~ Rodreguez's Model

The estimated return on a bond,or yield to maturity (YTM), may be estimated using a quick and dirty model proposed by Robert Rodreguez. The foundation of the model is simply the classic (D/orig) where D is the change in value of the account, and "orig" is the original base value. Expanding this model further, D is made up of two components - the coupon payments [Pmts] and the capital gains. The capital gains are expressed as the total capital gains over the life of the bond (FV-Vb), divided by the number of years to maturity. The result is an "average annual capital gains".

The original base value is estimated as a weighted average value of the bond. The "face value" received at maturity is given a weight of 1, whereas the "current value", or "Vb" is given a weight of 2. Add these two weighted values together (3 pieces) and divide by 3 to get the "weighted average value". Rodreguez tried several weighting schemes to find this crude weight that seemed to yield the best results.

[Pmts] + FV-Vb

The model is: YTM or K_db= --------------ⁿ----

1-yr FV +2Vb

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where:

YTM= Yield to maturity, or the return on the bond if held to the date of maturity.

K_db= return on a debt instrument [i.e. a bond], assuming 1-year interval between interest payments [which isn't reality - but it's close].

Pmts= the dollar value of the annual interest payments

FV= future value=face value=$1000 The lump sum paid at the date of maturity.

Vb=the street value of the bond as of the most recent trade

n= number of whole years to maturity.

Example: What is the expected yield to maturity of the following bond listed in the Wall Street Journal? ABC 10.9 s 34 closing at 123¹/₂ (Note: this is calculated as of 1999)

_1000-1235__

109 + 35

Kdb= ----------------------------- = .088431 = 8.84%

1000 + 2 (1235)

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