Author: shyam

Buying at highs and lows: Thinking in Probabilities

Mining past returns of the MIDCAP 100 index, if you invested for 50 days, the probability of returns greater than 10% is 32% and the probability of returns greater than 15% is 18%. On the flip side, over the same holding period (HP,) the probability of returns lesser than 0% is 35% and the probability of returns lesser than 5% is 52%. These data points are the first row of the following tables:

MIDCAP 100 return probabilities: buy and hold, lows and highs
MIDCAP 100 return probabilities: buy and hold, highs and lows

Suppose you want to hold for 50 days, then to maximize your returns, you will have to buy at the 500-day low to have an even shot at making a return greater than 10%. The better outcome would be if the holding period were to be extended to 200 days. At which point the probability of even making less than 5% is very low and that of making more than 15% is more than 80%.

Using this table, one can lookup the odds of different holding period returns at different highs and lows.

Code is on github.
Related: Highs and Lows

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Lumpsum vs. SIP: Thinking in Probabilities

This is a continuation of Lumpsum vs. Dollar Cost Averaging (SIP) that modeled different return series and concluded that a prudent investor would be better off with a SIP because of a smaller probability of incurring a large loss. However, we stopped short of comparing different indexes to see if the conclusion held.

The ‘average’ return

What happens if we take the average weekly return of an index and create a synthetic index that just gives those average returns without any variance? We end up with a parabolic looking cumulative return profile below:
cumulative small cap returns
The small cap index was chosen on purpose to illustrate how ‘average’ returns relate to real returns on an extremely volatile index.

The average return series is, of course, a fantasy. What we are interested in is in the probability of getting those returns.

Probabilities

Just like our first post, we start by modeling the returns of the NIFTY 50, MIDCAP and SMLCAP indexes as a Generalised Lambda Distribution and running a 10,000 path simulation to obtain a series of DCA vs lumpsum investment returns. We then feed that into a empirical cumulative distribution function so that we can query it for probabilities under different thresholds. To put that in a picture:
lumpsum vs SIP returns on small caps

The vertical lines mark the different thresholds we are interested in.

  • The grey line on the left is at zero. We have SIP showing a 4.44% probability of negative returns and lumpsum showing 3.49%. Yes, there is a non-trivial possibility that SIPs will give negative returns. However, looking at the shapes below zero, SIP losses may not be as large as lumpsum losses.
  • The red line in the middle is the start to finish return of the index. Here, we have SIP showing a 22.69% probability of exceeding those point-to-point returns and lumpsum showing 57.50%.
  • The orange line on the right is the compounded ‘average’ return. We have SIP showing a 7.82% probability of exceeding that and lumpsum showing 37.20%.

Here is the same MIDCAP:
MIDCAP lumpsum vs. SIP return densities

And for NIFTY 50:
NIFTY 50 lumpsum vs. SIP densities

What does all this mean?

  1. It is possible for SIP returns to be negative over large periods of time. Enough to cover your entire investing lifetime. So, if you are investing in small-caps, make sure you are not 100% allocated to it.
  2. Lumpsum investing gives you a higher probability of higher returns across all indexes. The probability of negative returns are on par with that of SIP’s.
  3. Lumpsums have fatter left tails. However, if you are looking only at NIFTY 50 and MIDCAP, those probabilities are tiny.
  4. Lumpsums have a higher probability of achieving ‘average’ returns compared to SIPs.
  5. Lumpsums seem to be benefiting from “time in the market” on indexes that rise over a period of time.

Code and charts on github.

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Highs and Lows

With the recent correction in the markets, there are a lot of lazy headlines out there screeming “Midcap Index hits 52-week lows!” First, there is nothing significant about 52-weeks.

Second, if you are worried about 52-weeks, then you shouldn’t be invested in midcaps. Most investors see this:


When they should be seeing this:
.

An excerpt from the book “Thinking in Bets” seems appropriate here:

Our problem is that we’re ticker watchers of our own lives. Happiness (however we individually define it) is not best measured by looking at the ticker, zooming in and magnifying moment-by-moment or day-by-day movements. We would be better off thinking about our happiness as a long-term stock holding. We would do well to view our happiness through a wide-angle lens, striving for a long, sustaining upward trend in our happiness stock.

Now read Pain is proportional to Frequency of Observations that I wrote back in 2016.

Code and other charts are on github.

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Book Review: Thinking in Bets

In Thinking in Bets: Making Smarter Decisions When You Don’t Have All the Facts (Amazon,) Annie Duke uses probability theory to illustrate how one should go about making decisions.

Notable excerpt:

We can’t just “absorb” experiences and expect to learn. As novelist and philosopher Aldous Huxley recognized, “Experience is not what happens to a man; it is what a man does with what happens to him.” There is a big difference between getting experience and becoming an expert. That difference lies in the ability to identify when the outcomes of our decisions have something to teach us and what that lesson might be.

The point made above cannot be stressed enough for investors. Just because some “guru” or “adviser” has been at his job for a long time, it doesn’t necessarily follow that he is an expert. Expertise comes from applying a scientific mindset to decisions. Very few actually do it in practice and most are happy to be in their own comfortable filter bubble.

You can read the notes that I took here.

Recommendation: if you have read similar books in the past, you can skip this one. No new paths blazed.

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Principal Component Analysis, Part I

Introduction

Principal Component Analysis (PCA) is a way of summarizing data. For example, if you take financial services, there are quite a few sector indices that cover it: Bank, Pvt. Bank, Public Bank, Financial Services, etc… There will be overlap between all these indices, so the question is, in what proportion should one invest in these individual indices in order to get the most optimal exposure to financial services? PCA is one way to answer this question. To get a better understanding of what it is, see: stats.stackexchange.

NASDAQ OMX India TR Indices

To start this series on PCA, we will first look at the USD denominated Total Return indices published by NASDAQ-OMX. Choosing these indices helps us avoid a lot of data pre-processing steps. First, they are Total Return, so they incorporate dividends, etc. Second, they are US dollar denominated, so we don’t have to worry about being long USDINR while looking at tech stocks. And third, they start from 2001, which goes way farther than the TR indices published by the NSE.

We use the following sector indices:
NASDAQ India Basic Matls TR Index (NQIN1000T),
NASDAQ India Cnsmr Goods TR Index (NQIN3000T),
NASDAQ India Financials TR Index (NQIN8000T),
NASDAQ India Health Care TR Index (NQIN4000T),
NASDAQ India Inds TR Index (NQIN2000T),
NASDAQ India Tech TR Index (NQIN9000T),
and the NASDAQ India TR Index (NQINT) to further divide time periods when it is above and below 50-, 100- and 200-day SMA.

The question we are trying to answer is that are the factor loadings stable? If they are not, then how do they change over time and across different market regimes. To answer this, we setup a sliding window of 5-year daily returns that is incremented by one year at a time. That gives us 11 datasets, starting from 2002-2007 through to 2013-2017. We run PCA on the daily returns of the sector indices listed above. We then plot the loadings of the first principal component.

NASDAQOMX India Sector Index PCA

A few things stand out:

  1. Dominated by Basic Materials, Financials and Industrials.
  2. Relative importance of IT has dropped.
  3. Financials dominate the below-SMA200 market regime implying that most of the time, the market is below 200-SMA because of financials.

What we had hoped to find was some sort of stability in the loadings either in the entire dataset or in specific SMA regimes. We could have then constructed a “good times” and “bad times” portfolio and switched between them based on SMA. But it looks like it is not possible with these indices.

Code and more charts are on github.

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