# QUERY REF. Valuation of debt securities

Question Consider a 6 % Treasury note with 1.5 years to maturity. Spot rates expressed as semiannual yields to maturity are 6 months–5%, 1 year–6% and 1.5 years–7%. If the note is selling for 992 compute the arbitrage profit. Answer The cash flows per 1000 par value will be 30, 30 and 1030 and then one calculates the PV. How does one arrive at these cash flows of 30, 30 and 1030??? What does arbitrage really mean in the cfa context??

Cash flow is based on annual coupon rate of 6% ==> Semiannually 1000*.06/2 = 30\$ Cashflows are like these 6 months : 30\$ 1 year: 30\$ 1.5 year : 30\$ + 1000 par = 1030 Arbitrage profits implies the difference in the PV of these cashflows discounted by the spot rates and the current price of the note. The way arbitrage is achieved is either by reconstitution of T-strips or stripping the note.

Thanks for that…when and where do we use the other given rates… 6 months–5%, 1 year–6% and 1.5 years–7% or we dont use them at all???

You don’t use them because they gave you the price of the bond. It;s probably an editing thing where the problem once didn’t have the bond price.

Here’s how the answer goes. First you take out the coupon payments of the bond. Just like the way ravinsu has done. Then you calculate the present value of those cash flows by discounting them at their respective semiannual spot rates. 6 months: 30/1.05 = 28.57 1 year: 30/(1.06)^2 = 26.7 1.5 years: 30/(1.07)^3 + 1000/(1.07)^3 = 840.79 Sum them all. \$28.57 + \$26.7 + \$840.79 = \$896.06 Ok now the arbitrage-free principal says that the sum of the present value of the cash flows of the bond discounted at their respective spot rates MUST equal to the current market price of the bond, otherwise there will be an arbitrage opportunity. As the price our bond is different from what we have calculated above so an an arbitrage opportunity exists. In order to earn a arbitrage profit, go and buy the following four individual zero coupon bonds from the strips market. 6 month zero-coupon bond valuing \$28.57 1 year zero-coupon bond valuing \$26.7 1.5 year zero coupon bond valuing \$24.49 1.5 year zero coupon bond valuing \$840.79 Now, you “repackage these cash flows of coupons strip and principal strip as a single bond”, and sell it that in the market for a price of \$992. You will earn a risk-less profit of \$95.94.

6 months: 30/1.05 = 28.57 1 year: 30/(1.06)^2 = 26.7 1.5 years: 30/(1.07)^3 + 1000/(1.07)^3 = 840.79 How do we arrive at the figures of 1.05 and 1.06 and 1.07???..what is the formula??

Read the chapter “Time Value of Money” from any introductory finance book you have got.

SpyAli, Great explanation of arbitrage