The Basics - Doubling Time

has the formula that we will fit everything into; the one that banks use to calculate "daily interest" in accounts:  A = P(1 + r/n)nt where the symbols mean

(This top box will more often be set to "Yield".)

That changes to extracting %yr Rate of growth of charts, dividends or earnings.

total amount
A ( Examples of A:

Right hand price on a chart.

Dividend now.

Earnings, Book Value or Number of shares out now.

first box
; answer at bottom) is given by

your original P=$10k ( Examples: Left hand price on a chart t years wide.

Dividend, Earnings, Book Value or Number of shares out t years ago.

second box
) invested at

Usually this will be chart slope and appear at the top.

The calculator can also get growth rate of interest.

Total return is growth plus yield.

interest rate
of r=7%/yr

compounded n times per year ( "Continuous" means time between calculations goes to zero.

Effectively, that eliminates the variable n completely.

fourth box
)third box)

and sitting there for t years ( In this case enter Yield you are testing.

For other examples, set the top box to "Yield", moving the other entries upward.
fifth box

Notice that setting n=a zillion (continuous) eliminates it and changes the formula to A = Pert. This formula is used by banks to calculate interest.

To do that it has to be changed to r=Ln(A/P)/t.

Notice that it is not yield.

That happens to be
the formula for the ert swoops upward on a normal plot.

A "log plot" makes it into a straight line by compressing the upper part of the Y-axis.
"log plots" that
market websites show us.

EXERCISE: Play with the interest rate, time and number of years to retirement. What appears above is the This is 73%/r in %/yr.

Thus inflation would halve your holding at minus 2%/yr.

for ten k invested in an ETF called HAC.TO and just left sitting there. Try various other times - to - retirement, using your entire RRSP-room for P.

Try an "interest rate" of 10%/yr which we have recently been getting by holding banks. There are several ETF choices below which return about that much.

Try an aggressive rate of 20%/yr which we have been getting from an ETF holding Amazon, Google etc. in the list below.



ETFs For The Short Term
When Over-Sold; calculator above)

These measurements are not up to date, so their measurements need to be re-done when new cash beomes available to invest.  

The ETFs above are purchased as single stocks, but are "baskets" holding shares in many companies. That means they are diverified to some extent, and holding many ETFs diversifies even more into different market sectors.

The list contains relatively few resources, which tend to be very volatille, and it is also light on industrial stocks, which tend to be listed only on American exchanges.

The websites linked for the baskets combine two types of return, dividend yield in %/yr plus Market price growth in %/yr. The measurements below the links split them out instead into three components; dividend growth first, then dividend yield and Market price growth.

The better the match between dividend growth and market growth, the more reliable an ETF is likely to be.

Note that the growth rates picked off the type of charts above should match the sum of dividend growth and dividend yield. Market growth below was picked off a different chart, which excludes dividends.

Example: $33.5k invested in 2001 in
HAC.TO would now (summer 2021) be worth 33.5*exp(20*0.07) = $136k by the formula in the Calculator below. If invested in the Canadian Low Beta ETF the total would have been $248k. (Try 10%, 20 years and 33.5 in the calculator below.)
The Basics - Rate of Return From Charts
StockScores.Com Rate of Return has two parts; cash paid to you and growth of the ETF.

The dividend is cash paid. Growth can be seen as an upward slope.

. Yahoo Charts The Yahoo chart slopes down. Stockscores' chart to the left slopes up because dividend is mixed in.

exclude them

Here is the HAC.TO Chosen because it pays no dividend. The upward slope is your total return.

chart again
, with a red dotted line drawn in after you hit annotate:

Evidently the Horizons has funds of many types and HAC buys fast-growing funds for part of the year.

When 7% has been achieved, it switches to holding bonds.
fund manager
has returned it to its If the upward slope is not maintained, return is less than 7%/yr.

straight line
after the Horizons did not predict COVID and its holdings fell.

HAC.TO rode the rebound back up to 7% and locked it in as bonds.
COVID crunch
. Let's see if the slope of the line checks out to be 7%/yr as predicted:

Removing Up and Down Price Jumps:

The red dotted line has been moved to JUST TOUCH the red EMA200 line in two places (eliminating volatility). Any straight line on the chart behaves like a bond yielding interest and the dotted line follows the price growth of the ETF, ignoring noise.

Picking Principal and Final Total Off the Chart:

The  site lets you enter three known values, but first of all,

  • set the top Calculate box in the calculator, to interest Rate(R), which is the unknown variable this time. (You would have to sell the ETF to get the gain as cash.)

    Next get the Total value A, which is picked off the right hand end of the dotted line after value accumulates for five years. Measure that by pointing at the end of the red dotted line with the mouse.

  • Enter the little gray number at the bottom, $24.64, in the second box.

    Now pick off the left hand end of the dotted line, which in our example, was $17.13.
  • In the third Principal box, enter this as the starting value

  • Make sure the compound rate in the fourth box is "Continuously".

  • The time you enter in the fifth box is five years, the width of the above plot. Press Calculate,
    and: . Voila!

    That ETF is indeed like a 7%/yr bond, doubling your holding every ten years.

  • Reason for choosing HAC: That ETF does not pay a dividend (like ZLB just below it). The website mixes dividend yield and price growth together, which is good because that shows the true R.O.R. to an investor. The other side of the coin is that the three components of return get confusing:
    Asset Growth: In the blue areas under the Stockcharts links (total R.O.R.), the first entry is the dividend "slope" which is growth rate of dividends paid out. The numbers may be picked out of Annual Reports etc. and plugged into the calculator above to indicate the rate at which a company is growing. Similarly, the Yahoo price charts give a slope that does NOT involve dividends; it approximates company growth too. That is the third entry in the blue areas.

    Earnings Payout: Part of the company's earnings may be returned as cash rather than being re-invested to make assets grow. That is the second number in the blue areas, and therefore it should be added to asset growth to indicate what the owner is getting from a stock.

    Comparing Indications: The simple calculator approach on StockCharts data adds the dividend yield to the Yahoo chart slope. It is probably the most realistic estimate because market slope reflects the judgement of investors while growth of dividends reflects the judgement of management.

    Thus in the blue areas, one can compare that estimate to the sum of dividend yield and growth to see how well a company's management is balancing things. In the case of ETFs, that comparison applies to the group in the whole basket.
    It is also possible to enter X and Y points for dividends, earnings, book value etc. in a spreadsheet, prepare a Ln(Y) column, and then run a straight (logarithmic) line among the points using the SLOPE() function. Multiplying by 100% will then yield an average R.O.R. for whatever metric you round up. Be aware, though, that if X is expressed as dates, you need to divide by 365Days/Yr.

    The Basics - Choosing an Entry Point
    Above the middle of volatility,
    store new $$$ in bonds etc.
    Buy and Hold after corrections. (Don't trade after that.)

    Here is the chart for Low Beta again, with

    There are several things to check for when choosing ETFs to buy and hold rather than trading in and out of. First, the EMA200 should touch the red dotted line at BOTH up and down wiggles. Secondly the volatility, as measured below, should be less than three times the annual growth. Finally the dividends should grow steadily at roughly the same %/yr rate as price.

    The list of ETFs above is not totally up to date. When funds are contributed to an RRSP, they should be held in cash until there is time to construct this RGB figure and up-date the location of the green lines.

    Note too that the volatility in the list above does not agree with the measurement below. That is because the market has gone up strongly since the measurement was made for the list. The bottom blue line has been placed above the COVID dip this time, reducing the volatility.

    Buy At the EMA: The EMA200 (Exponential Moving Average) is delayed by 187 days, and in the process strongly filters out volatility. Thus it locates a trend, and if the price is rising, it will lie below the current price (green line) most of the time. ASIDE: most "chartists" and brokers use the SMA200 - avoid doing that too because the EMA gives better R.O.R. measurements.

    The image to the right shows four approximate straight-line segments, with arrows pointing to the "corners" showing up after a run-up in the Price Chart starts or ends. The ETF holds only banks and its chart combines market price and dividend yield.

    The overall Price Growth rate plus dividends (it is a plot), was 8.5%/yr just before the 2019 pandemic, measured as shown above.
    Secular Bull and Bear markets alternate every 16 to 20 years, and the plot to the right shows that four years ago we just left a flat spot (Bear) like the one above. The market should rise for another ten years or so.

    However, during 2019 and 2020 COVID-19 has resulted in money-supply inflation. The price of gold is saying that Market Sentiment predicts inflation will result. It would be wise to expect a flat period in the next year or two and invest defensively.


    ZEB.TO: A Pure-Bank ETF

    We will open up two links in new tabs:
    a chart and a calculator, which can give growth rates (left hand side above) for dividends and market price.

    The ends of the green line measured
  • Date 2021 Aug 18 $33.33
  • Date 2011 Aug 13 $17.59 (10 yr.)
    Market Growth Rate = 6.4%/yr from the calculator.

  • 2021 dividends = $1.20
    Market price was $37 (above the green line), giving Yield 1.2/37 = 3.3%/yr.

  • 2016 dividends = $0.81 (5 years)
    Entering that as P and $1.2 as A in the calculator, r = 7.9%/yr.
    The chart above is from Yahoo and does not include dividends. The total return to shareholders is chart growth plus yield, or 9.7%. Note that management has been increasing dividends slightly faster than the market price, but the growth rates are comparable so we conclude that it is a stable investment.

    The chart measures $24.12 and $38.42 at the ends of a 5yr line, giving R.O.R. = 9.3%/yr.


    Measuring Chart Volatility

    The math is
    obscure, but the resulting procedure is something we can easily DO. Open up two independent tabs: a chart and a calculator.

    The same formula for Rate Of Return can give the amount of Up - And - Down variation within one year; just measure top-to-bottom at the end rather than side-to-side:
    BACK TO THE FUTURE From the "Roaring Twenties":
    a Trip Through the Dirty Thirties to Beyond The Trump Bump
    (Be in the market now: P/E is rising. Rotate out in 2032.)

    A Secular Bull Market is a period like the Roaring 1920s, where people just buy whatever is in fashion. Price rises faster than The slope in %/yr of price, dividend growth (not yield) and earnings should be the same.

    Net Asset (Book)
    Value rises. Price to Earnings ratio P/E The inverse, E/P is %/yr and should be more than dividend payout.

    That permits purchase of plant and equipment for future earnings.

    climbs too fast
    during Secular Bulls, and needs to be reduced.

    A Secular Bear Market followed; the Crash of 29 happened fast and ruined the economy as The banks sat on money rather than lending it and M1,2 etc. shrank.

    That meant cash was not available to buy things, and prices fell.

    deflation set in
    (due to Suppliers stopped investing in yet more things to buy.

    Central banks need to stimulate both supply and demand at such times.

    Central Bank policy).
    The result was the Dirty 30s, the second period to the right.

    16 Year Alternations: Note the second trace; gold is a safe haven Secular Bears are periods when fear of price drops causes price drops.

    When gold price starts rising, Market Sentiment soon drives stocks down.

    when P/E is high
    and When the ratio tips down, Market Sentiment drives gold up.

    A dropping orange trace usually means a strong P/E correction.

    drops again
    when people believe that P/E has corrected. A post-war Secular Bull market followed the Dirty Thirties and the ratio shown rose with the DOW. People buy gold Fear of inflation and fear of market correction.

    Then greed enters and people buy gold to get rich.

    when fearful
    , which was yet to happen.

    Another Bear Market (center) followed; the stagflation period, when gold prices and the dollar inflated and forced Central Banks to let economic activity and the stock market to both stagnate. Relief and the 90s boom came eventually.

    During the third Bear Market, starting at Y2K to the right, gold rose (driving down the trace above) until the DOW had climbed above its previous two peaks. Then sentiment changed, gold price dived, and the present Secular Bull got underway around 2016.

    Typically a Secular Bear includes two Black Swans, shattering the gentler volatility that charts exhibit during Secular Bulls. Three sideways trends appear above while P/E was corrected to fit prevailing interest rate policy of Central Banks.

    Bottom Line for Summer 2021:

    We are one-third through a Secular Bull, with continuing low interest rates. Two Black Swans are behind us; the Dot Com Bubble of 2001, and the Financial crisis of 2008. Looking at the chart of the DOW to the right, we have risen out of the resulting horizontal movement at the "Trump Bump" and interest rates remain low.

    Not shown is the recovery from COVID-19, which is underway right now. Secular Bulls and Bears typically last sixteen years each, so we have about one decade to Buy and Hold, before rotating into defensive stocks around 2030. ETFs can more than double in that time.

    The Voting and Weighing Machines: "The father of value investing, Benjamin Graham, explained this concept by saying that in the short run, the market is like a voting machine--tallying up which firms are popular and unpopular. But in the long run, the market is like a weighing machine--assessing the substance of a company. The message is clear: What matters in the long run is a company's actual underlying business performance and not the investing public's fickle opinion about its prospects in the short run."
    The Big Four forces in the market are:
    1. Inflation rates, which are driven by Mass Psychology, and which in turn drive Central Banks (like a dog chasing his tail).
    2. Interest rates, which are set by Central banks. High interest suppresses inflation but causes bonds to compete with stocks for buyers, driving down share prices.
    3. Money supply. which consists of M0, M1, etc. and shrinks, causing Deflation, when interest rates are high. Recently Quantitative Easing has been used to prevent that.
    4. Market sentiment (fear/greed) which can take us right back to inflation, as indicated above.

    To the right is the DOW and an inflation-adjusted version. To the left is the Crash of 29, which happened fast and ruined the economy as deflation set in when the Central Banks mis-handled things. After 16 years each (four Presidential Cycles) of a Secular Bear and a Secular Bull market, things got heated up.

    During the 1970s the expectation of higher future prices forced Central Bankers to reduce the money supply again to prevent inflation. Like the situation above, neither the market or the dog was able to stop the cycle, but this time Central Banks caused the economy to stagnate rather than collapsing.

    Another Bear - Bull pair brings us to the year 2000, when interest rate expectations had dropped. By pushing down rates even further, the Central Bankers finally managed to navigate two major financial shocks while keeping consumer prices stable, and stock prices also averaged sideways albeit with really bad volatility.
    During the 2000s there was quite a bit of inflation of the money supply due to low interest rates. However, Maket Sentiment was the opposite of the 1970s Stagflation period, and Consumer Prices did not inflate - instead, the excess dollars went into the stock market, driving down P/E to make up for very low bond returns.

    Right now we are past the Secular Bear and Market Sentiment is not very worried about inflation. It seems reasonable to expect another decade of rising stock markets before turbulence sets in again. (In 2031 we should probably switch to bonds and even gold.)

    Multiple Expansion and The Trump Bump:
    The US market tends
    to hover around P/E=20.
    The Canadian market is consistently lower; around P/E=15.

    To the right the most recent 30 years are broken into '90s Secular Bull market, the Y2K crash (Dot Com and Housing Bubbles) and now the beginning of a new Secular Bull, interrupted by COVID.

    The 1990s ended with over-buying driving P/E up to about 30. The second image over-laps a bit and then the bubble bursts. The second image ends just at the 2016 election.

    The third image over-laps again, before the "Trump Bump" due to sharp tax reduction that sent earnings up. The second half of the image shows four years of a new Secular Bull Market.

    Below those images is the ratio of upper blue Price line divided by orange Earnings. At the left, the "Dot Com" bubble developed during the 90's and burst just after Y2K (first gray bar.) The collapse brought Earnings (and P/E) down sharply.

    It also collapsed Market Sentiment (beginning of top middle image) after which the P/E multiple continued to slide for a while. People stayed complacent, pumping their savings into housing instead of the Market (borrowing too much). As a result, P/E dropped well below 20 (note orange earnings shooting up before the middle gray band).

    This housing bubble also burst; visible in the second gray bar at 2009. That led to a shift in Central Bank policy that remains to this day; Quantitative Easing was invented, along with very low interest rates. That led to a reset of Market Sentiment; people stopped fearing inflation and did not trigger it by hoarding things. Instead they pumped spare cash into stocks.
    The Bull/Bear alternations typically last four Presidential terms each. Thus it is early in a Secular Bull market, having just finished the first four-year term, so it seems good to stay in stocks.

    OOPS! The last two years have incurred the COVID-19 pandemic. The price of gold to the right is saying that Market Sentiment predicts inflation will result; inflation is dominating the Big Four - almost like the previous peak at Y2K. During 2019 and 2020 (recent white bar and previous gray bar), COVID-19 has resulted in money-supply inflation.

    Canadian housing prices have driven up the CPI inflation rate to nearly twice the 2%.yr target, and state-side Trump policies have greatly increased the national debt. Thus it seems wise to invest defensively until there is a correction in CPI, and the S&P500 also makes a correction.

    "Earnings Yield" vs P/E:
    The inverse of P/E is %/yr, and
    Graham's weighing machine
    adjusts it to about double competing return from bonds.

    To the right we can see the effect of interest rates falling strongly since 1950. The Secular Bear of the 1870s shows a sharp drop in purchasing power of the stock market. That means capital investment shrank, with bank rate around 5% and Earnings Yield around 10%/yr. The inverse of 10% is P/E of only Ten. The whole economy stagnated until the 1990s Secular Bull began.

    However, after the Financial Crisis of 2009, Quantitative Easing has encouraged positive Market Sentiment. Thus capital investment continued while P/E was being reduced, and then stock prices started rising toward the end of the Secular Bear when US corporate taxes dropped. With bank rate under 2%, Earnings Yield also dropped to around 5%/yr. The inverse of 5% is P/E of Twenty.

    That low rate also implies low dividend yield, since dividends ultimately come out of earnings. If we examine the Canadian ETFs above, their dividend yields are much higher and their price growth rates are very comparable to US stocks. However Canadian stocks are not well diversified - tending toward financial and resource stocks.