Question

you manage an algorithmic trading operation where computers are trading in the stock market Suppose automatically without human intervention using algorithms. Suppose that your algorithm called “Shining Star” (SS) makes an average profit of $6000 each trading hour in the stock market. However, your gut instinct is that the algorithm’s performance has decreased recently. We have provided a random sample of 75 of the more recent hours of trading performance.

Hourly Profit

$ (1,622.29)

$    2,916.77

$       356.03

$    3,204.53

$    3,829.72

$    1,166.44

$ (1,144.88)

$       (21.88)

$    3,563.70

$ (2,817.08)

$    1,593.21

$     (672.84)

$    2,064.04

$    2,129.55

$    4,572.09

$       146.06

$ (2,651.18)

$ (3,332.17)

$    4,434.95

$    2,231.24

$       (93.29)

$     (533.28)

$     (961.39)

$ (3,137.56)

$    1,035.10

$    6,026.95

$ (2,362.77)

$     (774.82)

$ (2,479.09)

$    1,123.78

$     (664.86)

$    4,432.62

$    2,451.76

$    4,621.02

$     (862.48)

$    1,334.23

$    4,927.53

$       483.45

$       312.57

$    6,140.44

$    3,231.92

$       716.18

$    1,673.86

$    3,421.32

$    3,338.60

$ (2,571.67)

$ (2,493.93)

$       639.48

$       540.53

$ (1,960.74)

$ (1,223.31)

$    4,068.08

$    5,288.04

$     (358.20)

$    2,121.62

$       552.09

$    2,735.47

$    1,287.17

$    2,086.94

$     (593.27)

$    5,812.52

$    4,292.32

$ (3,891.48)

$    3,250.49

$    1,532.81

$    3,014.27

$    4,116.66

$       515.98

$ (1,520.46)

$       680.54

$    1,031.76

$    2,116.75

$ (1,983.71)

$       318.83

$    3,205.22

PARTS

Write down a hypothesis test for checking if the performance has decreased. Suppose your significance level is 0.01 .

a) Write down the test statistic.

b) What is the name of the model/distribution that would be appropriate to use for the probability distribution of the test statistic? Also, please state your assumptions for picking that distribution.



c) Please provide as much information as you can about the relevant parameters for the distribution (e.g., mean and standard deviation) under the status quo or null.

a) What is your p-value for this test?

b) What is the critical threshold for your test statistic?

b) Has the performance of your SS algorithm decreased? Why or why not?

[
a) Now write down a hypothesis test for checking if the performance has increased. Suppose your significance level is 0.01 .

b) What is your p-value for this test?

c) Has the performance of your SS algorithm increased? Why or why not?

Answer 1

We use Minitab to solve this question-
MTB > OneT C1;
SUBC>   Test 6000;
SUBC>   Confidence 99.0;
SUBC>   Alternative -1.

One-Sample T: C1

Test of μ = 6000 vs < 6000

Variable   N Mean StDev SE Mean        99% Upper Bound     T       P
C1      75 2232   1575      182            2665           -20.71 0.000
___________________________________________________________________________

The null and alternative hypothesis are,

    VS    

a) The test statisyic is,
T = -20.71
b) We do not know population standard deviation therefore the model distribution that would be appropriate to use probability distribution of test statistic is t distribution.

c) From given sample information-
   Mean = 2232
   Standard Deviation = 1575
a) P-value = 0.000
b) Critical Thershold of test statistic is,
t0.01,74 = -2.378 ________using t table
c) T = -20.71 < t0.01,74 = -2.378 Reject Ho therefore performance of SS algorethm decreased.

a) At significance level 0.01, Observe that,
   p-value < 0.01 , Reject Ho therefore performance not increased.
b) P-value = 0.000
c) T = -20.71 < t0.01,74 = -2.378 Reject Ho therefore performance of SS algorethm decreased.