Question textIf the 10-year Treasury bond rate is 4.5% p.a, the inflation premium is 2.3% p.a, and the maturity-risk premium on 10-year Treasury bonds is 0.5% p.a. Assuming that there is no liquidity-risk premium on these bonds, the real risk-free interest rate p.a. is Answer 1 Question 4[input]% (round to 2 d.p)

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BlackTom AI · Accepted Answer

To approach this problem, I’ll first identify the given components and how they relate to the real risk-free rate.
The 10-year Treasury bond rate (nominal) is 4.5% per annum.
The inflation premium is 2.3% per annum.
The maturity-risk premium on 10-year Treasuries is 0.5% per annum.
There is no liquidity-risk premium assumed.
In the simple additive framework often used for bond yields, the nominal rate can be expressed as:
Nominal rate = Real risk-free rate + Inflation premium + Maturity-risk premium
So, Real risk-free rate = Nominal rate − Inflation premium − Maturity-risk premium.
Plugging in the numbers: 0.045 − 0.023 − 0.005 = 0.017.
This evaluates to 1.7% per year when rounded to two decimal places, which matches the provided answer.

Now, evaluating the logic for the components:
- The inflation premium (2.3%) accounts for expected price level increases; subtracting it isolates the real component.
- The maturity-risk premium (0.5%) compensates for the risk of holding longer maturities; removing it yields the pure real rate.
- The no liquidity premium assumption simplifies the calculation by excluding any extra yield for liquidity.

If you consider potential pitfalls:
- One might mistakenly subtract inflation from the nominal rate and ignore the maturity-risk premium, which would overstate the real rate.
- Alternatively, treating the relationship as a multiplicative Fisher-type equation (1+Nominal) ≈ (1+Real)(1+Inflation) would yield a slightly different result, but the problem’s framing uses a straightforward additive decomposition, which leads to 1.7%.

In summary, the real risk-free interest rate is 1.7% per year, based on subtracting both the inflation premium and the maturity-risk premium from the observed nominal yield.

MCD2170 Foundations of Finance - Trimester 3 - 2025

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