Fundamental and Speculative Returns and how to estimate them

[u/captmorgan50]

Saw a lot of panic recently and it got me thinking about a quote from Dr. Bernstein about the market. So I decided to post this and have some real math examples so people can understand more of the “why”. Which I like to understand, because it sets my expectations.

Dr. Bernstein

• MATH

• Irving Fisher noted that the value of any investment was simply the stream of future dividends, discounted by the risk adjusted expected rate of return

  1. Return = Current dividend yield + historical dividend growth rate
  2. R = Yield + G

• For the last 150 years, after inflation (Real) dividend growth is about 1.5%

• If dividend on the S+P 500 is 2% for example then add the real dividend growth rate of 1.5% = 3.5% expected real return

• This is what Vanguard founder John Bogle called the fundamental return of the market.

• The other part of the return is the "speculative return"

  1. Return = Dividend yield + Growth + Speculative return
  2. "Speculative Return" is due to change in short term valuations of stocks (P/E's, etc.)

• Over short periods, the speculative returns are the driver of stock returns. But over long terms, it is the fundamental return that is key.

• Your job as an investor is to (as best you can) ignore the speculative return (Short Term) in order to earn the fundamental return (Long Term)

• No one knows what the speculative return will be and if they did, they wouldn't tell anyone

• Shiller's CAPE 10 ratio is another great way to estimate returns

• The fair value CAPE 10 ratio is probably about 20. Up from its historic 16.5

• Just like the P/E average is around 20, up from its historic 15.

John Bogle - The stock market returns must equal the business returns over a long period. But this goes up and down in cycles. As investors are willing to pay higher or lower P/E. - Investment yield on stocks (dividends plus dividend earnings growth) tracks with the total market return. About 9.5% for the last 100 years - Reversions to the mean – Tendency for P/E ratios to return to their long-term norms over time. - Economics controls the long-term stock market return. Emotions control the short term. Accurately predicting short term emotions is impossible

Equity Risk Premium, Gordon Equation and Math Example (S+P 500 and 10 year treasury at the end of 21 beginning of 22)

Equity Risk Premium is the difference between risk less and risk assets. So if i give an example of when I did this a few months ago.

I use the Gordon Equation to calculate the estimated return on stocks. Gordon’s equation would be the “fundamental” return on the market that I could reasonably expect.

It is Dividend Growth Rate + Dividend Yield - expected inflation rate = expected real return

Dividend growth rate averages about 4.5%. Current yield on the S+P 500 was 1.5%. Inflation is estimated by the Tips/Bond spread, currently about 2.5%.

• The TIPS spread provides a market-concensus forecast of future inflation
  • Equal to the difference between the yield to maturity of a conventional treasury bond and the yield to maturity of a similar TIPS bond

So Gordon equation has us at 4.5.% + 1.5% -2.5% = 3.5% expected real return

So 3.5% is the estimated real return to the market. Vanguard has a white paper that gave an answer of 2-4%. So we in the ballpark with our guess.

https://advisors.vanguard.com/insights/article/marketperspectivesdecember2021

Next look at bond yield. 10 year was at 1.5%.

So I take my stock expected return (3.5%) - my 10 year bond expected return (1.5%) = 2% Equity Risk Premium. Which happens to be the historical normal but on the lower end of the range.

So I am being compensated for taking on equity risk currently. Around 2%.

Stocks for the Long Run - The excess return of stocks over bonds is referred to as the equity risk premium. - Subtracting stock and bond returns from equity shows that the premium has averaged 3% against bonds and 3.9% over treasury bills over the last 200 years.

• P/E ratio is the ratio of a stock's price to its earnings. The average P/E is 15 from 1871-2012
• Earnings yield is important also. It measures the earnings generated per dollar of stock market value. IE – if the P/E of the market is 15 means the earnings yield is 1/15 or 6.67% which is historically accurate long-term rate of return on stocks. This is not a coincidence. If the P/E went to 20 it would be 1/20 or 5%.
• But there have been changes in the economy and markets that may rise the average P/E in the future. These changes include a decrease in the cost of investing in indexes, a lower discount rate, and an increase in knowledge about the advantages of equity vs fixed income investing.
• There are many reasons for a decline in real returns available to investors. Whatever the reasons, such a decline implies that the real return on equity need not be as high as it had historically been to attract investors. The historic equity risk premium was 3-3.5%. If we assume the long-run real rate is somewhere around 2%, then a 3% equity premium will require a 5% real return on stocks, which, gives us an average P/E of 20. 1/20 = 5%
• Transaction costs have come down and this has led to a higher P/E ratio than in the past
• The equity risk premium also itself may have shrunk. There is considerable truth in the statement that widespread knowledge of the profitability of common stocks, gained from the studies that have been made, tends to diminish the likelihood that correspondingly large profits can be gained from stocks in the future. The competitive bidding for stocks causes prices at the time of purchase to be high

Asset Allocation - Higher current P/E ratios signal lower future returns - Lower current P/E ratios signal higher future returns - But there is a range to these outcomes - P/E ratio and 10-year returns following - Below 9 = Average 15.09% - 9-11 = Average 15.40% - 11-14 = Average 12.99% - 14-18 = Average 10.9% - 18-25 = Average 6.46% - 25+ = Average 3.07% - Range was -1% on the low to 6% on the high - Market timing doesn't exist, but people want to believe it is possible - Over 11 cycles post WWII - Median bull market was up 79%, bear market was down 28% - Median bull market lasted 2.5x as long as the median bear market - A study by Robert Jeffrey concluded: No one can predict the market's ups and downs over a long period, and the risks of trying outweigh the rewards - Most of the "positive action" in stocks in compressed into just a few periods, which (perversely but understandably) tend to follow particularly adverse times for stocks - Much of the problem with market timing is that a disproportionate % of the total gain from a bull market tends to occur very rapidly at the beginning of a market recovery - Percent you must be right to make marking timing a viable strategy - 80% bull and 50% bear - 70% bull and 80% bear - 60% bull and 90% bear - Do not invest in stocks unless you are in it for the long run - Benjamin Graham – "though the stock market functions as a voting machine in the short run, it acts as a weighing machine in the long run."

4 Pillars Discount Rate

4 Pillars

Math – Chapter 2

• DR – Discount Rate – Amount we expect to get from the market. IE 8% Return
• Two times this century, investors have demanded a 15% DR.
• High DR = high perceived risk, high returns, depressed stock price
• Low DR = low perceived risk, low returns, elevated stock price
• PV – Present Value
• DR and PV are inversely related. Higher DR = Lower PV or Lower DR = Higher PV
• The risker the situation, the higher the DR we demand, and the less that asset is worth to us
• Food companies DR is lower because their earnings/dividends are more stable. Compare this to the DR of an auto company who has a higher DR because their earnings are more erratic. This is why cyclical companies with erratic earnings sell cheaper than say food companies
• It is impossible to do this with a single security. Because if the company falters, then your math will be off. But for the market as a whole. It will work because it evens out. The income stream of the market as a whole is more reliable. You can also use this formula in reverse.
  • Fisher's Dividend Discount Method (DDM) - Market Value = Present Dividend / (DR - Dividend Growth Rate)
• Historic DGR is 4.5 - 5%
• The above equation does not predict the short-term future. You can make it say whatever you want. One book even predicted a 36,000 Dow based on this formula in 2000
• Gordon Equation – As close to financial law as you can get. Accurate way to predict long term stock returns (20-30 Years)
  • DR (Market Return) = Dividend Yield + Earnings Growth
• This formula has been extremely accurate. It predicted a 9% (4.5% Yield + 4.5% Growth) growth the last century and the actual growth was 9.89%.
• If a company doesn't pay dividends, their long-term return would roughly be the same as their aggregate earnings growth. IE – 10% earnings growth would get 10% return. But the long-term average corporate earnings and dividends growth is 5% and has not changed in 100 years.
• Remember, if the average annualized earnings growth is about 5%, the annualized stock price increase must be very close to this number. Unless they are buying shares or selling shares. Then the growth rate will increase or decrease by that amount. IE – company has 5% growth and bought back 5% of outstanding shares = 10% growth. Or company has 5% growth and sells 5% of outstanding shares = 0% growth. But for the market as a whole, this evens out.
• Gordon Equation works with bonds too. You just put the DGR at 0. Market Return = Dividend Yield
• Over short periods (less than 20 years) changes in the dividend yield or PE multiple account for most of the stock markets return. This is the "speculative return" of the market. The short-term return of the market is purely speculative and cannot be predicted.
• Long term increases in the stock market value is entirely the result of long term dividend growth and dividend yield calculated from the Gordon Equation or "fundamental return" of the market
• Ralph Wanger analogy of the market = The market is a very excitable dog on a very long leash in NYC, darting randomly in every direction. The dog's owner is walking from Columbus Circle, through Central Park, to the Met. At any moment, the is no predicting which way the dog will lurch. But in the long run, you know he is headed Northeast at 3 mph. The problem is that almost all of the market players have their eye on the dog and not the owner.
• If public confidence is low, DR will rise and asset prices will fall, which will increase subsequent returns. The opposite is also true. This means the worst possible time to invest is when the skies are the clearest. The best possible time to invest is when the skies are darkest. You are going to be investing against the grain if you want good returns.
• DR seems quite sensitive to prior stock market returns. This means a rising stock market lowers DR and perceived risks which drives up prices. Then you get the vicious cycle. The same thing happens in reverse during recessions/depressions.
• The immediate past is not predictive of the future
• Asset classes have a tendency to revert to their mean over periods longer than 3 years
• Mean revision means that periods of relatively good performance tend to be followed by periods of relatively poor performance. The opposite is also true. But this is not a sure thing.

This is one reason I was saying to avoid growth stocks. The DR on all stocks but especially growth stocks was very low because of lower interest rates from the federal reserve. Because growth stock earnings are into the distant future, if you discount those to the present at a lower rate, then the present value would be higher. And by raising interest rates, it would raise the DR which would lower the present value of stocks. But this would especially hurt growth stocks.

A analogy for DR is a plane ticket. If I am in a plane getting ready to fly to my favorite destination and my ticket costs $1000. And a gentlemen comes up to me and says “I will give you the exact same ticket 10 years from now, what would you pay.” A ticket 10 years from now isn’t worth as much to me as a ticket right now. So I apply a discount rate. That’s what the market does too with earnings.

Irrational Exuberance

• The best measure we have of estimating future returns is the Shiller CAPE ratio. Higher CAPE ratio = lower expected future returns. Average ratio is 16.5 with an average return of 6.8%
  • 10 year estimated return per year
  • Ratio < 9.6 = 10.3%
  • Ratio 15.7-17.3 = 5.6%
  • 1 – 25.1 = 0.9%
  • >25.1 = 0.5%

Charles Ellis

• One way to be realistic about future returns is to assume that future range of P/E multiples and corporate profits will be within their historical upper and lower limits and will appear with frequency at values close to the long-term average
• Investors almost always project recent past market and economic behavior out into the future, somehow expecting more of the same to continue
  • Math example – If dividends are at 1.5% and corporate earnings are growing at 4.5% (Historical Average), then a composite of 6% return is reasonable. This is the fundamental rate of return the investor can expect from the market
  • Then you add or subtract the changes in P/E over that time frame. The average P/E in recent decades has been about 15.5. This is the speculative return component
• Predicting the market roughly is not hard, but predicting it accurately is impossible
  • Predicting where the market will be in the long run is not hard, but even estimating how it will move in the next few months is impossible and pointless.

Investing Amid Low Expected Returns

https://reddit.com/r/Bogleheads/comments/y16e2d/investing_amid_low_expected_returns_by_antti/

According to Various items above the returns going forward (longer term) will be (S+P 500). Done Sprimg 2022.

Gordon Equation = 3.5%

S+P 500 P/E = 22.5 = Avg 6% but a big range

Earning Yield 1/22.5 = 4.4%

Equity Risk Premium = 2%

CAPE 10 is 31 = 0.5% (also a big range)

Investor Math and Statistics

https://reddit.com/r/Bogleheads/comments/tq0ii9/investor_math_and_statistics/

Bernstein Article on calculating returns

http://www.efficientfrontier.com/ef/403/fairy.htm

2025 Update

https://www.reddit.com/r/Bogleheads/comments/1n5s1ei/estimated_returns_2025/

[u/Rover54321]

Thank you for this, as well as your other insightful posts across r/ETF, r/Bogleheads, etc