cised over the quality and terms of the two issues compared, we estimate that the tax-exempt interest rate (rf) is approximately 75 percent of the taxable interest rate (r) for long-term securities.
It should be noted that these estimates apply only to long-term bonds. Comparing short-term prime housing notes (the highest quality government-guaranteed, tax-exempt security available) with U.S. Treasury bills of comparable maturity over year-end periods from 1961 to 1968 produced an average value for rf/r of about 0.58. It appears that the value of αb applicable to short-term issues is considerably lower than 0.75.
In footnote 82, we noted that the marginal risk premium on a security for a given investor would be ḡ + [(1 - m)/(1 - c)]d + ̄ - [1/(1 - c)] max [(1 - m)rz, rf]. This will vary systematically across investors because of the variation in tax rates across investors. In this appendix, the efficiency gains from redistributing risk among investors until all investors have the same risk premium at the margin are approximated.
To do this, the following simplifying assumptions on relative magnitudes are made:
(1) c = 0.2m; (2) rf = 0.75rz; (3) d + ̄ = 0.6rz; and (4) ḡ = rz.
With these assumptions, an investor's risk premium can be expressed as a function of his α = 1 - m/1 - c. This relationship was shown in figure 2.
To estimate the total efficiency gains resulting from a reallocation of risk across investors, the following assumptions were made: (1) the distribution of investors (weighted by their equity portfolio) across values of α is uniform between 0.35 and 1.0,100. and (2) each individual's risk premium is proportional to his holdings of risky securities.101.____________________