With the Federal Reserve's monetary stimulus programs, inflation is expected to be 5% in Year 1, 4% in Year 2, and back to the normal level of 2% thereafter. Suppose the yield on a 5-year Treasury note is 8% .
Please show calculations for parts a and b.
(a) What is the yield on a 5-year Treasury Inflation-Protected Security (TIPS)?
(b) Suppose the yield on a 5-year corporate bond is 15%, and its liquidity premium is 3%, what is its default risk premium?
(c) Is default risk premium likely to be pro-cyclical (i.e., increasing during economic expansion) or counter-cyclical (i.e., increasing during economic recession)? Why?
Let r be the CAGR of inflation rate
(1+r)^5 = (1+5%)*(1+4%)*(1+2%)^3
Solving the equation we get,
r = 3%
(a) yield on a 5-year TIPS = (1+8%)*(1+3%)-1 = 11.24%
(b) yield on 5-year corporate bond (without liquidity premium) = 15%-3% = 12%
yield on treasury note = 8%
default risk premium = 12%-8% = 4%
(c) Counter-cyclical: for illiquid securities (ie securities that have a liquidity premium), the chances of default increases during economic recession. This is because during recession, the securities are dumped thereby declining the credit worthiness
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