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Salil Mehta
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Salil Mehta is a statistician and risk strategist, who has developed a unique and engaging method for teaching statistical ideas. Salil has more than 16 years of experience, with a dozen years on Wall Street performing proprietary trading and economic research for firms such as... More
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Statistical Ideas
• ##### Tesla Rare Up-Streak

For those simply curious about rare market streaks, it is worth noting that today Tesla (TSLA) is on track for it's 7th straight up day. In the 3 years of Tesla's trading history, of less than 800 trading sessions, we've seen only two 7-day up streaks and one 8-day up streak. To complicate matters, this is occuring in a period of high increasing market volatility.

Tags: TSLA, Streaks
Jun 20 10:24 AM | Link | Comment!
• ##### Probability Of Not Getting X Down Days, In Y Months

This is a simple twist off of the positive up streaks we have seen in the markets so far this year. Here below is the start of the simple formulaic logic to solve for this chance occurrence, assuming a random walk without trend. We start with the probability of three down days.

q = chance of getting a down day is 50%
qqq = chance of getting a down day, three days straight, is 50%^3 = 12.5%

Now each month there are about 22 trading days, or 7 consecutive 3-day periods. This would be the same probability as solving this problem with rolling 3-day periods since we are, in this case, seeking to solve a streak calculation. So continuing the formula above, and solving for the chance of not seeing three straight down days in a month implies:

(1-qqq)^7
= 87.5%^7
= 38%

Then to compound this process of not seeing three straight down days, over a range of months in a row, we see how quickly this probability falls. See the leaf-like chart below.

Number of straight months | Probability of not seeing 3 down days over this time (50 *'s = 100%)
0 | ************************************************** (100%)
1 | ******************** (38%)
2 | ******** (14%)
3 | *** (6%)
4 | ** (2%)
5 | * (1%)

The chance of seeing four straight down days is the probability of seeing three straight down days multiplied by half of the fourth days also being down. So 12.5%/2=6.25%. Combined with the fact that there are 3/4 as many 4 day consecutive periods a month versus 3 consecutive day periods, the probability therefore of not seeing this rare event is even higher! Or(1-qqqq)^5=70%. Let's see this compound probability over a range of months, in this leaf-like chart below.

Number of straight months | Probability of not seeing 4 down days over this time (50 *'s = 100%)

0 | ************************************************** (100%)

1 | ************************************ (70%)

2 | ************************* (50%)

3 | ****************** (35%)

4 | ************* (25%)

5 | *********(17%)

Tags: SPY, DIA
Jun 12 1:30 PM | Link | Comment!
• ##### Tesla Motors' Share Price Changes

These statistical charts shows the directional distributions for Tesla Motors (TSLA), for up and down moves in its daily closing price, as well as the non-parametric autocorrelation in the same. For the initial chart below, for example, there were three trading days where the price change was <-15%. And there were four trading days where the price change was >15%.

The average for Losing tail is -2.4% (shows as 0.024 in the chart below), while the average for Gaining tail is 2.8% (shows as 0.028 in the chart below). Note that in order to balance the distributions, the median daily change of positive 0.1% was subtracted from all data so there is a slight adjustment for the net change.

(click to enlarge)

Additionally, we reinforce this analysis with the daily non-parametric serial correlation in Tesla stock, in addition to that of the S&P 500 to show how this is related. We see the low directional autocorrelation conditional for Tesla, based on various streak levels.

(click to enlarge)

Tags: TSLA
Jun 04 5:31 PM | Link | Comment!