I lost this post once already, hopefully it will be better-written this time.  I’ve been playing around with the stock market prediction model in order to give some idea of how the actual results could vary from the forecasts.

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Look at the graph above.  it shows potential price returns that vary from -1.51%/year to 4.84%/year, with a most likely value of 2.79%, placing the S&P 500 at 3200 in March 2027.  Add onto this a 2% dividend yield to get the total returns.

The 26 paths above come from the 26 times in the past that the model forecast total returns within 1% of 4.79%.  4.79% is at the 90th percentile of expected returns.  Typically in the past, when expected returns were in the lower two deciles, actual returns were lower still.  For the 26 scenarios, that difference was 0.63%/year, which would imply 10-year future returns in the 4.16%/year area.

model forecast total returns

The pattern of residuals is unusual.  The model tends to overestimate returns at the extremes, and underestimate when expected returns are “normal.”  I can’t think of a good reason for this.  If you have a good explanation please give it in the comments.

Now if errors followed a normal distribution, a 95% confidence interval on total returns would be plus or minus 3.8%, i.e., from 1.0% to 8.6%.  I find the non-normal confidence interval, from 0.5% to 6.8% to be more plausible, partly because valuations would be a new record in 2027 if we had anything near 8.6%/year for the next ten years.  Even 6.8%/year would be a record.  That”s why I think a downward bias on results makes sense, with high valuations.

At the end of the first quarter, the model forecast total returns of 5.06%/year for the next ten years.  With the recent rally, that figure is now 4.79%/year.  Now, how excited should we be about these returns?  Not very?  I can buy that.

But what if you were a financial planner and thought this argument to be plausible?  Maybe you can get 3.5%/year out of bonds over the next ten years.  With 4.79% on stocks, and a 60/40 mix of stocks/bonds, that means returns of 4.27%.  Not many financial planning models are considering levels like that.

But now think of pension plans and endowments.  How many of them have assumptions in the low 4% region?  Some endowments are there as far as a spending rule goes, but they still assume some capital gains to preserve the purchasing power of the endowment.  Pension plans are nowhere near that, and if they think alternative investments will bail them out, they don’t know what they are doing.  Alternatives are common enough now that the face the same allocative behavior from institutional investors, which then correlates their returns with regular investments in the future, even if they weren’t so in the past.

I don’t have much more to say, so I will close with this: if you want to study this model more, you need to read the articles in this series, and the articles referenced at the Economic Philosopher blog.  Move your return expectations down, and diversify away from the US; there are better returns abroad — but remember, there are good reasons for home bias, so choose your foreign investments with care.