Basis point value

The portfolio is valued at 100,000,000 and has been constructed to track a bond index for which the Euro-Bund Future is a very good hedge instrument. The basis point value (BPV) of the Euro-Bund futures contract is 72.03 and the yield is 5.595% calculated on an annual 360-day year basis. The bond index, which the portfolio has been designed to track, is quoted at 117.80. 

In this example, 3-99 cents is the basis point value (BPV) of the bond the change in its price given a 1 basis point change in yield. The general formula for deriving the basis point value of a bond is shown in (2.15). 

FYflMPi F CalniilafitiP Hnrige Si/e Using Basis Point Value ... 

Say a trader holds a long position of 1 million of the 8 percent bond maturing in 2019. The bond s modified duration is 11.14692, and its price is 129.87596. Its basis point value is therefore 0.14477. The trader decides to protect the position against a rise in interest rates by hedging it using the zero-coupon bond maturing in 2009, vi/hich has a BPV of 0.05549. Assuming that the yield beta is 1, what nominal value of the zero-coupon bond must the trader sell ... 

BPVf = the basis point value of the primary bond (the position to be hedged)... 

Example 14 Estimate of etbyl acetate at 450 K, using tbe normal boiling point values as a basis (see Example 13). = 32.23 kJ/mol, T,. =... 

In preparing the tabulation, a literature search was conducted to identify data source publications (1-13). Both experimental values for the property under consideration and parameter values for estimation of the property are included in the source publications. The publications were screened and copies of appropriate data were made. These data were then keyed into the computer to provide a database of values for compounds for which experimental data are available. The database also served as a basis to check the accuracy of the estimation methods. Upon completion of data collection, estimation of the values for the remaining compounds was performed. The numerous point values were processed using a computer program for minimum deviation. 

We can use these functions to describe curves by using the translates as basis functions for a point-valued parametric curve... 

This will hold when all of the basis functions are non-negative, because it is the basis function values which give the coefficients of the linear combination of control points for a given curve point. 

The importance of these observations lies in the fact that the 298 value is the basis point for the free-energy functions for both the solid and the gas. With a reasonably accurate estimate of the solid crystal entropy, the gaseous spectroscopic data and precise vapor pressure measurements, it is possible to calculate all the thermodynamic values for the metal, up to the highest temperatures of measurement. Also, a self-consistent heat capacity curve starting at 298 K is produced for the intensely-radioactive and scarce trans-curium metals, normal calorimetry may never be possible, and these techniques become extremely important tools. A detailed example of a typical calculation will be given under Californium below. 

Intensely sweet taste, licorice aftertaste- Strongly cationic, isoelectric pt greater than or equal to 11,7. uv max 278 nm (pH 5 6) 283, 290 nm (pH 13.0). About 750-1600 times sweeter than sucrose on a wt basis 30,000-i 00 000 times on a molar basis. Threshold values are near 10 %. The proteins lose sweetness on heating on splitting of disulfide bridges and also at pHs <2.5 which points to the importance of the tertiary structure for the sweetness, See Korver et a l, foe. cit. 

In the classical empirical theory of corresponding states, the units which are used to reduce the state variables are the critical-point values Pc, Vc, and Tc. There is, however, nothing unique about this choice of units. For example, an alternative formulation of the law of corresponding states has been developed by de Boer and his collaborators. In this formulation, which can also be shown to have an exact theoretical basis, the intermolecular field parameters are used to reduce the state variables. 

Option-adjusted spread The OAS is used for bonds with embedded options. This spread is calculated as the difference between the Z-spread and option value expressed in basis points. 

This means that p f) is the expected value of the present value of the bond s cash flows, that is, the expected yield gained by buying the bond at the price p f) and holding it to maturity is r. If our required yield is r, for example this is the yield on the equivalent-maturity government bond, then we are able to determine the coupon rate C for which p r) is equal to 100. The default-risk spread that is required for a corporate bond means that C will be greater than r. Therefore, the theoretical default spread is C — r basis points. If there is a zero probability of default, then the default spread is 0 and C = r. 

Craisider a hypothetical situation. Assume that an option-free bond paying a semi-annual coupon 5.5% on par value, with a maturity of 5 years and discount rate of 8.04% (EUR 5-year swap rate of 1.04% plus credit spread of 700 basis points). Therefore, the valuation of a conventional bond is performed as follows (Figure 9.4). 

Wote This table is indicative only and should not be used as a basis for current calculations. Refer to the EPA for the latest information and point values. 

In contrast to a conpon rate that remains unchanged for the bond s entire life, a floating-rate security or floater is a debt instrument whose coupon rate is reset at designated dates based on the value of some reference rate. Thus, the coupon rate will vary over the instrument s life. The coupon rate is almost always determined by a coupon formula. For example, a floater issued by Aareal Bank AG in Denmark (due in May 2007) has a coupon formula equal to three month EURIBOR plus 20 basis points and delivers cash flows quarterly. 

The first column in Exhibit 3.5 simply lists the quarterly periods. Next, Column (2) lists the number of days in each quarterly coupon period assumed to be 91 days. Column (3) indicates the assumed current value of 3-month LIBOR. In period 0, 3-month LIBOR is the current 3-month spot rate. In periods 1 through 16, these rates are implied 3-month LIBOR forward rates derived from the current LIBOR yield curve. For ease of exposition, we will call these rates forward rates. Recall for a floater, the coupon rate is set at the beginning of the period and paid at the end. For example, the coupon rate in the first period depends on the value of 3-month LIBOR at period 0 plus the quoted margin. In this first illustration, 3-month LIBOR is assumed to remain constant at 5%. Column (4) is the quoted margin of 15 basis points and remains fixed to maturity. 

It is important to stress that this result holds regardless of the path 3-month LIBOR takes in the future. To see this, we replicate the process described in Exhibit 3.5 once again with one important exception. Rather than remaining constant, we assume that 3-month LIBOR forward rates increase by 1 basis point per quarter until the floater s maturity. These calculations are displayed in Exhibit 3.6. As before, the present value of the floater s projected cash flows is 100. When the market s required margin equals the quoted margin, any increase/decrease in the floater s projected cash flows will result in an offsetting increase/... 

To illustrate, we will value the same hypothetical 4-year floater assuming that the required margin is now 20 basis points. For this to occur, some dimension of the floater s risk or the market must have increased since the floater s issuance. Now in order to be reset to par, our floater would hypothetically have to possess a coupon rate equal to 3-month LIBOR plus 20 basis points. Since the quoted margin is fixed, the floater s price must fall to reflect the market s perceived increase in the security s risk. 

The nominal spread for the nongovernment bond is 148.09 basis points. Let s use the information presented in Exhibit 3.15. The second column in Exhibit 3.15 shows the cash flows for the 7%, 5-year nongovernment issue. The third column is a hypothetical benchmark spot rate curve that we will employ in this example. The goal is to determine the spread that, when added to all the Treasury spot rates, will produce a present value for the non-government bond equal to its market price of 101.9141. 

Suppose we select a spread of 100 basis points. To each benchmark spot rate shown in column 3 of Exhibit 3.15, 100 basis points are added. So, for example, the 1-year spot rate 5.33% (4.33% plus 1%). This spot rate is used to calculate the present values shown in the fourth column. Because the present value is not equal to the nongovernment issue s price of 101.9141, the Z-spread is not 100 basis points. If a spread of 120 basis points is tried, it can be seen from the next-to-last column of Exhibit 3.15 that the present value is 103.1835 again, because this is not equal to the nongovernment issue s price, 120 basis points is not the Z-spread. The last column shows the present value of the cash flows is equal to the nongovernment issue s price. Accordingly, 150 basis points is the Z-spread, compared to the nominal spread of 148.09 basis points. 

EXHIBIT 3.16 Calculation of the Discount Margin for a Floater Floater Maturity = 6 years Coupon rate = Reference rate + 80 basis points Resets every 6 months Maturity value = 100 ... 

---