## Tuesday, 10 January 2012

### Formula for Approximating VWAP from OHLC Data

An answer to another question on the Quantitative Finance forum here gives a formula that approximates the volume weighted average price (VWAP) from OHLC data only, with an exhortation in a comment to do one's own research before using it. This blog post is my quick attempt at such research.

My simple test uses the relationship between the VWAP and the Pivot point calculated as (H+L+C)/3. This wiki entry on pivot points states "Trading above or below the pivot point indicates the overall market sentiment" and my test of being above or below is the VWAP being above or below: i.e. if today's VWAP is above today's pivot point (calculated from yesterday's H,L & C) then this is s bullish sign and therefore we can expect tomorrow's VWAP to be higher than today's. The converse is true for bearish sentiment. In Octave it is trivially simple to write a script to test whether this hypothesis is true and the terminal output of the results is shown in the box below.

The first line identifies the market being tested (a forex pair or commodity), the second "sign_correct" is the percentage of time the hypothesis appears to be true: i.e. for the first AUSCAD entry the figure 67.228 means that 67.228 % of the time the following day's VWAP is actually higher/lower than today's according to the "prediction" based on the categorisation of today's bar being bullish or bearish. The third "result" is the p-value of a 5000 repetition Monte Carlo permutation test to test the statistical significance of the given % accuracy. The permutation test was the "sign" test described in Evidence Based Technical Analysis and in the PDF available from its companion website.

Given that all the p-values are zero it can be stated that the VWAP being above or below the pivot point has a non random predictive accuracy for the next day's VWAP being higher or lower to a degree of accuracy that is statistically significant.
auscad
sign_correct =  65.695
result = 0
------------------
aususd
sign_correct =  67.228
result = 0
------------------
ausyen
sign_correct =  67.100
result = 0
------------------
bo
sign_correct =  63.989
result = 0
------------------
c
sign_correct =  63.530
result = 0
------------------
cc
sign_correct =  60.565
result = 0
------------------
cl
sign_correct =  63.318
result = 0
------------------
ct
sign_correct =  60.273
results = 0
------------------
dx
sign_correct =  63.811
result = 0
------------------
ed
sign_correct =  63.945
results = 0
------------------
euraus
sign_correct =  68.024
results = 0
------------------
sign_correct =  66.854
result = 0
------------------
eurchf
sign_correct =  65.707
result = 0
------------------
eurgbp
sign_correct =  66.760
result = 0
------------------
eurusd
sign_correct =  65.544
result = 0
------------------
euryen
sign_correct =  66.444
result = 0
------------------
fc
sign_correct =  61.905
result = 0
------------------
gbpchf
sign_correct =  67.497
result = 0
------------------
gbpusd
sign_correct =  66.936
result = 0
------------------
gbpyen
sign_correct =  66.936
result = 0
------------------
gc
sign_correct =  60.667
result = 0
------------------
hg
sign_correct =  58.554
result = 0
------------------
ho
sign_correct =  62.685
result = 0
------------------
kc
sign_correct =  61.732
result = 0
------------------
lb
sign_correct =  61.765
result = 0
------------------
lc
sign_correct =  62.372
result = 0
------------------
lh
sign_correct =  61.601
result = 0
------------------
ng
sign_correct =  62.356
result = 0
------------------
o
sign_correct =  60.705
result = 0
------------------
oj
sign_correct =  61.848
result = 0
------------------
pa
sign_correct =  62.497
result = 0
------------------
pb
sign_correct =  59.116
result = 0
------------------
pl
sign_correct =  60.737
result = 0
------------------
rb
sign_correct =  63.107
result = 0
------------------
s
sign_correct =  64.091
result = 0
------------------
sb
sign_correct =  61.106
result = 0
------------------
si
sign_correct =  59.563
result = 0
------------------
sm
sign_correct =  63.810
result = 0
------------------
sp
sign_correct =  66.954
result = 0
------------------
es
sign_correct =  66.744
result = 0
------------------
nd
sign_correct =  66.221
result = 0
------------------
ty
sign_correct =  65.260
result = 0
------------------
us
sign_correct =  65.893
result = 0
------------------
sign_correct =  67.357
result = 0
------------------
usdchf
sign_correct =  67.088
result = 0
------------------
usdyen
sign_correct =  66.947
result = 0
------------------
w
sign_correct =  65.118
result = 0

At the moment I use the value given by the pivot point calculation as my "price input" for the day but, based on these test results and the future results of some other tests I can think of, I may change to the VWAP approximation as my price input. More in a future post.