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Is diversification a sham? (financial advice)

  1. Sep 8, 2015 #1
    Is diversification a sham?

    Yet this is the advice financial advisors are constantly giving us.
    I can't stop thinking that it's all marketing hoax... giving people the false hope that there exists a real "strategy" and logic to anything.

    To me it's equivalent to proclaiming that sticking to one brand of lottery is a poor method whereas purchasing multiple brands of lottery tickets increases your chances of winning significantly.

    It just doesn't seem intuitive to me that splitting up a pot of money into multiple pots, each of which is now used to buy various 'diversified' lottery ticket brands, in any way increases your chance of winning. If it were the case then we'd be hearing abut the best ratio to use. Or, why not just ignore the 'poor' performing ones altogether.

    Examples of multiple lottery brands are for example Powerball / Mega Millions / The Big Game or in Canada
    Lotto 6/49, Lotto Max. If you only play one, would say those advisors, you're not being smart.

    Can someone with a stronger statistical background explain how diversification is a valid technique for increasing ones average winning ratio? And why this technique is suspiciously absent as a tool in any other risky behavior. I said "curiously" because I have a strong suspicion that it's a bogus methodology.

    It's like suggesting: "to reduce the risk of death in the sport of skydiving, you should also take up hang gliding. This will spread out the risk. as you're devoting less total time to just one thing."

    This is not homework. Just a thought experiment... one that's been bothering me for years.
     
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  3. Sep 8, 2015 #2

    andrewkirk

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    Diversification is not always about increasing the probability of winning. It can also be about reducing the size of potential losses. It does that by reducing variance.

    Diversification only increases the probability of winning when that probability is already reasonably high. To be specific, when the expected payoff of a strategy is more than zero, the probability of a positive payoff can be improved by combining a number of such strategies. It does that by reducing the variance. It does not however increase the expected payoff.

    This can be visualised by imagining a bell curve the height of which represents the probability of profit equal to the value on the x axis, and the peak of the bell curve - the expected profit - is to the right of the y axis, ie in positive territory. Say 40% of the area under the bell curve falls to the right of the y axis, ie representing losses. Then if we can narrow the spread of the bell curve without changing where its peak lies, less of the area will be to the left of the y axis. This is not getting something for nothing because, as well as reducing the probability of losses, it also reduces the probability of large gains. We have foregone potential large gains in order to reduce the likelihood of losses.

    Diversification is the method by which we narrow that bell curve. It uses the simple fact that, if the variance of an investment in any one of n stocks is s, then the variance of an investment divided equally between all n stocks is s/n.

    Whether diversification can be used to 'increase one's winning ratio' depends on what game of chance you are talking about, and what you mean by a 'winning ratio'. In some situations and for some definitions of ratios, diversifying strategies can improve the ratio. In others they cannot.
     
  4. Sep 8, 2015 #3
    Thanks for that eloquent explanation. I'll have to digest that.

    It appears that the counterexamples I gave are faulty because they exhibit an expected payoff that's less than zero. You're saying that only potentially positive payoff items may be skewed by narrowing its spread.

    I'm still not entirely clear. If one forgoes potential large gains in order to reduce probability of losses, how is one further ahead in one or the other extreme of bell curve spreads?

    Perhaps the answer is in how much one weighs a potential loss vs. an equivalent gain. If the loss, for example, is deemed much more 'important' than any equivalent gain. In other words, there is an additional, non-mathematical component - an emotional bias, that we're trying to accommodate. The raw numbers (gain vs. loss) can not be magically changed, but one's comfort level may be adjusted by twiddling the tone controls on the bell curve. Am I on the right track?
     
  5. Sep 8, 2015 #4

    lisab

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    So...you're equating investing with playing the lottery?
     
  6. Sep 8, 2015 #5

    andrewkirk

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    Yes.
    The investor is only better off if they would regret a $50 loss more than they'd enjoy a $50 gain. Economists often utilise a mythical beast called a 'risk-neutral investor' who cares only about expected profits (in the formal statistical sense of expected value or mean) and not about the distribution of possible profits and losses. Option pricing theory is based around what a risk-neutral investor would do.

    In practice, humans are always somewhat risk averse. The branch of economics that deals with this is called Ultility Theory. THe Utility function maps the wealth of an investor to their satisfaction. Utility curves are always upward sloping (more is better) but concave down ($1000 more is not ten times as good as $100 more). Given such a utility curve, an investor will be happy to remove the top 25% best possible investment returns in order to also remove the 25% worst possible investment returns.
     
  7. Sep 8, 2015 #6

    andrewkirk

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    The interesting thing (to me) about this comparison is that the process works in reverse for any game where the expected payoff is negative, which is the case with just about all forms of gambling.

    Diversification increases the probability of receiving a payoff close to the mean. In investment, where the mean is positive, it increases the probability of a positive payoff. In gambling, where the mean is negative, diversification increases the probability of a negative payoff. It follows that, if one wishes to gamble, one is better off betting a lot of money on one number (switching the example to roulette) rather than smaller amounts on a bunch of numbers. But one will still expect to lose.
     
  8. Sep 8, 2015 #7
    This is true for most investors. In large part this is because most people are investing for retirement. A modest retirement is much better than a 50/50 chance of being rich or starving.

    But for those trying to build wealth, concentrating investments in an area where one has expertise is often a better solution. Concentration earns money. Diversification prevents loss.
     
  9. Sep 9, 2015 #8

    BWV

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    The other issue - which ties to the positive expected value, is the economic arguments on what risks an investor is paid to bear. If you and I wager on a coin toss, neither one of us would offer better than even odds. However in financial markets, investors must be offered a return, i.e. a positive expectation, for purchasing equity or debt securities. The economic argument is that the only risks investors are compensated for assuming are those that are non-diversifiable. This means the only stock market risk, not individual company risk warrants a risk premium. If, for example, you buy a speculative biotech stock that is either worthless or worth 10x depending on whether its drug gets approved by the FDA, the fair pricing of that security involves a discount rate that only depends on how sensitive to market risk (beta in finance jargon) the stock is. Another example would be making risky loans - if you loan money at 10% to borrowers with a 5% default rate, you would be insane to only make a couple of loans.
    You can earn the equity risk premium by purchasing a broadly diversified index fund, anything less than this just adds uncompensated risk to the returns.
     
    Last edited: Sep 9, 2015
  10. Sep 9, 2015 #9
    It isn't. The whole idea is to reduce variance, which in economics is called "risk."

    The assumption is that values of the commodities over which one is diversifying are uncorrelated or, even better, negatively correlated.
     
  11. Sep 9, 2015 #10

    nsaspook

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    Losing slowly is usually a good 'investment' strategy while gambling. Lose fast and the house has little incentive to provide 'free' drinks, rooms and perks. Losing smaller amounts over a longer period of time means the house wants you to continue and will try to keep you there with those 'free' drinks, rooms and perks. One will still expect to lose but it's nice not being treated like a 'loser'.
     
  12. Sep 9, 2015 #11

    Nidum

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    Bookies have a sophisticated system of laying off high risk bets placed with them by putting spread bets on other possible winners at other bookies .

    They used to do it mainly intuitively but some of of the larger bookies now use computers .
     
  13. Sep 9, 2015 #12

    BWV

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    Insurance companies do essentially the same thing
     
  14. Sep 9, 2015 #13
    Impressive amount of knowledge and expertise being demonstrated here! Thanks all so far! My inquiry has been better received and addressed than I had expected.
     
  15. Sep 9, 2015 #14
    The whole point of diversification is to avoid losing big.
     
  16. Sep 11, 2015 #15
    I add one more thing - poorly done diversification can be indeed a sham. There is a non zero correlation between return from different investments. Let's say you invest only in one sector. Like you have in portfolio only some tech companies. Or a few banking companies and some bonds issued by banks. Or real estate fund and construction companies. And a crisis comes, (or a dot com bubble) then all such sector is in trouble.

    On the good thing the correlation could also work in your favour - shares and gold. In case of some troubles the shares would plummet, but gold would go up.
     
  17. Sep 11, 2015 #16
    One decent measure of correlation is a stock's beta (β). Beta measures the correlation of the stock to the entire market. Stocks with a β of 1 move as the market moves. Negative β indicates stocks which move against market trends. Unfortunately there are few of these and they tend to trade at a premium.

    A more sophisticated methodology is to correlate the posited portfolio against itself, but that takes some computing power.
     
  18. Sep 11, 2015 #17

    BWV

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    The standard finance model is:

    re(portfolio)=α+β(remarket)+ε
    re=return in excess of T-Bills or some other proxy for a risk-free rate of return
    α = excess return (earned by stockpicking or trading skill, a zero sum game among investors)
    β=cov(portfolio,market)/variance(market)
    ε= idiosyncratic volatility

    standard finance theory would state:
    exp(re)>0
    exp(α)=exp(ε)=0
    so only β(market RE) is a source of expected return. Diversification reduces the variance of ε which is risk with no expected return

    σ2Portfolio2σ2Market2ε
    also, using geometric brownian motion to model stock returns (a reasonable assumption that keeps prices >0)
    dp/dt=μdt+δdz
    where μ is the drift or mean return and z is a normally distributed random variable
    it can be shown using Ito's Lemma that

    pt=p0Exp((μ-σ2/2)t+σzt)

    the -σ^2/2 corresponds to the difference between the arithmetic mean and geometric mean return (a year 1 return of +10% followed by a year 2 return of -10% is a 1% loss, not a zero return). This means that assuming uncompensated volatility by not diversifying diminishes the overall return (actually the expectation is the same, but higher volatility concentrates all the value in the right tail so the median goes to zero as σ→∞, holding r constant)

    the standard deviations of individual stocks twice or more the overall market volatility, so the vol reduction benefits from diversification are substantial
     
    Last edited: Sep 11, 2015
  19. Sep 11, 2015 #18
    Agree. But even investing in stocks of different economic sectors is a poorly done diversification. Sure the correlation might be low, but that's a very poor measure to use when investing. When there is a bull market you'll be exposed to the different sectors rotation, but in the event of a serious market turn, they'll all go down, with few exceptions (and the long-term correlation won't change much).
     
  20. Sep 11, 2015 #19

    andrewkirk

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    That equation is for arithmetic, not geometric Brownian Motion. The Geo BM equation is

    $$dP=\mu P dt+ \sigma P dz$$
     
    Last edited: Sep 11, 2015
  21. Sep 11, 2015 #20

    andrewkirk

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    Beta is more a measure of leverage than of correlation. Beta tells us nothing about how diversified a portfolio is - ie its level of unsystemic (aka idiosyncratic aka stock-specific) risk. It tells us how much systemic risk there is, and systemic risk is undiversifiable.
     
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