The Chair has noted an unusual percentage of up days recently in the US stock market. In academic studies of simulated trading, this sort of price action occurs when a couple of participants are told the true value of a stock in advance. The uninformed participants trade randomly, and the informed participants' trading moves the price in the direction of true value. I don't think that is what is happening now–insiders have sold 2.5 times as many shares as they have bought in the past two months. The wave of money is coming from elsewhere.

In an attempt to quantify what is happening, I divided the last 1800 days of S&P 500 trading into 90 20-day periods. For each period I calculated the average daily percentage change and the standard deviation of the daily changes. I divided the average daily change by the standard deviation to get an estimate of how far the market was moving relative to volatility.

In the 20 trading days ending February 10, 2012, the average daily net change of the S&P 500 emini contract was 0.19% with a standard deviation of 0.48%. The ratio of average change to standard deviation was 39%, the 7th highest ratio in the 90 20-day periods (and the 8th highest absolute value ratio). After 12 of the previous 14 instances in which the ratio was greater than 25%, the S&P 500 emini was up during the next 20 days, but one was followed by a steep decline, and the t score was less than 1.

20 days    Avg. daily   Std            Next 20 days
Ending     change (20)  dev     Ratio     change
 3/19/2010    0.2%      0.5%    50.2%      2.9%
12/31/2010    0.1%      0.3%    49.9%      2.3%
 6/13/2005    0.2%      0.5%    42.4%      1.5%
 4/6/2009    1.1%      2.7%    40.0%      8.8%
 12/1/2005    0.2%      0.5%    39.9%     -1.4%
 11/3/2010    0.2%      0.5%    39.0%      2.1%
 2/10/2012    0.2%      0.5%    38.9%
 10/6/2010    0.3%      0.8%    34.8%      3.6%
10/17/2006    0.2%      0.4%    34.6%      1.9%
 4/12/2007    0.2%      0.5%    34.6%      3.0%
 1/12/2012    0.3%      1.0%    29.5%      3.8%
 5/10/2007    0.1%      0.5%    28.8%      0.6%
 8/21/2006    0.1%      0.5%    28.7%      1.3%
 7/30/2009    0.3%      1.3%    25.7%      4.8%
 7/22/2011    0.2%      1.0%    25.3%    -16.2%

Rocky Humbert writes:

It's impossible to know the cause and effect; but if you move from vol=25 to vol=15, stocks SHOULD go up, ceteris paribus. And if we are about to shift from vol=15 to vol=25, p/e's should shrink.

Steve Ellison replies:

Dividing my 90 20-day periods into a 2×2 matrix, price change up or down and volatility low or high (defined as the standard deviation being above or below the median of the last 30+ 20-day periods), I found the following distribution:

Price up   30    30

down       6     24

              low   high


Price went up in 83% of low volatility periods and only 56% of high volatility periods.

Rocky Humbert replies:


Thank you as always for your numbers on the table! If I understand this correctly, it confirms my superficial hypothesis … and it's also part and parcel of how the GARCH etc people manage money. Mr. Rogan writes: "How can it be rational for people to react to some short-term decrease in volatility by bidding up prices, when they have no idea if that change will hold the next day?"

To Mr. Rogan: The risk of a position is not what it did yesterday. It's what it will do tomorrow. You are making the quaint assumption that it is less "risky" to buy after a price dump. That might be true after some period of time, but it's not true in the days or weeks after a sharp price drop. For investors who use VaR, they are willing to buy/own more of an asset that exhibits less price volatility REGARDLESS OF THE INTRINSIC VALUE of the asset. This is one of those things that got us into the financial crisis. But it is rational if you believe that the market generally gets the nominal pricing correct. I am not going to defend VaR, but neither am I going to call it systematically irrational. I dare say that if you were putting 50% of your net worth into a buy&hole stock, you'd feel more comfortable picking a stock that "only" moves +/- 15% per year versus a stock that moves +/- 90% per year.

From Wiki:

In financial mathematics and financial risk management, Value at Risk (VaR) is a widely used risk measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, probability and time horizon, VaR is defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading in the portfolio) is the given probability level.[1]For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day in 20. A loss which exceeds the VaR threshold is termed a "VaR break."[2] Thus, VaR is a piece of jargon favored in the financial world for a percentile of the predictive probability distribution for the size of a future financial loss.VaR has five main uses in finance: risk management, financial control, financial reporting and computing regulatory capital. VaR is sometimes used in non-financial applications as well.[3]Important related ideas are economic capital, backtesting, stress testing, expected shortfall, and tail conditional expectation.[4]





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