Tag: risk

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.)

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.

Risk Management is Not Free, Part III: Hedging

We often hear about portfolio hedging – how you can short NIFTY futures or buy puts – to reduce portfolio losses. The chapter, Hedging with Futures on Varsity, is a good introduction to the mechanics involved. However, real life involves tradeoffs.

How much to hedge?

This one is pretty straightforward. A fully hedged portfolio means that your total returns are driven purely by excess returns. Given that excess returns are typically not more than 5%, it may not make sense for most investors. So, most do a partial hedge. And a partial hedge means that when volatility strikes, you are still exposed to downside risks.

The other problem with hedges is that most investors think of risk in terms of absolute draw-downs (not volatility.) i.e., “My portfolio is down 15%,” not “My portfolio lost half of what the market lost.” So hedging first requires a change in how investors perceive risk.

Portfolio betas are not invariant

Suppose you want to be long quality stocks but want to hedge part of the portfolio by shorting the NIFTY, then how do you go about calculating the portfolio’s beta? Your assumptions of the risk-free rate and the look-back period will greatly influence the final value. Also, beta is not a static number that you can assume and keep unchanged through time.

1-year beta
3-year beta

Hedging costs increase with volatility

Volatility is huge part of derivative pricing. When you trade futures, you have to post margin to your broker and options have an implied volatility baked into their premiums. So irrespective of how you choose to hedge your portfolio, you will find that when volatility arrives, hedging costs increase.

For example, the margin requirement for a single lot of NIFTY futures in late December was roughly Rs. 1,05,000/- With NIFTY ~12,100, that is roughly 11.5% of notional. But now, because of the virus induced spike in volatility, the margin requirement has gone up to about Rs. 1,50,000/- with NIFTY ~8250, or 24.25% of notional.

So, when you want your portfolio to be hedged the most, the cost of doing so has more than doubled. To fund this, you now have to choose between reducing the hedge ratio (and taking on more market risk) and liquidating the long-side of the portfolio to the extent of the deficit (while selling in a down market.)


There are no simple answers and each investor needs to arrive at these trade-offs based on their risk perception and tolerance.

Please read Part I and Part II of this series.