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# L1.T4.12. Spot rates

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
AIMs: Calculate and describe the impact of different compounding frequencies on a bond’s value. Calculate holding period returns under different compounding assumptions. Derive spot rates from discount factors. Calculate the value of a bond using spot rates.

Questions:

12.1. The spot rate curve is flat for all maturities at 4.0%. A $100 face value bond with a three-year maturity pays an annual coupon of 6.0%. If we first price the bond under annual compounding, but then re-price the bond under continuous compounding, what is the change in bond price the results solely from the change to continuous compounding? a. No change (the yield is unchanged) b. Increase of$0.17 (i.e., from annual to continuous)
c. Decrease of $0.19 d. Decrease of$0.23

12.2. An initial investment of $100 made ten (10) years ago has grown to$415 today. What is the (realized) holding period return under an assumption, respectively, of semiannual (s.a.) and annual (CAGR) compounding?
a. 14.23% (s.a.) and 14.75% (CAGR)
b. 14.75% (s.a.) and 15.29% (CAGR)
c. 15.29% (s.a.) and 15.72% (CAGR)
d. 15.72% (s.a.) and 16.36% (CAGR)

12.3. The following discount function contains semi-annual discount factors out to two years: d(0.5) = 0.9970, d(1.0) = 0.9911, d(1.5) = 0.9809, d(2.0) = 0.9706. What is the implied eighteen-month (1.5 year) spot rate (aka, 1.5 year zero rate)?
a. 0.600%
b. 1.176%
c. 1.290%
d. 1.505%

12.4. If the spot rate term structure is flat, what is true of the discount function (i.e., the set of discount factors) as function of maturity?
a. Flat
b. Increasing with maturity
c. Decreasing with maturity
d. Insufficient information: we need the yield (YTM) to answer

12.5. The spot rate term structure is upward-sloping: 1.0% at 0.5 years, 2.0% at 1.0 years, 3.0% at 1.5 years, and 4.0% at 2.0 years. What is the price of two-year $100 face value bond that pays a semi-annual coupon with a 6.0% per annum coupon rate? a.$99.74
b. $101.67 c.$102.27
d. \$103.95