Question

6-8 5-9 Expected on page 206.) EXPECTATIONS THEORY One-year Treasury securities yield 4.85%. The market anticipates that 1 year from now, 1-year Treasury securities will yield 5.2%. If the pure expectations theory is correct, what is the yield today for 2-year Treasury securities? Calculate the yield using a geometric average. EXPECTATIONS THEORY Interest rates on 4-year Treasury securities are currently 6.7%, while 6-year Treasury securities yield 7.25%. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now? Calculate the yield using a geometric average. EXPECTED INTEREST RATE The real risk-free rate is 2.05%. Inflation is expected to be 3.05% this year, 4.75% next year, and 2.3% thereafter. The maturity risk premium is estimated to be 0.05 x (t - 1)%, where t number of years to maturity. What is the yield on a 7-year Treasury note? INFLATION Due to a recession, expected inflation this year is only 3.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.25%. Assume that the expectations theory holds and the real risk-free rate (r") is 2.5%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 1.5%, what inflation rate is expected after Year 1? DEFAULT RISK PREMIUM A company's 5-year bonds are yielding 7% per year. Treasury bonds with the same maturity are yielding 5.2% per year, and the real risk-free rate (r") is 0

Answer 1

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Answer- 6-7)

Given: 1-year treasury security rate 1-year treasury security rate 1 year from now Assume pure expectation theory holds 4.85% 5.2% Required: Yield on a 2-year security Note: When pure expectation theory holds, it is assumed that there are no maturity risk premium for treasury securities. 2 Assumption: If pure expectation theory holds, then the compounded return of the 1-year treasury security rate multiplied by the compounded return of the 1-year security rate 1 year from now is equal to the compounded return of the 2-year treasury rate. In other words, if you invest on a 4-year treasury security today, and reinvest its maturity value 4 years from now in a 2-year treasury security, you will earn the same effective rate or interest as if you invested in a 6-year treasury security today. 1 = Translating that into algebraic form: (let x = 2-year security rate) (1.0485)? (1.052) (1 + x)2 1.103022 (2) (1 + x)2 1.103022 1+x = 1 (2) 1 + x 1.050248542 1.050248542 – 1= x x= 5.0248%

Answer 6-8)

Calculate yield rate for 2-year security 4 years from now using the following formula: (1+Y, four years from now) w)? (1+Y) (1+YA)* Here, Y = 2-year rate Y4 = 4-year rate Yo = 6-year rate Substitute the values in the formula. 6 (1+Y, four years from now)? = (1+y) (1+YA)* (1+Y, four years from now)? (1+0.0725) (1+0.067)" 1.52189 1898433 (1+Y, four years from now)? 1.296157203121 (1+Y, four years from now)2 =1.174156880638 1+Y, four years from now = (1.174156880638)Ż 1+Y, four years from now =1.083585 Y, four years from now = 1.083585-1 = 0.083585 = 8.3585%(or) 8.36%(after rounding off to 2 decimal places) Therefore, the yield rate for 2-year security 4 years from now will be 8.36%.

Answer 6-9

Nominal yield = Real risk free rate + Average inflation + Maturity risk premium Average inflation or 7 year bond = (3.05% +4.75% + 5* 2.3%)/7 = 2.76% Maturity risk premium = 0.05 *(7-1)% = 0.3% Nominal yield on 7 Yr T-note = 2.05% + 2.76% +0.3% = 5.11% --> Answer
Answer 6-10)

1 year yield = real rate + year 1 inflation = 2.5+3.25=5.75 3 yr t bond rate = 1 year yield+1.5 = 5.75+1.5=7.25 3 yr t bond rate =real rate+(inflation yr 1 + 2*inflation year 2)/3 7.25 = 2.5 +(3.25+2*inflation year 2)/3 inflation year 2 and beyond = 5.5%