschopp et al. 1977, and Witek et al. 1986), the Pazdrak et al. (1993) LOAEL of 0.4 ppm was considered a minimal LOAEL in a group of potentially sensitive individuals (some subjects had dennal hypersensitivity to fonnaldehyde) and selected as the basis of the acute MRL. 

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