Author: shyam

Volume Clock, an Introduction

Typically, prices and volumes are charted based on time aggregations. The most common aggregation is the daily chart.

The daily chart shows the high/low/open/close and volume traded of a particular instrument. Intraday traders might prefer a more granular version of this. Maybe a minute chart does the trick for them.

Chrono-clocks are intuitive because that’s how we perceive events around us and have been trained to think.

However, time is not the only way to aggregate prices. If prices are information, then volume indicates the speed with which it arrives. You can divide the day into equal volume buckets (eg. in 5000 contract increments) and transform the time-series from chrono-time to event-based time.

In fact, working in volume time presents significant statistical advantages. First, this time transformation removes most intra-session seasonal effects; second, it allows a partial recovery of Normality and the IID assumption; third, sampling in a volume-clock metric addresses the problem of random and asynchronous transactions, which is a major concern when computing correlations on high-frequency data.

The Volume Clock: Insights into the High Frequency Paradigm (SSRN)

We know that trading turnover throughout the day is not constant. If you plot turnover over a trading day, it typically traces a ‘U’ shaped plot. Even widely traded index futures like the NIFTY have “slow” and “fast” periods. A volume clock is one way to match the sampling frequency with information flow frequency.

When you aggregate by volume, each slice of time will have different lengths. For example, we streamed NIFTY futures over a couple of weeks and aggregated it by 2500, 5000 & 10000 lots traded. The y-axis is the width of the time-slice of each volume-tick.

The size of the volume bucket would depend on what one is trying to analyze. Here’s the 2500 lot bucket by itself:

“There are minutes where nothing happens; and there are seconds where minutes happen” – Lenin, the High Frequency Trader.

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Midcap Select Index Futures

The National Stock Exchange (NSE) will soon be launching futures and options contracts on the Nifty Midcap Select Index (livemint.) This is a good deal if it gets meaningful traction.

Most midcap investors benchmark to the Midcap 150 index. They will have a decent way to hedge that with the Select index futures.

The equity curves overlap fairly well. And so do monthly returns.

We have a Midcap 150 Index trend-following strategy running that looks great on paper but is not currently feasible due to the high intra-day tracking error of the Midcap 150 ETFs and impact costs.

If the Select index derivatives take off, then we’ll be looking at implementing something similar using futures instead of ETFs.

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The Shifting Sands of Auto-Correlation

Autocorrelation represents the degree of similarity between a given time series and a lagged version of itself over successive time intervals. Our previous post on using run length encoding discussed how you can inspect the streakiness of returns. ACF allows you to inspect the relationship between day-0 and day-n returns.

Let’s have a look at the ACF of NIFTY and BANKNIFTY returns. Here is a plot of the ACFs of both real returns and up/down returns in 2015.

Zoom into the up/down ACF of NIFTY, see how day-0 direction correlates strongly to day-1, day-2 and day-3? Combine this with what we got from running an rle and you might just have a trend-following strategy.

Before we run off to make our millions, lets see how other years faired. Enter 2021.

While NIFTY’s day-0 direction correlates strongly to day-1, it is the inverse of day-2’s and day-3’s. Did it become mean-reversion-y? One implication of this give-up is that a trend model tuned to work well with 2015 data is unlikely to repeat its performance in 2021.

However, ACFs from 2015 through 2021 have day-1 correlations as always positive. What if you just bet that an up day will be followed by another up day and vice versa?

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Euclid vs. Hamming Distance

Our previous post explored the differences between CAPM Beta and Hamming distance. Think of Beta as a linear regression between two time-series and Hamming distance as the number of days when the direction of returns differed. The usefulness of the Euclidian distance for non-reverting timeseries is somewhere between the two.

Extending the previous example using HDFC and keeping everything else the same, here’s what the Euclidian distance measure looks like.

Higher the distance, the farther apart their curves and worse the index hedge. Here’s the equity curve that can help map returns to distance.

Reproducing the Beta and Hamming Distance charts:

From a linear portfolio point-of-view, which of these series is more “predictable?” Is it possible to specify bands beyond which things “break?” And does using shorter look-backs help?

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Beta vs. Hamming

The beta of a portfolio is often used to hedge it against the market. We did a brief intro in our post: A Gentle Introduction to Hedging. And previously, we discussed how the Hamming distance can unearth relationships by simplifying the data that we have. Here, we bring the two concepts together.

Linear-payoffs

CAPM Beta is a glorified linear regression between two return streams. It is useful in the context of linear-payoff portfolios.

For example, a typical long-only fund can use its portfolio beta to measure sensitivity to the market and to hedge against it. A single-stock portfolio with only HDFC in it will exhibit varying beta wrt different markets.

If you are after a linear-payoff (long stocks or futures outright,) beta can be a useful metric to track.

Convex-payoffs

Betas are useless if you are trying to hedge or analyze a portfolio with convex payoffs. Like, say, an options portfolio. Here, you care more about up/down days over an index. This is where Hamming distances are useful.

A Hamming distance of 70 over a 250-day return stream means that by flipping the direction of just a third of the sample, the up/down series will equalize.

In our HDFC-only single-stock portfolio example above, we see that its beta over NIFTY/BANK-NIFTY is vastly different whereas its Hamming distances closely track each other. This behavior can be used to construct trades that go beyond being long-only equity.

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