FRM (Financial Risk Manager) Financial Markets and Products (Part I) Flashcards

24 sample cards from the Financial Markets and Products (Part I) deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Define backwardation.

   A market condition where the futures price is below the spot price ($F_0 < S_0$), a downward-sloping forward curve, often driven by a high convenience yield.

2. In the cost-of-carry model, what sign of $(r + u - y)$ produces backwardation?

   A negative net cost of carry, i.e. $r + u - y < 0$ (convenience yield dominates), gives $F_0 < S_0$ and backwardation; positive gives contango.

3. Why might forward and futures prices differ when interest rates are stochastic?

   Daily marking to market correlates margin cash flows with rates. If futures prices are positively correlated with rates, futures > forwards (gains reinvested at higher rates); if negatively correlated, futures < forwards.

4. Write the formula for converting an annual rate $R_c$ compounded $m$ times per year into its value $A$ after $T$ years on principal $P$.

   $$A = P\left(1 + \frac{R_c}{m}\right)^{mT}$$

5. Write the future value with continuous compounding at rate $R$.

   $$A = P\, e^{RT}$$

6. How do you convert a rate $R_m$ compounded $m$ times per year to an equivalent continuously compounded rate $R_c$?

   $$R_c = m \ln\!\left(1 + \frac{R_m}{m}\right)$$

7. How do you convert a continuously compounded rate $R_c$ to an equivalent rate $R_m$ compounded $m$ times per year?

   $$R_m = m\left(e^{R_c/m} - 1\right)$$

8. For a given nominal rate, how does the effective annual yield change as compounding frequency increases?

   The effective annual yield increases with compounding frequency, approaching the continuous-compounding limit; for rate $R$ the effective annual rate is $e^{R} - 1$ when compounded continuously.

9. Define the spot (zero) rate.

   The yield on a zero-coupon bond, i.e. the single interest rate for an investment that pays off entirely at one future date with no intermediate cash flows.

10. Define the forward rate.

    The interest rate, implied by current spot rates, for a future period of time—e.g., the rate agreed today for borrowing/lending between times $T_1$ and $T_2$.

11. Give the formula for the continuously compounded forward rate $R_f$ between times $T_1$ and $T_2$.

    $$R_f = \frac{R_2 T_2 - R_1 T_1}{T_2 - T_1}$$ where $R_1, R_2$ are the spot rates to $T_1$ and $T_2$.

12. Define the par rate (par yield).

    The coupon rate that makes a bond's price equal to its face (par) value given the current term structure; equivalently the coupon yielding a price of 100% of par.

13. Define the discount factor $DF(t)$ for time $t$.

    The present value today of $1 received at time $t$. With continuous compounding $DF(t) = e^{-R_t t}$; with discrete compounding $DF(t) = \frac{1}{(1 + R_t)^{t}}$, where $R_t$ is the spot rate.

14. Write the price of a coupon bond using discount factors.

    $$P = \sum_{i=1}^{n} c_i \, DF(t_i) + F \, DF(t_n)$$ where $c_i$ are coupons, $F$ is face value, and $DF(t_i)$ are the discount factors.

15. Define yield to maturity (YTM) of a bond.

    The single discount rate that sets the present value of all the bond's future cash flows equal to its current market price; the internal rate of return if held to maturity.

16. Write the bond pricing equation in terms of yield to maturity $y$ (annual compounding).

    $$P = \sum_{i=1}^{n} \frac{C}{(1+y)^{i}} + \frac{F}{(1+y)^{n}}$$ where $C$ is the periodic coupon and $F$ the face value.

17. State the inverse relationship between bond price and yield.

    Bond prices and yields move in opposite directions: when yields rise, bond prices fall, and when yields fall, prices rise (the price-yield curve is downward sloping and convex).

18. How does a bond's price relate to par when its coupon rate is above, equal to, or below its YTM?

    Coupon > YTM: bond trades at a premium (price > par). Coupon = YTM: at par. Coupon < YTM: at a discount (price < par).

19. Define the term structure of interest rates.

    The relationship between interest rates (spot/zero rates) and their maturities, depicted by the yield curve for otherwise identical (default-free) instruments.

20. Name three theories explaining the shape of the term structure.

    Expectations theory (forwards reflect expected future spot rates), liquidity preference theory (investors demand a premium for longer maturities), and market segmentation theory (rates set by supply/demand within maturity segments).

21. What does an upward-sloping (normal) yield curve typically imply under the expectations theory?

    Markets expect future short-term interest rates to rise; long-term rates exceed short-term rates.

22. What is bootstrapping in the context of the term structure?

    A sequential method of extracting zero/spot rates from the prices of coupon-bearing bonds, solving for each successive spot rate using previously derived discount factors.

23. What is the relationship between forward rates and spot rates when the spot curve is upward sloping?

    When the spot (zero) curve is upward sloping, forward rates lie above the spot rates; when it is downward sloping, forward rates lie below the spot rates.

24. Why is YTM an imperfect single measure of a coupon bond's return?

    It assumes all coupons are reinvested at the YTM and that the bond is held to maturity; it also applies one rate to all cash flows, ignoring the actual term structure of spot rates.

What this deck covers

Financial Markets and Products (Part I) flashcards FAQ