Index Funds and Variable Annuities

This article appeared in the February 1992 NAPFA News. NAPFA is the National Association of Personal Financial Advisors. The analytical model is available through my Spreadsheets page. Note that I’m not a financial advisor.

Index funds tend to have low portfolio turnover, resulting in fewer realized gains that must be distributed to shareholders. Realized gains are immediately taxable. Unrealized gains provide a tax-deferred, compounding effect.

A variable annuity is a vehicle primarily used to defer taxes on gains. It is similar to a non-deductible IRA. However, even if you could invest in your favorite mutual fund, the annual expense ratio would be higher than the same fund without the variable annuity feature.

Many investment advisors use the Standard & Poor’s 500 (S&P 500) Composite Stock Price Index as a benchmark for equity investments. It is therefore appropriate to examine the results of investing in an S&P 500 index mutual fund and the same fund offered through a variable annuity.

As you’ll see from the analysis of investments of $1 per year, the benefits of using a variable annuity are questionable. In both cases, I assumed the historical S&P 500 total return (capital appreciation + dividends) of 10 percent.

Without Variable Annuity

Based on the Vanguard S&P 500 Index fund distributions of the past decade, I assumed 50 percent of the total return (minus expenses) will be distributed and taxed each year. Note the low .2 percent annual expense ratio. The distribution can be reinvested, but the taxes should be subtracted from the value of the account. This results in the figures for the column labeled “End.” Assuming a 40 percent tax rate during the life of the investment and a 30 percent retirement tax rate on the accumulated appreciation upon full withdrawal, the account would be worth $102.02 after 30 years (“TV” column).

With Variable Annuity

Here I assumed the variable annuity would have no distributions until termination. The annual expense ratio is 1 percent. With a 30% tax rate upon full withdrawal, the account would be worth $113 after 30 years.

Is having 10.8 percent more after 30 years worth the lack of liquidity?

Bold text items can be changed in the spreadsheet.

WITHOUT VARIABLE ANNUITY WITH VARIABLE ANNUITY
F 50% Fraction of (Return-Expenses) Paid Out F 0% Fraction of (Return-Expenses) Paid Out
I $1 Annual Investment I $1 Annual Investment
T 40% Tax Rate for Distributions T 40% Tax Rate for Distributions
E 0.2% Expenses E 1.0% Expenses
R 10% Return R 10% Return
TF 30% Tax Rate for accumulated appreciation TF 30% Tax Rate for accumulated appreciation
* Value after paying taxes on distributions * Value after paying taxes on distributions
** Termination Value after taxes on dist. & apprec. ** Termination Value after taxes on dist. & apprec.

I Start Dist. Apprec. End* TV** I Start Dist. Apprec. End* TV**
1 1 1.00 0.049 0.049 1.08 1.06 1 1 1.00 0.000 0.090 1.09 1.06
2 1 2.08 0.102 0.102 2.24 2.20 2 1 2.09 0.000 0.188 2.28 2.19
3 1 3.24 0.159 0.159 3.50 3.40 3 1 3.28 0.000 0.295 3.57 3.40
4 1 4.50 0.220 0.220 4.85 4.69 4 1 4.57 0.000 0.412 4.98 4.69
5 1 5.85 0.287 0.287 6.31 6.06 5 1 5.98 0.000 0.539 6.52 6.07
6 1 7.31 0.358 0.358 7.88 7.53 6 1 7.52 0.000 0.677 8.20 7.54
7 1 8.88 0.435 0.435 9.58 9.09 7 1 9.20 0.000 0.828 10.03 9.12
8 1 10.58 0.518 0.518 11.40 10.77 8 1 11.03 0.000 0.993 12.02 10.81
9 1 12.40 0.608 0.608 13.38 12.56 9 1 13.02 0.000 1.172 14.19 12.64
10 1 14.38 0.704 0.704 15.50 14.47 10 1 15.19 0.000 1.367 16.56 14.59
11 1 16.50 0.809 0.809 17.80 16.52 11 1 17.56 0.000 1.580 19.14 16.70
12 1 18.80 0.921 0.921 20.27 18.72 12 1 20.14 0.000 1.813 21.95 18.97
13 1 21.27 1.042 1.042 22.94 21.08 13 1 22.95 0.000 2.066 25.02 21.41
14 1 23.94 1.173 1.173 25.82 23.60 14 1 26.02 0.000 2.342 28.36 24.05
15 1 26.82 1.314 1.314 28.92 26.31 15 1 29.36 0.000 2.642 32.00 26.90
16 1 29.92 1.466 1.466 32.26 29.21 16 1 33.00 0.000 2.970 35.97 29.98
17 1 33.26 1.630 1.630 35.87 32.33 17 1 36.97 0.000 3.328 40.30 33.31
18 1 36.87 1.807 1.807 39.76 35.68 18 1 41.30 0.000 3.717 45.02 36.91
19 1 40.76 1.997 1.997 43.96 39.28 19 1 46.02 0.000 4.142 50.16 40.81
20 1 44.96 2.203 2.203 48.48 43.14 20 1 51.16 0.000 4.604 55.76 45.04
21 1 49.48 2.425 2.425 53.36 47.30 21 1 56.76 0.000 5.109 61.87 49.61
22 1 54.36 2.664 2.664 58.63 51.76 22 1 62.87 0.000 5.659 68.53 54.57
23 1 59.63 2.922 2.922 64.30 56.56 23 1 69.53 0.000 6.258 75.79 59.95
24 1 65.30 3.200 3.200 70.42 61.72 24 1 76.79 0.000 6.911 83.70 65.79
25 1 71.42 3.500 3.500 77.02 67.27 25 1 84.70 0.000 7.623 92.32 72.13
26 1 78.02 3.823 3.823 84.14 73.24 26 1 93.32 0.000 8.399 101.72 79.01
27 1 85.14 4.172 4.172 91.81 79.66 27 1 102.72 0.000 9.245 111.97 86.48
28 1 92.81 4.548 4.548 100.09 86.57 28 1 112.97 0.000 10.167 123.14 94.59
29 1 101.09 4.953 4.953 109.01 94.01 29 1 124.14 0.000 11.172 135.31 103.42
30 1 110.01 5.391 5.391 118.64 102.02 30 1 136.31 0.000 12.268 148.58 113.00
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