# Always Use Spot Rate for Discounting?

1. An analyst has gathered the following information: 3-Year Treasury Rate: 3.75% (constant across all 3 years) Treasury Spot Rate year 1 3.00% year 2 3.50% year 3 4.00% Based on the arbitrage-free valuation approach, a \$1,000 face value bond that pays a 5 percent annual coupon and matures in 3 years has a current market value closest to: A. \$1,027.75. B. \$1,028.67. C. \$1,034.85. Correct answer is B… As a general rule, are we supposed to use the treasury spot rates whenever calculating / discounting a security? What is wrong with using the 3 year treasury rate of 3.75% for all 3 years?

3.75 is the yield of a 3 year Treasury Security. As per no arbitrage, all the cashflows must be discounted by their appropriate spot rates.

^ so based on that logic, if the question does not state “no arbitrage / arbitrage free approach”, we can safely use the 3-year constant treasury rate and not the appropriate spot rate? thanks!

Yeah, but I doubt they would ask something like that since they are trying to test a specific LOS

I still don’t get it. At 3.75% spot you get answer C but if you use the 3-year spot, you get answer A

If you are getting A as the answer it could be from rounding =(50/1.03)+(50/1.035^2)+(1050/1.04^3) =48.54+46.68+933.45 = 1028.67

when you discount the coupons store them in your calc 1 at a time, so u dont have to write em down, saves tonnes of time. STO 7 STO 8 STO 9 are my fav then a quick RCL 9 + RCL 8 + RCL 7. If you have to STO/RCL 4, go 7,4,1,0 down the left side Good looks Matt

Thanks guys. The STO and RCL worked well. I’ve used it before but only for large numbers. Rounding error played a big difference on this one. Good luck on Saturday.