CFA一級(jí)知識(shí)點(diǎn)大剖析之Fixed Income

　　1. Which of the following statements about option-adjusted spread and nominal spread is least likely accurate?
　　A. Option-adjusted spread will be lower than the nominal spread if the option favors the investor.
　　B. The difference between option-adjusted spread and nominal spread is zero for mortgage-backed securities because mortgage-backed securities do not contain embedded options.
　　C. The longer the deferred call period, the closer the value of the option-adjusted spread will be to the value of the nominal spread.
　　Correct answer = D
　　Z-Spread＝OAS＋option cost, Nominal spread可以約等于Z-spread，可以用來(lái)判斷變化的方向，但是準(zhǔn)確的關(guān)系是上面的公式。
　　A選項(xiàng)，如果option對(duì)投資者有利的話，OAS是低于nominal spread的，比如callable bond，所以A是正確的。
　　B選項(xiàng)，MBS是包含一個(gè)embedded option的，因?yàn)镸BS給發(fā)行者一個(gè)right of the underlying borrowers in a pool of loans to prepay principal above the scheduled principal payment，所以O(shè)AS和nominal spread之差不是零，C是錯(cuò)誤的。
　　C選項(xiàng)，The longer the deferred call period, callable bond就越接近于不含權(quán)債券，那么OAS和nominal spread就越接近，D是正確的。
　　2.  Which of the following correctly describes a derivative that is a series of interest put option having expiration dates that corresponding to the reset dates on a floating-rate loans and to protect a floating-rate lender from a decline interest rate?
　　A.        interest rate cap
　　B.        interest rate floor
　　C.        interest rate collar
　　Correct answer = B
　　An interest rate floor is a series of interest put options, having expiration dates that corresponding to the reset dates on a floating-rate loans .The floor rate is minimum rate on the payments on a floating –rate loan.
　　3.  OAS will greater than nominal spread if the option favors the issue，這句話錯(cuò)在，不是nominal spread，而是z-spread。nominal spread和z-spread其實(shí)不是一種spread
　　Solution：首先nominal spread和z-spread不是一種spread。nominal spread是z-spread一個(gè)近似和替代，大致相等，但也有差異，（當(dāng)收益率曲線是陡峭的，本金償還速度比較快的時(shí)候，他們的差距是大的）
　　另外Z-spread=OAS+OPTION COST，含有對(duì)issuer有利的期權(quán)的時(shí)候，（callable bond）OPTION COST大于0，則Z-spread>OAS
　　4. An 8% coupon bond with a par value of 100, matures in 6 years and is selling at 95.51 with a yield of 9%.  Exactly one year ago this bond sold at a piece of 90.26 with a yield of 10%. The bond pays annual interest. The change in price attribute to the change in maturity is close to。。。
　　Solution：債券價(jià)格的變動(dòng)是由2方面引起的，一個(gè)是時(shí)間引起的變動(dòng)，一個(gè)是利率引起的變動(dòng)。
　　本題要求的是時(shí)間變動(dòng)后引起的價(jià)格變動(dòng)的多少。解題思路是這樣的：
　　pmt=8，n=7，一年前的 I/Y=10%，F(xiàn)V=100，求剛發(fā)行是bond的價(jià)格是90.26
　　接著pmt=8，n=6， I/Y=10%，F(xiàn)V=100，求PV， PV=91.28。所以91.28-90.26=1.03
　　那么如果題目是讓你求利率變動(dòng)引起的價(jià)格變動(dòng)的多少就是這樣求的：
　　pmt=8，n=7 ，  一年前的 I/Y=10%，F(xiàn)V=100，求剛發(fā)行是bond的價(jià)格是90.26
　　接著pmt=8，n=7 ， I/Y=9%，F(xiàn)V=100，求PV，因?yàn)橹灰罄首兓牟煌圆粻砍兜綍r(shí)間的變化，算出I/Y=9%的時(shí)候，PV=94.96。所以94.96-90.26=4.7