1. Taxable Equivalent Yield (TEY) - A staple used in comparing tax-exempt yields on municipal bonds to taxable yields on corporate and other bonds, it is the yield at which an investor would be indifferent to either, e.g. the yield that equates that of a tax-exempt bond to that of a taxable one.

TEY=6%/(1-.28)=8.33%
Where:
6% is the tax-exempt yield on a municipal bond.
28% is the investor\'s tax bracket.


One takes the tax-exempt yield and divides it by the reciprocal of the investor's tax bracket to "gross up" that yield to its taxable equivalent.


In this example, a client in the 28% tax bracket investing in a 6% tax-exempt municipal bond would need to find a taxable bond yielding 8.33% to be indifferent to the two yields.

Note that the higher the individual's tax bracket, the greater the merit of investing in municipal bonds. Conversely, an investor in a lower tax bracket would benefit little from investing in a municipal bond.
  1. Tax-Adjusted Return - This illustrates the return on an investment after taxes are taken into account. The after-tax return should reflect both federal and local taxes. The calculation is an important tool in comparing after-tax returns of different investments. The formula reads as follows:

After-tax yield=(Return from appreciation + (capital gains and dividends x (1-individual marginal tax bracket))). The after-tax calculation for an investor in a 28% marginal tax bracket with a 13% return (10% from appreciation and 3% from capital gains and dividends) would be obtained as follows: 0.1216 = (.1 + (.03 x (1-.28)))
  1. Weighted-Average Return - This is the return of a group of securities weighted for each by its weight relative to the total portfolio. An example of the calculation follows:

Company Market Price % of Total Return Weighted return
α 27 35.06% 26% 9.12%
β 42 54.55% 3% 1.36%
µ 8 10.39% 19% 1.97%
77 100% 48% 12.45%


Each market price is divided by the sum of the prices to arrive at the total. The percentage weight of each stock is, in turn, multiplied by its return to arrive at its weighted return. The weighted returns are summed to arrive at the portfolio's weighted return.


One may use a similar approach to calculate the weighted average beta of a portfolio or the weighted average duration of a portfolio.



Duration, Convexity and Capitalized Earnings

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