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Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice. An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility .
For a standard bond, the Macaulay duration will be between 0 and the maturity of the bond. It is equal to the maturity if and only if the bond is a zero-coupon bond . Modified duration, on the other hand, is a mathematical derivative (rate of change) of price and measures the percentage rate of change of price with respect to yield.
Repricing risks arise from timing differences in the maturity for fixed-rate and repricing for floating-rate bank assets, liabilities and off-balance-sheet positions. [3] Any instance of an interest rate being reset—either due to maturities or floating interest rate resets—is called a repricing. The date on which it occurs is called the ...
Formally, the duration gap is the difference between the duration - i.e. the average maturity - of assets and liabilities held by a financial entity. [3] A related approach is to see the "duration gap" as the difference in the price sensitivity of interest-yielding assets and the price sensitivity of liabilities (of the organization) to a change in market interest rates (yields).
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The formula for calculating 30-day yield is specified by the U.S. Securities and Exchange Commission (SEC). [1] The formula translates the bond fund's current portfolio income into a standardized yield for reporting and comparison purposes.
Although the amortizing bond and the zero-coupon bond have different sensitivities at the same maturity, if their final maturities differ so that they have identical bond durations then they will have identical sensitivities. [7] That is, their prices will be affected equally by small, first-order, (and parallel) yield curve shifts.