Math People-- Question About Exponential Growth

Discussion in 'Strategy Building' started by Corso482, Mar 24, 2003.

  1. This is prolly a simplistic question to those with acutal math ability, but for me it's confusing--

    A friend of mine has owned CVX for years and was rationalizing to me that it's good when the stock declines, because when he reinvests the dividends, he'll be able to pick up more shares as the price goes lower.

    He claims reinvesting dividends into a declining stock will lead to exponential growth. In his words, the "dividends expound faster when the price is lower."

    Now, am I wrong to think that you will only experience exponential growth if CVX stays above the price you bought it at? Otherwise, if the stock declines, the only thing the dividends do is cushion your loss, i.e. no growth, let alone exponential growth.
  2. Swish


    Exponential growth is not the way to think about it. There are clearly a few assumptions in what your friend has said:

    1. Eventually the stock will go back up.
    2. That cvx's dividend payout will remain the same over time.

    Your friend has an investor's mindset - basically a buy and hold philosophy. I disagree with his assumptions, but this is the trash that the perma-bull brokerage industry has rained down on an unsuspecting public for many decades.

    Any fixed (or positive) rate of return that is reinvested will result in exponential growth - if the underlying asset retains its value. If the underlying asset declines in value - all bets are off unless the asset eventually recovers.

    This site is generally more populated by intraday and short term traders who could care less about the dividend payouts on a stock and have little patience to wait for a sagging stock to recover.
  3. Basically, I agree with everything. If you assume no possiblilty of loss, then a constant dividend (or any other) yield results in "exponential" growth, actually just "almost exponential", since the dividend/interest payments are not continuous but concentrated (they are made once a quarter/year/month/whatever).

    So, if you have no possibility of loss (which would be the case with a savings bond), you have "almost exponential" growth. Of course, even a savings bond can become worthless, namely if the currency (in this case US dollar) should become worthless. So, if you want to be exact, you will have to admit that we assume that currency cannot be devalued in order to be able to claim exponential growth for savings bonds.

    Now, in the case of a stock, you can make a similar argument: If a stock always stays at 20 and pays out dividends regularly, and you re-invest all dividends in the stock, then your position in the stock will grow exponentially.

    If the stock declines in value, your position will grow even faster than that (if you take the number of shares as your measure of position size). The growth will still be exponential, but with a higher exponent, meaning the number of shares will increase even faster than originally expected.

    You could argue that it is no less reasonable (in principle) to asume the stock cannot lose its value than to assume money cannot lose its value.

    It's just that stocks more often go to zero than currencies, especially the US dollar.

    When you think about it, the best thing for someone who buys a stock would be if the stock went down really hard, then he would buy it, and afterwards it would start to go up. An "investor" just keeps buying until the stock starts going up, therefore the investor will be the one who will have the largest gains PER TRADE PER SHARE. Of course, his risk is also quite large, since any stock CAN go to zero.
  4. Take a look at a 20 year exponential chart of Nortel. Your friend's strategy worked great until a couple of years ago.
  5. As chuck pointed out, take a look at the monthly charts of all your favorite listed stocks and notice that the buy-and-hold philosophy did pretty darn well as far as profit opportunity goes. In the 10 year period from 1990-2000 many listed stocks made 400-500% gains and more.

    Not bad for perma-bull trash.
  6. Ask yourself a simple question: "Is my friend rich or not?"
    If he is rich, then take his advice, if he is not rich, who cares what his theories are.:p
  7. rather than "Is my friend rich or not?" should be, "does my friend have more hair than I do"
  8. A bit over 6 percent per annum has been the real (net of inflation) return on buying, holding, and reinvesting dividends over the last 80 years (and I think, perhaps even longer than that.)

    So, yes, that's exponential.

    My own thinking is that if these dividends were only reinvested during periods of historical value -- low PEs or high dividend yields -- you could substantially improve on these returns.

    Perhaps your friend is onto something in only reinvesting dividends during price declines. The actual performance will depend, I presume, on how he actually defines a 'decline' and on what he does with dividend payouts during price appreciations. (Hopefully he's not just spending them.)

    I would have to question the wisdom in doing this with only one stock though. Unless he has some Buffet-like insights into the business itself, I think he'd better of diversifying into broad market groups.

    The worst thirty year period for this was buying the '29 high to '59 -- 2% pa nominal capital appreciation. If companies were still paying dividends during this period (I have to believe they were), it's not too bad for a simplistic B&H.
  9. your friend says that if his stock goes down then he will get exponential growth. PURE BS. Think about it. If his stock goes down, his dividends have to make up the decline for him to even break even. If he reinvests his dividends and the stock continues down, he will never even get his original investment back.
  10. The buy and hold philosophy is true WITHIN CONTEXT.
    - the stock is fundamentally SANE. How to know that it is sane ? It distributes dividends (since they can cheat you must check the quality of this dividends by many criterias and that's a long work)
    - the whole stock market is fundamentally SANE.

    What brokers promote are UNSANE STOCKS OR UNSANE STOCK MARKET CONTEXT so that Buy and hold strategy cannot work for the majority of the public which come only after the big marketing campaign of stock market near its high.

    Also the majority come with gamblers mentality whereas Buy and Hold Strategies need time and money, for the biggest players it is the Assurance comapnies that are the most capable of doing it whereas the Bank sector are gamblers (nevertheless it is not their money but their clients money the OPM - others people money - that they risk. In fact they lose money in their clients account whereas their trading account in offshore countries or friendly hedge funds are prospering: this is a legal but somehow stealth scheme which is very difficult to prove legally but since it is their interest and since there is no law that forbid it - in 1929 there was such a law but it has been suppressed and even that law was easily avoided).

    You must chose either to be investor either to be a trader and not mix the worst of the two.

    #10     Apr 26, 2003