Category: Investing Insight

Investing insight to make you a better investor.

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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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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The Inflation Drag on Returns

What do you think is the annualized inflation adjusted NIFTY 50 return is from 1991 through 2016? Hint: Gross returns were ~13%
Gross vs. Real NIFTY 50 returns
It was 5%

The Midcap index was created much later. So to keep things on an even keel, if you run both NIFTY 50 and NIFTY MIDCAP 100 between 2002 and 2016, it turns out that their real returns were about 7% and 13% respectively.

So,

  1. The asset class that you pick should jive with your time horizon. No point investing in NIFTY 50 (or large-caps, for that matter) if you have a 10+ year time-horizon.
  2. The market demanded high gross returns because of high inflation. If the RBI’s commitment of a 4-6% inflation band gets fully priced in, expect gross returns to come down in the future.
  3. Neither market returns nor inflation is under your control. However, your lifestyle inflation is all on you.

Code and additional charts are on github.

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