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Exam FM — Determinants of Interest Rates Practice Flashcards

Thirty original exam-style multiple-choice problems on the determinants of interest rates for SOA/CAS Exam FM, covering rate components, the Fisher equation, central banks and loanable funds, the term structure and yield-curve theories, spot and forward rates, and bond covenants and default risk.

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  1. Rate components
    A 20-year corporate bond yields $8.10\%$. An analyst decomposes the yield using the additive build-up $r \approx r^{*} + IP + DRP + LP + MRP$. She estimates the real risk-free rate $r^{*} = 1.40\%$, the inflation premium $IP = 2.60\%$, the default-risk premium $DRP = 2.00\%$, and the maturity-risk premium $MRP = 1.30\%$. Calculate the implied liquidity premium $LP$. (A) $0.50\%$ (B) $0.70\%$ (C) $0.80\%$ (D) $1.00\%$ (E) $1.30\%$
    **Answer: (C).** Using the additive build-up and solving for the liquidity premium: $LP = r - (r^{*} + IP + DRP + MRP)$. $LP = 8.10\% - (1.40\% + 2.60\% + 2.00\% + 1.30\%)$. $LP = 8.10\% - 7.30\% = 0.80\%$.
  2. Rate components
    Two bonds are identical except for their issuers. Bond X is a 10-year U.S. Treasury yielding $4.30\%$. Bond Y is a 10-year corporate bond from a single issuer, is thinly traded, and yields $6.95\%$. The only differences in the additive build-up between the two bonds are the default-risk premium and the liquidity premium. A rating agency estimates the default-risk premium on Bond Y at $1.85\%$. Calculate the liquidity premium on Bond Y. (A) $0.45\%$ (B) $0.80\%$ (C) $1.85\%$ (D) $2.65\%$ (E) $4.50\%$
    **Answer: (B).** The Treasury and the corporate share the same real risk-free rate, inflation premium, and maturity-risk premium (same maturity, default-free benchmark), so the entire yield difference is the default-risk premium plus the liquidity premium. Yield spread $= 6.95\% - 4.30\% = 2.65\%$. This spread equals $DRP + LP$, so $LP = 2.65\% - 1.85\% = 0.80\%$.
  3. Rate components
    An investor is comparing two newly issued bonds from the **same** issuer, both option-free and identically secured. Bond P matures in 3 years; Bond Q matures in 25 years. Which single rate component is most responsible for Bond Q being issued at a higher yield than Bond P? (A) The real risk-free rate $r^{*}$ (B) The inflation premium $IP$ (C) The default-risk premium $DRP$ (D) The liquidity premium $LP$ (E) The maturity-risk premium $MRP$
    **Answer: (E).** The two bonds share the same issuer (same credit quality, so the same default-risk premium) and the same currency and base economy (same real risk-free rate and inflation premium). The defining difference is time to maturity. The **maturity-risk premium** compensates for the greater interest-rate (price) sensitivity of longer-maturity bonds and grows with term, so it is the component driving Bond Q's higher yield. Liquidity differences are not indicated by the maturity difference alone.
  4. Rate components
    A money-market instrument has a nominal annual effective yield of $5.30\%$. Over the same horizon the real risk-free rate is $1.80\%$ and the instrument carries no default, liquidity, or maturity premium. Using the additive (approximate) build-up, an analyst infers the inflation premium and reports it as the expected inflation rate. Which of the following is closest to the inflation premium the analyst reports? (A) $3.21\%$ (B) $3.44\%$ (C) $3.50\%$ (D) $5.30\%$ (E) $7.10\%$
    **Answer: (C).** With no default, liquidity, or maturity premium, the additive build-up reduces to $r \approx r^{*} + IP$. $IP = r - r^{*} = 5.30\% - 1.80\% = 3.50\%$. Note: option (B) $3.44\%$ is the exact-Fisher inflation rate $\frac{1.0530}{1.0180}-1$, but the problem specifies the **additive** build-up, so the inflation premium is the simple difference, $3.50\%$.
  5. Fisher equation
    A bond's nominal annual effective rate is $i$ and the annual inflation rate is $\pi = 5\%$. An investor wants a real annual effective return of exactly $3\%$ using the **exact** Fisher equation. Calculate the required nominal rate $i$. (A) $7.86\%$ (B) $8.00\%$ (C) $8.15\%$ (D) $8.20\%$ (E) $8.30\%$
    **Answer: (C).** Exact Fisher: $1 + i = (1 + r)(1 + \pi)$. $1 + i = (1.03)(1.05) = 1.0815$. $i = 0.0815 = 8.15\%$. (The approximation $r + \pi = 3\% + 5\% = 8.00\%$, option (B), understates the required nominal rate by the cross term $r\pi = 0.15\%$.)
  6. Fisher equation
    An investment earns a nominal annual effective rate of $11.5\%$ during a year in which the inflation rate is $7.0\%$. Using the exact Fisher equation, calculate the real annual effective rate of return. (A) $4.06\%$ (B) $4.21\%$ (C) $4.50\%$ (D) $4.65\%$ (E) $4.83\%$
    **Answer: (B).** Exact Fisher: $1 + r = \dfrac{1 + i}{1 + \pi} = \dfrac{1.115}{1.070}$. $1 + r = 1.042056$, so $r = 0.042056 \approx 4.21\%$. (The approximation $i - \pi = 11.5\% - 7.0\% = 4.5\%$, option (C), overstates the real rate.)
  7. Fisher equation
    Over a one-year period an investor's purchasing power, measured in real terms, grows by exactly $2.5\%$. The nominal annual effective rate of return earned was $9.675\%$. Using the exact Fisher equation, calculate the inflation rate over the year. (A) $7.00\%$ (B) $7.05\%$ (C) $7.18\%$ (D) $7.33\%$ (E) $12.42\%$
    **Answer: (A).** Exact Fisher: $1 + i = (1 + r)(1 + \pi)$, so $1 + \pi = \dfrac{1 + i}{1 + r}$. $1 + \pi = \dfrac{1.09675}{1.025} = 1.07000$. $\pi = 0.07000 = 7.00\%$. (The approximation $i - r = 9.675\% - 2.5\% = 7.175\%$, near option (C), overstates inflation.)
  8. Fisher equation
    An economy has a real annual effective rate of $r = 4\%$ and an inflation rate of $\pi = 9\%$. A student computes the nominal rate two ways: once with the exact Fisher equation and once with the approximation $i \approx r + \pi$. Calculate the absolute difference between the exact and approximate nominal rates. (A) $0.00\%$ (B) $0.13\%$ (C) $0.36\%$ (D) $0.45\%$ (E) $1.30\%$
    **Answer: (C).** Exact: $1 + i = (1.04)(1.09) = 1.1336$, so $i = 13.36\%$. Approximate: $i \approx r + \pi = 4\% + 9\% = 13.00\%$. The difference is exactly the dropped cross term $r\pi = (0.04)(0.09) = 0.0036 = 0.36\%$, and $13.36\% - 13.00\% = 0.36\%$.