The risk-free return we can know with near certainty. Use the 10-year TIPS. The equity return and standard deviation trickier, sure. But don't we gain enormous insights if we do the math?
I wonder if we are comparing apples to oranges when only the risk-free rate is inflation-adjusted, but expected stock returns and the SD thereof are not based on inflation-adjusted numbers. One effect would be setting the risk-free rate too low. E.g. the current
TIPS yield as I type this is 2.07% but one can also get a risk-free 4.387% from the
nominal 10 year treasury. Drop these different numbers into Merton's equation (or a DCF equation) and you'll get very different results.
Measuring both the risky and risk-free sides in like terms, either inflation-adjusted or not, is also consequential because the effects of inflation sometimes overwhelm returns. For an example, look at
Turkyie's Borsa Instanbul 100 Index. It's up 28.5% YTD in nominal terms, and that looks very good to those of us accustomed to low-single digit inflation. But in fact TTM inflation in Turkyie was 47% as of November, and their risk-free rate is currently 50%! So it's possible for the stock market to deliver strong returns that are actually losses in inflation-adjusted terms, and in many countries the inflation adjustment could flip the attractiveness of a historical series of returns, as is the case for Turkish stocks.
Maybe in the U.S. the adjustment is usually only 2-3% per year (with compounding) but even that little difference will add up in a historical series used to justify an estimate of expected returns.
You'd use expected return not historical. (Also going to note that with the 100% allocation to stocks rule of thumb and the 4% SWR rule of thumb, people are implicitly using backward looking returns.) But regarding forward looking returns, we have a bunch of similar approaches--all of which are already calculated for you and me by the big financial services firms like Vanguard, Fidelity, Goldman Sachs etc. You can also just use the formulas yourself which financial writers (John Bogle, William Bernstein, Larry Swedroe, Rick Ferri, etc) have described and illustrated for us.
BTW, Vanguard's most recent forecast suggests a 3.8% nominal return for US stocks, 3.9% nominal return for TIPS, and 17% volatility. I like to work in real returns, so if we adjust those numbers for their expected 2.4% inflation, we're talking a 1.4% expected real return for US stocks and a 1.5% expected real return for risk-free assets.
Those are pretty pessimistic: Using the CAPE 10 approach--CAPE is nearly 40--we're looking a real return of around 2.5% for US equities.
If one uses the Gordon dividend model to DIY your own estimate, you're talking about adding together a 1.2% dividend yield and expected real growth in the economy so depending on the forecaster, in line with the above percentages?
I would expect there to be a lot of diversity in the models and outcomes produced by various academics and firms. The estimators who are willing to release more nuance and details, like
Vanguard historically has done, will apply a 2% or wider band of "plus or minus" range to the central point on their return rather than just publishing one number as their estimate. This reflects how it's hard for any mathematical model to account for investors' willingness to pay high PE ratios at some times and sell at low PE ratios at others, or more specifically to require high equity risk premiums at some times but not others. These psychological-cultural factors are based on things that can't be predicted with enough certainty to fit into the equations, like legislation, foreign affairs / wars, consumer behavior, climate events, technological developments, monetary policy decisions by humans, and worker productivity.
I lost the link, but at one point last week found a Vanguard forecast from 2012. They were pessimistic for many good reasons. They were wrong not because the reasons were wrong, but because over the next ten years investors became willing to pay higher valuations for almost all asset classes ("the everything bubble") as the money supply increased.
So again, we're back to "if I knew these inputs, I'd already know how to invest." The presence of
precise estimates of forward equity returns, even if produced with mathematical inputs, should not imply that we have
accurate estimates. Maybe my critique of the Merton model boils down to taking a wild-ass-guess like Vanguard's estimate of equity returns and obscuring the uncertainty around that guess, treating it like an accurate measurement of something.
Inflation - If we could be confident about inflation numbers, we'd be making millions doing bond swaps. Economists currently lack a working model of inflation that hasn't been debunked by previous experience, so this is an unknowable.
The above statement seems like maybe an oversimplification. My understanding (which is imperfect!) is the Phillips curve, monetarist (Milton Friedman), Cost-Push and Demand-Pull and the new Keynesian models aren't perfect. But I believe people think they're workable?
They're certainly better than nothing, but they do not always converge on the same recommendations/predictions, and they have each been contradicted by historical experience. My statement that the economics profession currently lacks a working model of inflation is summarized in succinct terms by
this video by an economist.
If anything, it seems that perhaps all our previously developed inflation models are too simplistic. Each failed to anticipate the chain of events that eventually contradicted it. Perhaps a real-world model would be some algorithmic amalgamation of each, and have some sort of branching logic or dynamic factor weighting that would rely more or less on aggregate demand (focus of Keysians), money supply (focus of Monetarists), etc. etc. Then the model would require constant tweaking to keep up with the constant changing of the economy, culture, and technology.
Equity and Risk-free SD[/b] - The standard deviation of equities has ranged from 28.8% for International to 16.1% for large cap US. For fixed income, it's ranged from 10.2% for high yield to 2% for t-bills. Yes, we can break this down and solve for any portfolio, but there remain measurement issues such as selecting a good starting and ending point, and changes in volatility/variance within different periods of time. Looking toward the future, if I knew the next year would be a low or high SD year for stocks, I'd make millions investing in options straddles or strangles.
I don't think the starting and ending date thing is issue here. We're looking forward. Also as a point of fact, we do know pretty accurately the volatility on US stocks for next month because of the VIX.
Researchers have found the VIX tends to imply volatility over 4% higher than what is actually realized 30 days later, and that there are long periods of VIX underestimation and overestimation. VIX is perhaps a superior measurement compared to forward estimates of equity returns produced by a half-dozen analysts, for motives we may not fully understand. VIX is after all a market measure, where thousands of people have money on the line. However it is still a human estimate that was historically unable to predict volatility events like the COVID crash, the taper tantrum, the GFC, and so on. If anything, VIX seems like a lagging indicator, telling us something about what volatility was in the recent past.
So if we're looking forward, I think the best we could do is guess the long-term historical average volatility. That is, to look backward. But of course that's not going to predict the next volatility event either. It would additionally be expected to fail at predicting multi-year changes in volatility, up or down.
We're left with expected equity returns and SDs being backward looking, and inflation estimates being backward looking. Are we predicting data series in the future or are we actually measuring what would have been the best portfolios in the past? Maybe this question gets to the epistemic issue of using math (deductive process) with historical data series to predict the future (inductive process). The presence of the math can trick us into thinking we're not basing everything on inductive reasoning, and drawing past trendlines into the future.
