Sam Parker is a community member whose math skills surpass mine by a factor of roughly 50 times. Sam has helped me with several projects since John Walter Russell’s death last year. Set forth below are the words of an e-mail that Sam sent me a few days ago. Please click on the link at the bottom of the post to view Sam’s graphic.
Hope you are well.
Attached is an example of my initial stab at modeling valuation informed investing. I have derived a set of differential equations that govern cash, stock, and total portfolio values for any target stock allocation (vs p/e10, see the first chart: 80% stocks for p/e10<10, dropping linearly to 20% stocks at p/e10=28.
My equations include the effects of average dividend yield on stocks and interest rate on cash, but I do not include these here. My goal in this simple example was only to show how the market can go nowhere, yet after several cycles we could still double our money.
I assume SPY is 110 ± 30, oscillating sinusoidally but going nowhere.
In the second chart you’ll see plotted versus time (months or years; doesn’t matter cuz I’m not including interest and dividends yet) the assumptions of this first model: The top, golden curve is SPY; the dark blue line is earnings of S&P500; and the low, magenta curve is p/e10, which oscillates between overvalued (26) down to 16-ish (somewhat below historical fair value).
After some cipherin’, I arrive at the last chart on page 3. SPY price level is oscillating around 110 ± 27% (so repetitively up 75% and down 43%, going nowhere), while our portfolio goes up about 43% then drop about 21%, gaining nearly 13% per cycle, thus almost doubling after the market gets nowhere in 5 cycles.
So beta is reduced nearly 50% while an impressive alpha is generated, albeit at lowered tax efficiency, higher trading fees, and less dividends than a buy-and-hold portfolio.