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 :slight_smile:

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.