Long-Term Returns

Section A.2 Long-Term Returns

We’ll use the following function to compute long-term returns. It takes a start date and a duration, and computes two ratios:

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The total price return based on actual annual returns.
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The total price return if annual returns are clipped at 0 and 10—that is, any negative returns are set to 0 and any returns above 10 are set to 10.
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Listing A.2.1. Python Code

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def compute_ratios(start=1993, duration=30):
    end = start + duration
    interval = annual.loc[start: end]
    ratio = interval['Ratio'].prod()
    low, high = 1.0, 1.10
    clipped = interval['Ratio'].clip(low, high)
    ratio_clipped = clipped.prod()
    return start, end, ratio, ratio_clipped

With this function, we can replicate the analysis The Economist did with the S&P 500. Here are the results for the DJIA from the beginning of 1980 to the end of 2023.

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Listing A.2.2. Python Code

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$ compute_ratios(1980, 43)
(1980, 2023, 44.93751117788029, 15.356490985533199)

A buffer ETF over this period would have grown by a factor of more than 15 in nominal dollars, with no risk of loss. But an index fund would have grown by a factor of almost 45. So yeah, the ETF would have been a bad deal.

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However, if we go back to the bad old days, an investor in 1900 would have been substantially better off with a buffer ETF held for 43 years.

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Listing A.2.3. Python Code

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$ compute_ratios(1900, 43)
(1900, 1943, 2.8071864303140583, 7.225624631784611)

It seems we can cherry-pick the data to make the comparison go either way—so let’s see how things look more generally. Starting in 1886, we’ll compute price returns for all 30-year intervals, ending with the interval from 1993 to 2023.

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Listing A.2.4. Python Code

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$ duration = 30
ratios = [compute_ratios(start, duration) for start in range(1886, 2024-duration)]
ratios = pd.DataFrame(ratios, columns=['Start', 'End', 'Index Fund', 'Buffer ETF'])
ratios.index = ratios['Start']
ratios.tail()
       Start   End  Index Fund  Buffer ETF
Start                                     
1989    1989  2019   13.160027    6.532125
1990    1990  2020   11.116693    6.368615
1991    1991  2021   13.797643    7.005476
1992    1992  2022   10.460407    6.368615
1993    1993  2023   11.417232    6.724757

Here’s what the returns look like for an index fund compared to a buffer ETF.

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Listing A.2.5. Python Code

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ratios['Index Fund'].plot()
ratios['Buffer ETF'].plot()

decorate(xlabel='Start year', ylabel='30-year price return')

The buffer ETF performs as advertised, substantially reducing volatility. But it has only occasionally been a good deal, and not in my lifetime.

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According to ChatGPT, the primary reasons for strong growth in stock prices since the 1960s are “technological advancements, globalization, financial market innovation, and favorable monetary policies”. If you think these elements will generally persist in the future, a buffer ETF is probably not a good deal for you.

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