Principal strip

A principal strip is a zero-coupon bond created from a bond s principal payment. 

EXHIBIT 4.1 Bloomberg Yield Analysis Screen for a UK Gilt Principal Strip... 

Exhibit 4.10 shows the price/yield relationship for the UK gilt principal strip that is shown in Exhibit 4.1. Recall, using a settlement date of... 

For example, consider the UK gilt principal strip discussed earlier that matures on June 7, 2021 and on a settlement date of May 30, 2003 is priced to yield 4.435%. Exhibit 4.1 presents Bloomberg s Yield Analysis screen for this security. Let s change (i.e., shock) the note s required yield up and down by 20 basis points and determine what the new prices will be in the numerator of equation (4.1). If the required yield were decreased by 20 basis points from 4.435% to 4.235%, the strip s price would increase to 46.99. Conversely, if the yield increases by 20 basis points, the strip s price would decrease to 43.99. Thus,... 

For example, consider once again the UK gilt principal strip whose duration we just computed is 17.636. The approximate percentage price change for a 10 basis point increase in the required yield (i.e.. Ay = +0.001) is... 

Assumptions The initial yields for the 2-year Italian government and UK gilt principal strip are 2.147% and 4.435% respectively. 

We demonstrated this property earlier using a UK gilt principal strip priced to yield 4.435% with a duration of 17.631. For a 10 basis point change in yield, the estimate was accurate for both an increase and decrease in yield. However, for a 200 basis point change in yield the approximate percentage price change was off considerably. 

For example, for the UK gilt principal strip, the convexity adjustment to the percentage price change based on duration if the yield increases from 4.435% to 5.435% is... 

For the UK gilt principal strip we have been using in our illustrations, the convexity measure is 3.3068. 

Let s return to Exhibit 4.1 which is the Bloomberg Yield Analysis screen for the UK gilt principal strip in our illustration. Bloomberg s... 

TERM 6ILT TRUE YIELD SPOT COUPON YIELDS STRIP YIELD PRINCIPAL STRIP YIELD... 

Two observations are worth making. First, the zero-coupon bonds are shown to be trading cheap relative to the spot curve throughout the term structure. This indicates that investors at the time were not prepared to hold strips unless they could earn a spread above their theoretical yields. This probably reflected the inverted yield curve during the period, which meant that strips would be expensive relative to coupon bonds of the same maturity. It should be noted, however, that strips were expensive relative to the spot curve from the 11- to the 15-year point on the curve. Second, principal strips trade at lower yields than coupon strips of the same maturity, reflecting the fact that investors prefer holding the former. 

Principal strips trade at a premium to coupon strips. Investors find principal strips more attractive because of their greater liquidity and, in some markets, for regulatory and tax reasons. This holds true even, at times, when their outstanding nominal amounts are lower than those of coupon strips. 

The final principal strip trades expensive relative to their theoretical values. The shape of the strip yield curve might be expected to be similar to that of the coupon curve, which normally slopes gently upward. However, because investors, as noted above, prefer principal to coupon strips, final principal strips have greater weight than coupon strips. 

FIGURE 16.10 shows the cash flow for the Treasury s principal strip. Its yield is 4.0751 percent, corresponding to a price of 67.10027 per 100 nominal, which represents a spread above the gross redemption yield of the coupon Treasury. This relationship is expected, given a positive yield... 

FIGURE 16.10 Cash Flow Analysis of the 4 Percent Treasury 2014 Principal Strip, at a Yield of 4.075 Percent... 

Finally, FIGURE 16.11 shows the cash flow analysis for the coupon strip maturing on February 15, 2014, and trading at a yield of 4.089 percent, for a price of 67.01 per 100 nominal. This illustrates an anomaly noted earlier although the law of one price states that all strips maturing on the same date should cost the same—after all, why would investors require a different yield for a payment of interest than for one of principal —principal strips in fact trade at lower yields than coupon strips, because they are more liquid and so more sought after. 

Principal strips trade at a premium to coupon strips. Investors... 

Market makers who strip Treasuries earn their profits through arbitrage that exploits the mispricing of the coupon bond. To preclude arbitrage opportunities, the bid price of an issued Treasury must be lower than the offer price of a synthetic one—that is, one reconstituted from a bundle of coupon and principal strips—and the Treasury s offer must be higher than the synthetic s... 

---