Category: Investing Insight

Investing insight to make you a better investor.

Fat Tails, Everywhere

There is no asset free of extreme tail losses. If an asset produces any sort of return, it is going to be exposed to some sort of tail event.

One can try to find uncorrelated assets so that those losses don’t occur at the same time. However, correlations between asset returns are not stable – they change over time and behave quite erratically during market panics.

In the end, to be an investor is to accept the fact that large losses occasionally happen.

Fat Tails, Expected Shortfall

No matter how you slice it, there is no escaping tail events in investing. It is the nature of the beast and every attempt you make eliminating the risk results in you giving up a significant portion of your returns. But given two investment opportunities, how do you go about figuring out which one is more susceptible to tail events?

Expected shortfall (ES) is a risk measure that can be used to estimate the loss during tail-events. The “expected shortfall at q% level” is the expected return on the portfolio in the worst q% of cases. ES estimates the risk of an investment in a conservative way, focusing on the less profitable outcomes. For high values of q it ignores the most profitable but unlikely possibilities, while for small values of q it focuses on the worst losses. Typically q is 5% and in formulae, p (= 100% – q) is often used as a substitute.

ES of Weekly Returns

Here’s a dilemma that most investors face: Mid-caps have given higher returns in the past compared to large-caps. But, how do their tail-risks compare?

Turns out, ES of the NIFTY MIDCAP 150 TR index is -6.73% vs. NIFTY 50 TR’s -5.65%. This is how much an investor would have lost in the worst 5% of weeks since 2011.


In our previous post, we showed how strata-sampling can be used to make sure that you don’t end up ignoring tail-risk in your simulations. By definition, tail-events are rare. So, the differences are subtle.

Tactical Allocation

Reducing tail-risk is one of the biggest draws of tactical allocation. Anything that reduces deep drawdowns has the effect of keeping investors faithful to their investment process.

One way to setup a tactical allocation strategy is to use a Simple Moving Average (SMA) to decide between equity and bond allocations. Different SMA look-back periods will result in different levels of risk and reward. From an ES point of view, here’s how things for NIFTY shakes out:

Since 1999
Since 2010

Using an SMA and re-balancing weekly significantly reduces tail-risk.

How far back should you go?

The problem with tail-events is that there aren’t enough of them to build an effective model. There’s always a temptation to use as much data as possible so that these events find sufficient representation. However, markets evolve, regulatory structures change and past data stop being representative.

For example, if you run a tactical allocation back-test with all the data that is available, you’ll conclude that shorter the SMA, the better:

However, if you remove 2008 and its aftermath and look only are the data from 2011 onward, you get a different picture:

While metrics like ES and strategies like SMA are useful, the data that they are presented will give different results based on the regime that they are drawn from.

Risk management is a continuous process and cannot be reduced to single number.

Fat Tails, Sampling

While developing a model, historical data alone may not be sufficient to test its robustness. One way to generate test data is to re-sample historical data. This “re-arrangement” of past time-series can then be fed to the model to see how it behaves.

The problem with sampling historical market data is that it may not sufficiently account for fat-tails. Typically, a uniform sample is taken. The problem with this is it under-represents the tails. This leads to models that work on average but blow up on occasion. Something you’d like to avoid.

One way to overcome this problem is through stratified sampling. You chop the data into intervals and use their frequencies to probability weight the sample. This preserves the original distribution in the sample.

Notice the skew and the tails in the “STRAT” densities for both NIFTY and MIDCAP indices. This distribution is far more likely to result in a robust model compared to the one that just uses uniform sampling.

You can check out the R-code here.

Fat Tails, an Introduction

Benjamin Graham described Mr. Market as a manic-depressive, randomly swinging from bouts of optimism to moods of pessimism. While equities and markets exist in perpetuity and can create wealth in the long-term, most investors don’t have the luxury of remaining invested forever. We have extensively discussed the problem of sequence-of-returns risk for investors who have finite investment horizons in our Free Float newsletters (Intro, How-to.)

A bigger problem than sequence, is the severity of low-probability events. Also called fat-tails or black-swans.

NIFTY 50 Monthly Returns
NIFTY MIDCAP Monthly Returns
NIFTY 10-year government bond Monthly Returns

While an investor can mitigate an unfortunate sequence of returns through diversification, a market tsunami can hit all assets at the same time.

US/India Equity and Bonds during the Corona Panic

The charts show how years of returns can get wiped out in a month in the markets. While investors mostly focus on the average, the tails end up dictating their actual returns.

While using traditional statistical tools like average, std-deviation, correlation, etc. makes sense 99% of the time, they breakdown during that 1% of the time where an investor needs them to hold. This is the main motivation behind studying tail-risk events.

Tactical Allocation, An Introduction, Part II

We introduced tactical allocation in our Free Float newsletter last week. We saw how, by using a simple moving average to toggle between equities and bonds, one can reduce drawdowns in their portfolios. In the ensuing discussion, we mentioned how excess-returns found during back-tests could be an artifact of illiquidity and high transaction costs of the markets in the past. It is not like people who traded markets before us were dumb (or somehow, we suddenly added 50 IQ points in the last 20 years.) There has to be a reason why the money was left on the table.

Indian markets have seen significant changes over time. It has got more deeper and wider with better liquidity, lower transaction costs and higher levels of automation. One way to gauge the efficacy of strategies is to use a metric like Sharpe or Information Ratio over rolling-windows through time. Also, the drivers of total returns in allocation strategies will be different across different time-horizons leading to different tax liabilities. It is useful to decompose returns to handicap them from a tax angle.

200-day Tactical Strategy
50-day Tactical Strategy
  • There are quite a few time-periods where tactical allocations will under-perform buy-and-hold equities.
  • Over a 10-year horizon, on an annualized basis, bonds have contributed about 1-4% to over-all returns.
  • Sharpes have been falling through time. One should expect this strategy to attenuate further.
  • Bonds have a bigger say in determining over-all returns in low equity return environments. So, use both assets!
  • Bond returns have been less volatile that those of equities’. However, that doesn’t mean that have been constant through time.
With and without bonds

In high equity-returns environments, bonds are usually an after-thought. However, running these strategies “equities-only” is ill-advised. In the chart above, returns in the recent 10-year periods have been palatable only because of the returns contributed by bonds.

Our personal experience has been that when equities drawdown, investors switch over to tactical strategies, only to abandon them once stocks recover. Thus, leaving their downsides exposed during the next drawdown; ensuring that they end up with the worst of both worlds.

Excess returns aside, SMA strategies are also useful in managing risk. With lower risk, one can employ a bit of leverage to boost returns. We have done deep-dives into variations of these strategies in the past. Interested readers can have a look at our SMA Collection.