How to Calculate P Value From Test Statistic

Prudent buying and selling points can enhance S&P 500 return.

A gross (before-expenses) return on the S&P 500 over several years is annualized to provide the average return per year. To get a return for the S&P 500, one invests in a fund that tracks the index. Fund expenses, simplified as expense ratios, work to lessen capital gains. Inflation and taxes upon withdrawal further work against an investor to lessen net return.

Step 1

Use index values to calculate gross return. As an example, say a $1,000 investment was made on April 25, 2005. Suppose that all the funds were withdrawn on April 26, 2010. On April 25, 2005, the S&P 500 Roth Index (symbol "^GSPC") was at 1162.10 points. Five years later, on April 26, 2010, the index was at 1212.05. The difference between the two values is:1212.05-1162.10 = 49.95. This number is divided by the starting value to get a decimal of 0.0429, or 4.29 percent over five years.

Step 2

Annualize gross return. The average per-year return would be 4.29 / 5 = 0.858 percent. Average annual dollar return was 42.9 / 5 = $8.58.

Step 3

Factor in the annual expense ratio. The fund prospectus for the United Association S&P 500 Index (Class I) gives a 0.28 percent expense ratio. For simplicity, assume gross annual return of 0.858 percent and annual expense ratio of 0.280 percent. Calculating again: 0.280/0.858 * 100 percent yields 32.6 percent. Now the annual return is 8.58 * (1-0.326), or $5.78. Over five years, the dollar return would be 28.9 (5.78 *5).

Step 4

Pay taxes. There are no taxes due between 2005 and 2009 because the money is invested in the fund, not available for spending. Upon collection in 2010, the money is subject to the 2010 tax rate on capital gains. Assuming capital gains tax rate is 15 percent, after-tax return is 85 percent (100-15) of what it was before. Result: 0.85 * 28.9 = $24.57. The after-tax return is now effectively 2.457 percent over five years.

Step 5

Remember inflation. Assume inflation is constant at 1 percent each year. Inflation-adjusted return can be calculated according to Investopedia's formula. With 2.475 percent return and 1 percent inflation, post-inflation return is (1.02475 / 1.01) – 1 = 0.0146, or 1.46 percent. This corresponds to 10.46 after-tax, after-inflation dollars over five years; 10.46/5 = $2.09 per year.

Tip

To clarify expense ratio: Assume an investment of $1,000 produced a nominal 2 percent annual return, with 1 percent annual expense ratio. After one year, a 2 percent return yields $20 gains (1,000_0.02 = 20). The expense ratio works out as: 1,000_0.01 = $10. Therefore, at the end of the year, $10 is subtracted from the account. The subtracted $10 is 50 percent (10/20 = 0.5) of nominal return, leaving the other $10, not $20, as actual (pre-tax, pre-inflation-adjusted) capital gains.

Warning

The expense ratio operates regardless of whether returns are positive or negative. If return is negative, the expense ratio takes another percentage-based bite out of the invested amount, deepening the loss.

It might be argued that fund expense ratios, inflation and taxes are not strictly "the return," but are instead "outside" concerns. This is technically true, but such expenses are inevitable. Ignoring them gives unrealistically high hopes for investment return. Granted, the capital gains tax rate may be zero if the investor is in a low-enough regular-income tax bracket. By incredible coincidence, inflation rate may also be zero during investment period. Such a financial scenario, however, is very unlikely, and masks complications for the vast majority of investors the vast majority of the time.

• S&P 500 Index price data

• Fund expense ratio

• Capital gains tax rate on withdrawal year

• Inflation data for investment duration

• Calculator

• Pen and paper

How to Calculate P Value From Test Statistic

Source: https://www.sapling.com/6454574/calculate-sp-500-return

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