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A simple and effective way to estimate future S&P 500 return

Source: https://onemaninvesting.wordpress.com/2019/09/09/a-simple-and-effective-way-to-estimate-future-sp-50...

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When it comes to retirement planning or some asset allocation decisions, it is important to not only understand the risk you take, but also the potential return an investment could have. A lot of people use the S&P 500’s average historical return to have an idea of what return they might expect. I think it can be quite dangerous because it totally ignores valuation. If tomorrow morning you buy $SPY at $300/share ( ~ 20 P/E ratio) and I buy it at $600/share ( ~ 40 P/E ratio), how can we possibly expect to have a similar return? I’m not saying anyone should time the market based on valuation (it simply doesn’t work), I just think investors should not always use the historical average to estimate the S&P 500 future 10-20 years annual return.

But there must be a somewhat significant correlation between the S&P 500’s average annual real return and each rolling 10-year CAGR, right?

I looked at the data (available here) from 1881 to 2008 and looked at the correlation between the average 8.31% real return and every 10-year rolling CAGR. It was 0. What does it mean? Don’t use historical averages, especially if you have a time horizon under 20 years.

So how can we have a better idea of S&P 500’s future return? Based on Vanguard’s white paper that can be found here, the metric that explains future stock returns the most is the CAPE ratio. The CAPE ratio is a price-earnings ratio where the earnings are cyclically adjusted, meaning it uses a 10-year real earnings average.

Obviously, the CAPE ratio and subsequent S&P 500 returns are inversely correlated, and I found that the correlation was quite strong at -0.55. Here’s a scatter plot comparing the CAPE to the S&P 500 subsequent 10-year real CAGR:

Logarithmic regression of S&P 500 Subsequent 10-year real returns by CAPE level

As shown above, the relationship between valuation and return can be seen quite easily, especially when the CAPE is under 10 or above 30. Extremes have more predictive power, but overall, the r-squared is still 0.33, which is quite good compared to a lot of other metrics.

Even if you time horizon is longer than 10 years, the CAPE ratio is even a better at forecasting forward S&P 500 returns. The correlation is even stronger when it comes to forward 20 years CAGR is even stronger (negatively) at -0.65. Also, 45% of the variance in S&P 500 20 years real CAGR can be explained by the CAPE ratio:

Logarithmic regression of S&P 500 Subsequent 20-year real returns by CAPE level

If we used the trend line equation to estimate forward S&P 500 returns, how accurate would it be? Here’s how the model fared against S&P 500’s actual forward real returns:

S&P 500 Forecasting model vs actual forward 10 year real return (1881-2007)S&P 500 forecasting model vs actual forward 20 year real return (1881-1997)

As you can see, there can be large discrepancies (sometimes over 10%) when it comes to forecasting 10 years forward real returns. However, 20 years forward real returns are more accurate and the model rarely sees 3% or higher discrepancies. Here’s a table showing the average, minimum and maximum real return for each CAPE bracket:

10 YEARS REAL CAGR

CAPEAverageMinimumMaximum
< 914.72%6.56%19.96%
10 to 149.38%0.59%18.81%
15 to 196.43%-4.63%16.13%
20 to 245.72%-3.97%15.21%
25 to 313.14%-3.97%8.47%
30 to 341.99%-1.01%5.94%
> 35-1.24%-5.92%4.49%

20 YEARS REAL CAGR

CAPEAverageMinimumMaximum
< 99.29%6.13%13.61%
10 to 149.45%4.90%13.32%
15 to 196.97%0.64%11.85%
20 to 244.88%0.54%10.38%
25 to 313.21%0.10%8.33%
30 to 343.01%-0.22%5.50%
> 353.85%0.41%5.14%

I know the model is far from being perfect, but I think a model that is too good to be true… Is too good to be true. And as I mentioned earlier in the article, it is still better to use the model than simply rely on historical averages. I will soon write another article using not only valuation, but also behavioral data and mean-reversion to have a more accurate forecasts, so keep visiting my blog from time to time to see what’s new!

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Re: A simple and effective way to estimate future S&P 500 return

I do not put much faith in any models. For me, the best method is to know the companies you invest in and know as much as you can about trends in the economy. It is usually more prudent to have diverse holdings and not panic when the market is volatile.

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