2019 CFA level 2 finquiz notes fixed inc
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2019 CFA level 2 finquiz notes fixed inc
Reading 34The Term Structure and Interest Rate DynamicsSpot Rates and Forward RalesThe price of risk-free single-unit payment at time T is referred to 2019 CFA level 2 finquiz notes fixed inc o as 'Discount Factor’, denoted as p (T|.p m = -----!—- =.———1 ' íl-ĩỊ>ữíraie]ĩ [l-r(T)lrPractice: Example 1, Reading 34.Discount Function is the discount factor for a range of maturities in years (T) greater than zero while the spot yield curve represents the term structure of interest rates at an 2019 CFA level 2 finquiz notes fixed inc y point in time. The shape and level of spot yield curve changes over time because the spot rate represents the annualized return on an option-free an2019 CFA level 2 finquiz notes fixed inc
d default risk-free zero-coupon bond with a single payment of principal at maturity. Under the spot yield curve, there is no reinvestment risk and theReading 34The Term Structure and Interest Rate DynamicsSpot Rates and Forward RalesThe price of risk-free single-unit payment at time T is referred to 2019 CFA level 2 finquiz notes fixed inc bonds, priced at par. over a range of maturities is called par curve. Typically, recently issued |"on the run") bonds are used to build the par curve because on the run issues are generally priced at or close to par. The one-year zero-coupon rate is equal to the one-year par rate.Forward rale is an 2019 CFA level 2 finquiz notes fixed inc Interest rate for a loan Initiated r years from today with maturity of T years. It is denoted by f |T*. Ĩ). The term structure of forward rates for a2019 CFA level 2 finquiz notes fixed inc
loan made on a specific initiation date is called the forward curve in a forward contract, the parties to the contract do not exchange money at contraReading 34The Term Structure and Interest Rate DynamicsSpot Rates and Forward RalesThe price of risk-free single-unit payment at time T is referred to 2019 CFA level 2 finquiz notes fixed inc incipal payment of bond at time T* + T.The forward pricing model is stated as below: p (T* ♦ T) ■ p (T*) X F (T*.T)' p |T’+ T) is the cost of a zero-coupon bond, having maturity of ĩ* + T years.>The right hand side of the equation reflects a forward contract where, p |T*) X F(T',T| is the present va 2019 CFA level 2 finquiz notes fixed inc lue of a zero-coupon bond with maturity T at time T*.>The equation implies that Initial costs of the two Investments must be the same because both inv2019 CFA level 2 finquiz notes fixed inc
estments have same payoffs at time ĩ' + T. If the initial cost is not same, an investor can earn risk-free profits with zero net investment by sellingReading 34The Term Structure and Interest Rate DynamicsSpot Rates and Forward RalesThe price of risk-free single-unit payment at time T is referred to 2019 CFA level 2 finquiz notes fixed inc for a risk-free unit-principal payment r + T years from today, valued at time r. such that the present value equals the forward contract price. F(T*.T). E.g. f (5. I) Is the rate agreed on today for a one-year loan to be made five years from today. Forward rate can be viewed as a rate that can be lo 2019 CFA level 2 finquiz notes fixed inc cked in by extending maturity by one year. Forward rate can also be viewed as a break-even interest rate because it is the rate at which an investor I2019 CFA level 2 finquiz notes fixed inc
s indifferent between buying a six-year zero-coupon bond or in vesting in a five-year zerocoupon bond and at maturity reinvesting the proceeds for oneReading 34The Term Structure and Interest Rate DynamicsSpot Rates and Forward RalesThe price of risk-free single-unit payment at time T is referred to 2019 CFA level 2 finquiz notes fixed inc ates.X Spot rate for T" ♦ T is r(T* + T).X Spot rate for T* is r (T*).Practice: Example 2, Reading 34.Spot rate for a security, having maturity of T > I can be estimated by calculating geometric mean of spot rate for a security with a maturity of T = 1 and a series of Ĩ - 1 forward rates as shown be 2019 CFA level 2 finquiz notes fixed inc low:r (T) = (11 + r |1)1 [1 + f (1.1)] |1 ♦ f (2.1)1 (1 ♦ f |3,1|]... [1 * f(T-1.1)1) M7[|+r('”+r)] ■[|+/(7’,)]E.g. suppose T* = 1, T = 5, r (I) = 2%,2019 CFA level 2 finquiz notes fixed inc
and r (6) = 4%:(104) = 1.044 -»f (1,5) =4 405%FinQuiz Notes 2 0 19Copyright® RnQviz com. All rights reserved.https: //khoth u Vi e n .comReccing 34ThReading 34The Term Structure and Interest Rate DynamicsSpot Rates and Forward RalesThe price of risk-free single-unit payment at time T is referred to 2019 CFA level 2 finquiz notes fixed inc spot curve This rnp'ies that when the yield curve is upward sloping, r(T* + T) > r(T’| and the forward rate rises as T’ increases: which means that the forward rate from T* to T Is greater than the long-term |T + T) spot rate: f(T‘.T| > r(T* * Ĩ). Opposite occurs when yield curve is downward-slopin 2019 CFA level 2 finquiz notes fixed inc g. In the above exampie. 4.405% > 4%.r When the yield curve is flat, all one-period forward rates = spot rate.Practice: Example 3 4 4, Reading 34.rest2019 CFA level 2 finquiz notes fixed inc
rain rapidly growing economy, a central bank may raise interest rates that results in rise in short-term yields to reflect hike in rates, while long-tReading 34The Term Structure and Interest Rate DynamicsSpot Rates and Forward RalesThe price of risk-free single-unit payment at time T is referred toReading 34The Term Structure and Interest Rate DynamicsSpot Rates and Forward RalesThe price of risk-free single-unit payment at time T is referred toGọi ngay
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