Price value of a basis point

Some managers use another measure of the price volatility of a bond to quantify interest rate risk—the price value of a basis point (PVBP). This mea-... 

To illustrate the computation, let s examine a 4.2% coupon, lO-year Spanish government security that matures on July 30, 2013. Bloomberg s Yield Analysis Screen is presented in Exhibit 4.7. If the bond is priced to yield 3.724% on a settlement date of June 6, 2003, we can compute the PVBP by using the prices for either the yield at 3.734 or 3.714. The bond s initial full price at 3.724% is 104.5673. If the yield is decreased by 1 basis point to 3.714%, the PVBP is 0.085 (1104.5673 - 104.65221). Note that our PVBP calculation agrees with Bloomberg s calculation labeled PRICE VALUE OF A 0.01 that is presented in the Sensitivity Analysis box located in the lower left-hand corner of the screen. 

As an alternative to Eurex s 10-year Euro-Bund future, Euronext LIFFE offers a similar contract again based on a nominal 100,000 contract size, tick value of 10, and the same expiry cycle. The Euro-Schatz counterpart, however, offers a contract size of 200,000. The smallest allowable price movement is one half of a basis point and hence the value of a tick remains at 10. 

A key element of the description of a stochastic process is a specification of the level of informatimi oti the behaviour of prices that is available to an observer at each point in time. As with the martingale property, a calculation of the expected future values of a price process requires information on current prices. Generally, fmancial valuation models require data on both the current and the historical security prices, but investors are only able to deal on the basis of current known information and do not have access to future information. In a stochastic model, this concept is captured via the process known as filtration. 

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. 

For longer-dated debt instruments investors have the a choice of the very long-term notional 30-year, 6% coupon Euro-Buxl contract which covers cash market bonds with a matnrity of between 20 and 30.5 years, or the notional 10-year, 6% coupon Enro-Bnnd contract which covers the 8.5-10.5 years maturity section of the yield curve. The nominal size for each contract is 100,000 both have a minimum allowable price movement (tick) of 1 basis point, which is valued at 10, and a contract cycle of March, Jnne, September, and December, of which the three nearest-to-delivery, snccessive contracts will be available for trading. 

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). 

An FRN with a par value of 100, a quoted margin of 10 basis points over six-month LIBOR is currently trading at a clean price of 98.50. The previous LIBOR fixing was 5.375%. There are 90 days of accrued interest, 92 days until the next coupon payment and five (10) years from the next coupon payment before maturity. Therefore we have ... 

An economical evaluation of phenol processes is complicated by the number and variety of competing processes. Table XXII compares some key features of various phenol processes, based on two excellent, recent reviews (4,15). Hay et al. (15) point out that synthetic phenol processes currently account for 98% of the phenol produced in the United States and Canada. The various phenol processes currently used are listed in Table XXIII. An economic comparison between a number of phenol processes is given in Table XXIV. Based on this table, the Raschig, Cumene, and Dow toluene processes are equivalent with regard to return price. Therefore, selection must be made on the basis of other factors, such as value of intermediates and by-products, ease of operation, and initial investment. 

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. 

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. 

The zero-volatility or static spread is the spread that when added to the government spot rate curve will make the present value of the cash flows equal to the bond s price plus accrued interest. When spread is defined in this way, spread dnration is the approximate percentage change in price for a 100 basis point change in the zero-volatility spread holding the government spot rate curve constant. 

Finally, the option-adjusted spread (OAS) is the constant spread that, when added to all the rates on the interest rate tree, will make the theoretical value equal to the market price. Spread duration based on OAS can be interpreted as the approximate percentage change in price of a nongovernment for a 100 basis point change in the OAS, holding the government rate constant. 

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 ... 

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