Question

Explain clearly how you i proceed to Test the weak form of Efficient market hypothesis using autocorrelation of return for time lags pre and during covid19. Provide analysis of your results. will give positive review

Answer 1

Efficient Market Hypothesis is one of the central ideas of Mordern Finance. Market Efficiency means that the market price of security reflects all available information. In other words, an efficient market responds quickly to new information and thev key to market efficiency is high level of competition amoung participants in market. This also implies that new information cannot be useo create a trading strategy to beat the market. (Investors cannot make abnormal profits in share market). Based on different information sets , there are three form of market efficiency, Weak form Efficiency being one of them.

There are 2 test that can be performed in Weak form Efficiency a) Run Test b) Auto Correlation Test

The auto correlation test is applied to identify the degree of auto correlation in a time series . It measures the correlation between the differences in current and lagged observation of the time series of stock return. If coefficient of correlation tends to be zero, the randomness is there i.e market is weakly efficient otherwise it is not weakly efficient.

Given below the data to apply auto correlation test for finding whether market is weakly efficient or not using time lag of 10 days.

Trading Days	Closing Sensex
1	13450
2	13440
3	13430
4	13380
5	13370
6	13340
7	13330
8	13335
9	13310
10	13270
11	13250
12	13290
13	13330
14	13290
15	13300
16	13320
17	13330
18	13340
19	13320
20	13340

Calculation of Changes in index value(with time lag of 10 days)

Trading day	Closing Sensex	Change(X) day	Trading Sensex	Closing	Change(Y)
1	13450	0	11	13250	0
2	13440	-10	12	13290	40
3	13430	-10	13	13330	40
4	13380	-50	14	13290	-40
5	13370	-10	15	13300	10
6	13340	-30	16	13320	20
7	13330	-10	17	13330	10
8	13335	5	18	13340	10
9	13310	-25	19	13320	-20
10	13270	-40	20	13340	20

Calculation of Correlation of Coefficient:

X	x	x2	Y	y	y2	xy
-10	10	100	40	30	900	300
-10	10	100	40	30	900	300
-50	-30	900	-40	-50	2500	1500
-10	10	100	10	0	0	0
-30	-10	100	20	10	100	-100
-10	10	100	10	0	0	0
5	25	625	10	0	0	0
-25	-5	25	-20	-30	900	150
-40	-20	400	20	10	100	-200
X=-180	x=0	​​​​​​​x2 =2450	​​​​​​​Y =+90	​​​​​​​y=0	​​​​​​​y2=5400	​​​​​​​xy=1950

Covariance = ​​​​​​​xy/n = 1950/9 = 216.67

SD of X = ​​​​​​​x2 /n =(2450/9) = 16.5

SD of Y = ​​​​​​​ y2/n =(5400/9) = 24.5

r = Covariance/SD of X. SD of Y

= 216.67/(24.50)(16.50)

=+0.525

As r does not tend to 0, the market is not weak