Amortization, bond pricing, duration and convexity, immunization, forwards and options.
39 cards · mixed cards · AI-written, checked twice. Edit anything.
- What is amortization in the context of loans?
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The process of paying off a loan through a series of equal payments, each covering both principal and interest.- Formula for outstanding loan balance at time k (using retrospective method)
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B_k = L(1+i)^k - PMT * [((1+i)^k - 1) / i], where L is initial loan, i is periodic rate, PMT is payment- What does Macaulay duration measure?
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The weighted average time to receive a bond's cash flows, measured in years.- Relationship between modified duration and Macaulay duration
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Modified duration = Macaulay duration / (1 + y), where y is the bond's yield per period- What does modified duration measure?
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The approximate percentage change in a bond's price for a 1% change in yield.- Define convexity for a bond.
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A measure of the curvature in the relationship between bond prices and yields; the second derivative of price with respect to yield.- Bond price approximation using duration and convexity
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Delta P = -D_mod * P * Delta y + 0.5 * Conv * P * (Delta y)^2, where D_mod is modified duration, Conv is convexity- What is a par bond?
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A bond whose coupon rate equals its yield to maturity, so it trades at face value.- What is a premium bond?
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A bond whose coupon rate exceeds its yield to maturity, so it trades above par value.- What is a discount bond?
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A bond whose coupon rate is less than its yield to maturity, so it trades below par value.- Bond pricing formula for annual coupons
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P = C * [1 - (1+y)^(-n)] / y + F * (1+y)^(-n), where C is annual coupon, y is yield per period, n is periods, F is face value- What is immunization against interest rate risk?
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A portfolio strategy that sets the investment horizon equal to the portfolio's duration, so the price effect and reinvestment effect offset.- What is cash flow matching (or dedication)?
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A bond portfolio strategy where cash flows exactly match a schedule of future liabilities, eliminating reinvestment and price risk.- Define a forward contract.
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An agreement to buy or sell an asset at a specified price (forward price) on a specified future date.- Relationship between spot rate and forward rate
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Forward rate f(0,t) = [(1+s(t))^t / (1+s(t-1))^(t-1)] - 1, where s is spot rate, t is time period
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