Market conventions

For callable bonds, the market convention is to calculate a yield to call in addition to a yield to maturity. A callable bond may be called at more than one price and these prices are specified in a call price schedule. The yield to call assumes that the issuer will call the bond at some call date and the call price is then specified in the call schedule... 

The original form of this call pricing mechanism was the Spens clause, which required the issuer to call in the bonds at an above-market price if certain events detrimental to the interests of the bondholders took place. Following a decision by the International Primary Markets Association (IPMA) in July 2001, the market convention is that the Spens clause is no longer used, although it remains in many ontstanding issues. Instead, the market now uses a formula to calculate the redemption yield of a bond in the event it is called prior to maturity. This is set out in the UK Debt Management Office (DMO) paper dated 8 June 1998. 

Issues are initially priced and sold at a fixed spread over the reference rate. The price of an FRN can fluctuate considerably during the life of the issue, mainly depending on trends in the issuer s credit quality. The frequent resets in the reference rate means that changes in market interest levels have a minimal impact on an FRN s price. For investors, movements in an FRN s price are reflected in changes in the discount rate. The discount rate is effectively the yield needed to discount the future cash flows on the security to its current price. It thus functions in the same way as the yield to maturity for a fixed-rate instrument. And like a fixed-rate bond, the market convention is to use a constant spread... 

These matching errors are less alarming than they might appear, because all known price information is built into the real yield formula as soon as it is published. Two things really matter, in terms of the achieved real yield relative to the quoted real yield at purchase firstly, the difference between future inflation over the life of the bond and the 3% inflation assumption used in the market convention for calculating yields, and secondly (as with any coupon bond) reinvestment risk. However, we are getting ahead of ourselves—the next section handles the market s yield conventions. 

With an eight-month lag, we will know the next coupon cash flow and possibly the subsequent one, but no others. The formula takes the latest known RPI value and from that month projects all future monthly RPI values using an inflation assumption (currently 3%), which is a market convention. So an unknown RPI in month t is given by... 

So we have formally introduced the notion of break-even inflation, a term at the heart of inflation-linked bond analysis and trading. In principle it is the rate of inflation that will equate the returns on an inflation-linked bond and a comparator nominal bond issue of the same term. In theory, calculating it by simply subtracting a real yield from a nominal yield is a crude form of a properly compounded calculation, particularly when bond market conventions are semi-annual and what you should want is an annual measure of inflation. 

Although there is no formal break-even calculation convention, or way of selecting the best nominal comparator for that matter, historically break-even inflation in the United Kingdom has been calcnlated in a slightly more complicated way. Because UK real yields require an inflation assumption—3% is the market convention— there wonld be an inconsistency between the break-even inflation (BEI) rate and the inflation assumption used. The market tends to use the last formula above to arrive at a first cut BEI, then it uses that BEI rate as the new inflation assumption to calculate a new real yield. This is done iteratively nntil the assumed inflation rate and the BEI rate converge on a final cnt BEI. 

Calculation of the coupon income is the difference between the accrued interest bought in at the time of purchasing the cash market bond subtracted from the accrued interest received when the bond is sold. Market conventions play an important role here, for example How many days between trade and settlement How many days in a month How many days in a year In the United Kingdom the market convention is actual number of days in a month and a 365 days in a year. In Germany the convention is actual number of days in month and 360 days in a year. 

The market convention is to quote annualized interest rates the rate corresponding to the amount of interest that would be earned if the investment term were one year. Consider a three-month deposit of 100 in a bank earning a rate of 6 percent a year. The annual interest gain would be 6. The interest earned for the ninety days of the deposit is proportional to that gain, as calculated below ... 

The market convention is sometimes simply to double the semiannual yield to obtain the annualized yields, despite the fact that this produces an inaccurate result. It is only acceptable to do this for rough calculations. An annualized yield obtained in this manner is known as a hand equivalent yield. It was noted earlier that the one disadvantage of the YTM measure is that its calculation incorporates the unrealistic assumption that each coupon payment, as it becomes due, is reinvested at the rate rm. Another disadvantage is that it does not deal with the situation in which investors do not hold their bonds to maturity. In these cases, the redemption yield will not be as great. Investors might therefore be interested in other measures of return, such as the equivalent zero-coupon yield, considered a true yield. 

Because a callable bond has more than one possible redemption date, its future cash flows are not clearly defined. To calculate the yield to maturity for such a bond, it is necessary to assume a particular redemption date. The market convention is to use the earliest possible one if the bond is priced above par and the latest possible one if it is priced below par. Yield calculated in this way is sometimes referred to as yield to worst (the Bloomberg term). 

To calculate a money yield for an indexed bond, it is necessary to forecast all its future cash flows. This requires forecasting all the relevant future CPl-U levels. The market convention is to take the latest available CPI reading and assume a constant future inflation rate, usually 2.5 or 5 percent. The first relevant future CPI level is computed using equation (12.7). 

Pompey s final exit from the tale, after throwing off Dr. Moneypenny s overcoat, points to the ways in which blackness is a marketplace commodity. Once the figure of blackness is no longer commodified through conventions, he is no longer visible. Blackness exists only in relation to the market conventions that cloak it. A Predicament, then, schematizes... 

Thus the OAS is an indication of the value of the option element of the hond as well as the premium required by investors in return for accepting the default risk of the corporate bond. When OAS is measured as a spread between two bonds of similar default risk, the yield difference between the bonds reflects the value of the option element only. This is rare and the market convention is measure OAS over the equivalent benchmark government bond. OAS is used in the analysis of corporate bonds that incorporate call or put provisions, as well as mortgage-backed securities with prepayment risk. For both applications, the spread is calculated as the number of basis points over the yield of the government bond that would equate the price of both bonds. 

The one time-period or 180-day equivalent rate is (e° ) -1 or 2.0201 percent. This is therefore the risk-free interest rate to use. The volatility level of 10 percent is an annualized figure, following market convention. This may be broken down per time period as well, and this is calculated by multiplying the annual figure by the square root of the time period required. This calculation follows. 

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