CFA Level 2 - Fixed Income Spot Rates - Answer: the annualized market interest rates for a single payment to be received in the future. Generally, we use spot rates for government securities (risk free) to generate the spot rate curve. Spot rates can be interpreted as the yields on zero coupon bonds. Spot rates b/c of this may be referred to as zero coupon rates forward rate - Answer: an interest rate (agreed to today) for a loan to be made at some future date. spot rate (calculation) - Answer: the price today of $1, zero coupon bond is known as the discount factor, which we will call Pt. B/c it is a zero-coupon bond, the spot interest rate is the yield to maturity of this payment, which we represent as St. The relationship between the discount factor Pt and the spot rate St for maturity T can be expressed as: Pt= 1/(1+St)to the T Spot yield curve or spot curve - Answer: the term structure of spot rates - the graph of the spot rate St versus the maturity T - is known as this. The shape and level of the spot curve changes continuously with the market prices of bonds. Forward rate (calculation) - Answer: the annualized interest rate on a loan to be initiated at a future period is called the forward rate for that period. The term structure of forward rates is called the forward curve. CFA Level 2 - Fixed Income f(j,k) = the annualized interest rate applicable on a k year loan starting in j years. F(j,k) = forward price of a $1 par zero coupon bond maturing at time j+k delivered at time j. F (j, k) = the discount factor associated with the forward rate F (j, k) = 1/(1_f(j,k)) to the k. yield to maturity - Answer: or yield of zero coupon bond with maturity T is the spot interest rate for a maturity of T. However, for a coupon bond, if the spot rate curve is not flat, the YTM will not be the same as the spot rate. Expected returns on bonds - Answer: the ex-ante holding period return that a bond investor expects to earn the expected return will be equal to the bond's yield only when all three are true - the bond is held to maturity - all pmts (coupon and principal) are made on time and in full - all coupons are reinvested at the original YTM the second requirement implies that the bond is option free and there is no default risk CFA Level 2 - Fixed Income the last requirement, reinvesting coupons at the ytm, is the least realistic assumption. If the yield curve is not flat, the coupon payments will not be reinvested at the ytm and the expected return will differ from the yield. realized return on bonds - Answer: the actual return that the investor experiences over the investment's holding period. realized return is based on actual reinvestment rates forward pricing model - Answer: values forward contracts based on arbitrage free pricing f9j,k) = P(j+k)/Pj forward rate model - Answer: relates forward and spot rates as follows: (1+S(j+k))to the (j+k)=(1=Sj)to the j*(1+f(j,k))to the k par rate - Answer: the yield to maturity of a bond trading at par. par rate curve or par curve - Answer: par rates for bonds with difference maturities. by definition, the par rate will be equal to the coupon rate on the bond. Generally, par curve refers to the par rates for government or benchmark bonds.