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Jul

13

A simple thought experiment on US Mutual

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I was doing some research on the net about my idea to save Social Security and reduce the NYSE’s volatility.  I came across the following article that had some helpful statistics on how the S&P500’s annual return has recently been 10.60% with a 4.20% monthly standard deviation.  It also mentions that a group of preferred stocks has recently had an 8.17% annual return and a 1.11% monthly standard deviation.  I used a simple linear extrapolation to find a 7.30% return for a certainty equivalent.  I bring this example up because the group of preferred stocks seem like the sorts of stocks that US Mutual would buy long on. 

I then made a mistak and misinterpreted a recent academic paper on the internet.  It was about the value premium.  Ie, some stocks are undervalued by the market, meaning they have a higher book-to-market ratio, these are the Value stocks, others have a lower book-to-market ratio, the Growth stocks.  I misinterpreted some statistics in the paper to guesstimate that the mean return of stocks that US Mutual would sell short on would be .06 with a monthly standard deviation of .093.  Unfortunately, there is no basis to think that these stats are likely.  What matters more is that there is a significantly smaller natural difference in the returns than the standard deviations.  This is likely under the algorithm since it gives more weight to standard deviations than returns in ranking stocks and there also tends to be a positive correlation between returns and standard deviations.   

So if we spent two thirds of a dollar to buy long on stocks whose returns and standard deviations were .082 and .011 and a third to sell short on stocks whose returns and standard deviations were .060 and .093 then, presuming independence, the stats would be (.082*2/3-.06/3=) .035 and (Sqrt(2/3*.011^2+1/3*.093^2)=) .054, with a certainty equivalent, using the formula inferred above, of -.008.  If the standard deviation were reduced to .04 because the two groups of stocks tended to vary together then the certainty equivalent would only go up to .003. 

This goes to show just how important the use of US Mutual’s market power would be for its overall performance.  Let’s guesstimate conservatively that the return of the stocks we bought long on would go up by twenty percent(as we would on average target 20% ownership of them) and its standard deviation would go down by twenty percent, so its stats would be .098 and .009.  Let us also assume that both the return and the standard deviations of the stocks we sold short on would go down by 40 percent so their stats would be .036 and .056. Then, the fund’s stats would be .054 and .033(presuming independence), with a certainty equivalent of .028.

And so, it seems that US Mutual, in order to reduce the volatility of the NYSE and hedge against a worse case scenario of a general downturn, would need to reduce its guaranteed return.  However, the system, as described here, would still be an improvement over the current social security system and have an advantage over other mutual funds with its lower overhead costs.  One can also argue that the reduced volatility of the NYSE would be in the public interest for the promotion of greater economic stability. 

dlw

Comments

12 Responses to “

A simple thought experiment on US Mutual
”

  1. Alan Avans on July 13th, 2006 11:28 pm

    Dlw, don’t you know that short-selling is communist? ;)

  2. dlw on July 14th, 2006 12:05 am

    Settling for public mutual fund holdings with a 2.8% certainty equivalent with a rather low Beta is definitely communist, but it still would save Social Security and reduce the volatility in our Stock Market…

    dlw

  3. Frank Dean on July 14th, 2006 11:14 am

    The big problem with your idea is that the volume of shorting implied by your strategy will be impossible for a large player to implement without causing substantial price movements, which will destroy returns. For example, the recent short interest in Intel Corporation is 40+ million shares. The number of shares outstanding for Intel is about 5.8 billion. So the short interest is less than 1% of the long interest. This is pretty typical across all stocks.

    Your plan would introduce a huge fund with short interest 50% of the long interest into the market. I don’t think the assumptions you’re making about volatility,returns and independence would survive.

  4. dlw on July 14th, 2006 1:00 pm

    Thankyou for writing Frank.

    I think part of the idea was to exert some market power by US Mutual on those stocks it sold short on and to reduce their returns and to change stock market behavior.. The fact that my idea will be very different from existing practice does not concern me.

    I don’t see this as destroying all returns. I see it as targeting those stocks who have been most volatile and under-perfoming for either removal from the stock market or serious reform. I also see it as pouring cold water on strategies that try to time the market and end up contributing to the volatility of stocks.

    The assumptions I made above were not critical for the algorithm I described in earlier posts. I think it is folly to suggest that reducing the return on the bottom 5% of unstable under-performing stocks would spill over to reduced return on the rest of the stocks when one is also buying long at the same time.

    But the key here is the need to use more sophisticated modelling to test out the possible behavioral implications of the idea.

    dlw

  5. The Anti-Manichaeist » Blog Archive » What Would be the Impact of a 20% less Volatile NYSE? on July 14th, 2006 1:57 pm

    [...] Frank Dean recently commented on how radically different the behavior of US Mutual would be from current investment behavior.  Usually, the volume of short interests, or those who sell short a stock, is only 1% of the volume of buy interests.  He fears that my ”strategy will be impossible for a large player to implement without causing substantial price movements, which will destroy returns.”  But what’s key here is that it would only reduce the returns for the most volatile and underperforming stocks in the NYSE and it would increase the returns for the most stable performers.  [...]

  6. Frank Dean on July 15th, 2006 1:17 pm

    Having looked at the paper, and your math more carefully (I may have made an error of reading or interpretation; it’s possible the 10.6% annual return of one group and 1.06% monthly return of another are causing confusion), but:

    (1) the monthly returns are 1.17% and 1.06%, not .17% and .06% for the Russell 3000 Value and Growth indexes respectively.

    (2) the preferred shares have an ANNUAL return of 8.17%, which works out to a monthly return of 0.66%

    The portfolio suggested would be 2/3 long on stocks with a .082 annual return and 1/3 short on stocks with 0.0106 monthly return. Or, using the same period to measure the returns:
    2/3 long, 0.66% monthly return, low volatility
    1/3 short, 1.06% monthly return, high volatility

    I’m not sure what your portfolio is designed to achieve.

    On another point, you imply that US Mutual will make money because of market power; i.e. its long purchases will drive these stocks up, and its short sales will drive those stocks down. True. Except these paper returns are not available to US Mutual, because in order to realize the returns as cash, it will have to sell and buy its long and short positions respectively, causing price movements that will reduce the value of its portfolio. You can’t count the effect of market power when it works in your favour, and then ignore it when it works against you.

  7. dlw on July 16th, 2006 12:34 am

    Thankyou. I realize that I misread the paper, seriously.

    You are right about my point. I expect the natural standard errors to diverge more than the natural returns, given that my proposed method would weight the standard errors more in the index used to select stocks. I guess I still need to work to get better numbers to corroborate my idea with. It would have a decent beta if the stocks we bought long had lower betas and the stocks we sold short had higher betas. And that is part of what the portfolio is designed to acheive that it would perform well even in the worse-case scenario of a general downturn. It is also meant to help grow the Social Security Trust Fund without raising taxes or forcing people to pay their Social Security taxes, improve on the return that would be guaranteed for Social Security savings and help to reduce the general volatility of the NYSE.

    I don\’t have to worry as much about selling long positions because, US Mutual would be targeting a 6% control of the predicted total value of the NYSE long-run and so the holdings would be relatively stable provided that their predicted median statistics are also relatively stable. So the weekly adjustments in holdings would be relatively small and spread out over time which would reduce the extent that market power would work against the fund.

    As for the stocks we sold short on, I expect there would be more turnover. I think initially after we established US Mutual some stocks might go bust or leave the NYSE, while other stocks would evidence more risk aversion. I think US Mutual would discourage short-run speculation if it tends to increase volatility. I think that if we could reduce the overall volatility of the NYSE by 20% that it would attract more capital to the NYSE and increase the value of stocks relative to bonds and increase the equity premium. I think that once a new equilibrium of NYSE equity-buying and selling behavior is established after the transition period then the fund would simply tend to bleed overvalued stocks whose value is more unstable and whose median log-returns tend to be lower. (I think that if the paper I misinterpreted above had used median rather than mean regressions that they might have found a statistically significant differences in the returns between Value and Growth stocks. There seems to be a volatility difference between the two types of funds.) Then, when a stock\’s value has been bled so its starts to do better and US Mutual starts buying its short position back, it would be weakened and the threat of US Mutual taking a short position again woul be serious enough that the price would not rise as much.

    thankyou for your comments and critical feedback.

    dlw

  8. kurye on September 30th, 2009 5:01 pm

    thank you for share

  9. dlw on October 13th, 2009 12:02 am

    no problem.

  10. motorlu kuryeler on January 12th, 2010 8:05 am

    emege saygi tesekkürler devamini bekleriz.

  11. estetik on June 29th, 2010 5:21 pm

    Hi great article. I want to publish this article on my own if allowed.

  12. dlw on June 29th, 2010 5:27 pm

    Go ahead.

    dlw

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