Answer to Question #131511 in Financial Math for laxmi

Question

On the new issuance, Market is expecting 25bp premium to secondary market. What would be the expected auction yield/price of new treasury bond?

Answer 1

The price of a new treasury bond can be obtained using the price value of a basis point,which is the change in the price of the bond if the required yield changes by 1 basis point. With a market expecting a 25 basis point, the bond price can be obtained considering the scenario below;

Let's say, a bond A, with coupon rate of 8%, yield to maturity of 8%, maturity of 2yrs, per value of $100 and a price of $100. The expected auction price can be calculated as below

By changing the yield 25 basis points, so the yield is 8.25%. Therefore,

C = $40, y = 0.0801 / 2 = 0.04125 and n = 2(2) = 4.

Inserting these values into the present value of the coupon payments formula, we get

$$P=C[\frac{1- \frac{1}{(1+r)^n}}{r}]=40[\frac{1- \frac{1}{(1+0.04125)^4}}{0.04125}]= \$ 144.769$$

Computing the present value of the par or maturity value of $1000 gives :

$$\frac{M}{(1+r)^n}=\frac{\$1000}{(1.04125)^4}=\$850.707$$

Add a basis point to the yield, we get the value of bond A as P=$144.769+$850.707=$995.476 with a bond quote of $99.5476. Therefore for bond A the price value of a basis point is about $100-$99.5476=$0.4524 per $100.