Investments, tenth edition

5.1 

  Taxes and the Real Rate of Interest 

 Tax liabilities are based on  nominal  income and the tax rate determined by the investor’s 

tax bracket. Congress recognized the resultant “bracket creep” (when nominal income 

grows due to inflation and pushes taxpayers into higher brackets) and mandated index-

linked tax brackets in the Tax Reform Act of 1986. 

 Index-linked tax brackets do not provide relief from the effect of inflation on the taxa-

tion of savings, however. Given a tax rate ( t ) and a nominal interest rate,  rn,  the after-tax 

interest rate is  rn (1  2   t ). The real after-tax rate is approximately the after-tax nominal rate 

minus the inflation rate:   

 

rn(1 2 t) 2 i 5 (rr 1 i)(1 2 t) 2 i 5 rr (1 2 t) 2 it 

 (5.5)   

 Thus the after-tax real rate falls as inflation rises. Investors suffer an inflation penalty 

equal to the tax rate times the inflation rate. If, for example, you are in a 30% tax bracket 

and your investments yield 12%, while inflation runs at the rate of 8%, then your before-

tax real rate is approximately 4%, and you  should,  in an inflation-protected tax system, net 

after taxes a real return of 4%(1  2  .3)  5  2.8%. But the tax code does not recognize that 

the first 8% of your return is just compensation for inflation—not real income—and hence 

your after-tax return is reduced by 8%  3  .3  5  2.4%, so that your after-tax real interest rate, 

at .4%, is almost wiped out.    

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P A R T   I I

  Portfolio Theory and Practice

    5.2 

Comparing Rates of Return for Different 

Holding Periods 

  Consider an investor who seeks a safe investment, say, in U.S. Treasury securities.  

4

   We 

observe zero-coupon Treasury securities with several different maturities. Zero-coupon 

bonds, discussed more fully in Chapter 14, are sold at a discount from par value and pro-

vide their entire return from the difference between the purchase price and the ultimate 

repayment of par value.  

5

   Given the price,  P ( T ), of a Treasury bond with $100 par value and 

maturity of  T  years, we calculate the total risk-free return available for a horizon of  T   years 

as the percentage increase in the value of the investment.

   

   

 

r

f

(T ) 5

100

P(T )

2 1 

 (5.6)   

 For   T   5  1, Equation 5.6 provides the risk-free rate for an investment horizon of 1 year.  

 Suppose prices of zero-coupon Treasuries with $100 face value and various maturities 

are as follows. We find the total return of each security by using Equation 5.6: