8.7 Realized Compound Yield: Formula and Problems
The formula below is one which you should already know. Does it make sense to you? Can you explain it?
[latex]\frac{{[[$ CPN/P) (FVAF)] +(Par Value)]^{1/np}}}{[$ CPN/P) (PVAF)]+[ParValue)(PVF)]} -1\times P= RCY[/latex]
Do you know all the abbreviations?
You will note in the formula that the numerator is the terminal value, or future value, of the bond. This is the zero-coupon equivalent of a positive coupon bond, assuming a certain reinvestment rate. The denominator is, of course, the present value, or price, of the bond, given a certain market yield, or yield-to-maturity.
Problems
For each of the following, you are given the following. In all cases, assume that n = 10 and P = 2 (i.e., semi-annual). There are no taxes. Solve for the RCY.
- CPN = .06; YTM = .06; REIN = .02
- CPN = .05; YTM = .06; REIN = .04
- CPN = .07; YTM = .06; REIN = .06
- CPN = .05; YTM = .06; REIN = .08
- CPN = .07; YTM = .06; REIN = .08
Sample Solution (Question #1):
{[(30) (22.019) + (1,000)] ÷ [(1,000)]}1/20 – 1 = 0.02568 (semi-annual) × 2 = 0.05136
Sample Solution (Question #2):
{[(25) (24.297) + (1,000)] ÷ [(25) (14.8775) + (1,000) (0.5537)]}1/20 – 1 = 0.02798 (semi-annual)
0.02798 × 2 = 0.05596
Sample Solution (Question #3): See “relationships” below.
- If REIN = YTM, then RCY = YTM
- If REIN > YTM, then RCY > YTM (and vice versa)
Sample Solution (Question #5):
{[(35) (29.778) + (1,0000] ÷ [(35) (14.8775) + (1,000) (0.5537)]}1/20 – 1 = 0.03263 (semi-annual)
0.02798 × 2 = 0.06527
