Always Use Spot Rate for Discounting?

face, general, valuation, following

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

CFA Candidates

Rank: 2

UID: 223315
帖子: 199
主题: 82
注册时间: 2011-7-11
最后登录: 2013-9-12

2^#

发表于 2011-7-11 18:24 | 只看该作者

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.

TOP

koba

CFA Candidates

Rank: 2

UID: 223280
帖子: 242
主题: 99
注册时间: 2011-7-11
最后登录: 2013-8-23

3^#

发表于 2011-7-11 18:24 | 只看该作者

^ 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!

TOP

MythosHF