Interest rate premiums A 5-year Treasury bond has a 5.2 percent yield. A 10-year Treasury bond yields 6.4 percent, and a 10-year corporate bond yields 8.4 percent. The market expects that inflation will average 2.5 percent over the next 10 years (IP10 _ 2.5%).
Assume that there is no maturity risk premium (MRP _ 0), and that the annual real riskfree rate, r*, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP _ LP _ 0.)
A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described above. What is the yield on this 5-year corporate bond?
Does this sound right to my question?
10 year at 8.4% with an inflation of 2.5 over that same time period.
risk free stays the same LP is zero so those are really irrelavant.
so we need to figure out a five year equation of the above but with five years
8.4% shouldn't change due to its pretty much locked in
now the 2.5% predicted inflation is over ten years.
So that 2.5 needs to be broke down over a ten year span which is a quart of percent per year for ten years..and that quarter of percent needs to be broken down to a monthly percent
So a year is .25/12=0.020834of a percent per month.
So for five years would it be 0.020834 permonth for five years.
12 months is a year for five years is sixty months.
So maybe 0.020834*60=1.25% for the inflation for that five year period.
To calculate the yield on a 5-year corporate bond, we need to consider the various components that make up the yield.
1. Real Risk-Free Rate (r*): Given that the annual real risk-free rate will remain constant over the next 10 years, we'll use the same rate for the 5-year corporate bond. Let's assume r* is 2%.
2. Inflation Premium (IP): The market expects inflation to average 2.5% over the next 10 years. Since the 5-year corporate bond is for a shorter maturity, we'll only consider half of the 10-year inflation expectation. So the inflation premium for the 5-year corporate bond is 2.5% / 2 = 1.25%.
3. Maturity Risk Premium (MRP): We are given that the maturity risk premium (MRP) is zero, so we won't include it in our calculation.
4. Default Risk Premium (DRP) and Liquidity Premium (LP): The 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond. However, we are not given these values, so we'll assume they are also zero (DRP = LP = 0).
Using these components, we can calculate the yield on the 5-year corporate bond:
Yield on 5-year corporate bond = r* + IP + DRP + LP
Yield on 5-year corporate bond = 2% + 1.25% + 0% + 0%
Yield on 5-year corporate bond = 3.25%
Therefore, the yield on the 5-year corporate bond is 3.25%.
To calculate the yield on the 5-year corporate bond, we need to determine the components that make up the bond's yield: the real risk-free rate, the default risk premium, the liquidity premium, and the inflation premium.
First, we need to identify the real risk-free rate. This information is not provided in the question, so we will need to make an assumption. Let's assume the real risk-free rate remains constant at 2% over the next 10 years.
Next, we can calculate the inflation premium. The market expects inflation to average 2.5% over the next 10 years, so the inflation premium is 2.5%.
Since the default risk premium and liquidity premium for Treasury securities are both zero, we can assume they remain the same for the corporate bond as well.
Now, let's calculate the yield on the 5-year corporate bond using the given information:
Real Risk-Free Rate (r*): 2%
Inflation Premium (IP10): 2.5%
Default Risk Premium (DRP): Same as the 10-year corporate bond, which is 8.4% - 6.4% = 2%
Liquidity Premium (LP): Same as the 10-year corporate bond, which is 0%
Yield on 5-year Corporate Bond = r* + IP5 + DRP + LP
Since the maturity risk premium is assumed to be zero, the inflation premium can be adjusted by dividing it by half:
IP5 = IP10 / 2 = 2.5% / 2 = 1.25%
Yield on 5-year Corporate Bond = 2% + 1.25% + 2% + 0% = 5.25%
Therefore, the yield on the 5-year corporate bond is 5.25%.