Always Use Spot Rate for Discounting? face, general, valuation, following

w1977

105. 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?

ftwcfa

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.

koba

^ 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!

MythosHF

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

bluejazzy

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

LokiDog2

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

Bluetick1010

Good looks Matt