NIFTY All Time High - Should You Worry?

Well, after adjusting for inflation or FX, is far cheaper than it was when it hit the similar highs back in 2007. It is cheap in real term (inflation adjusted), in terms of fiat currencies (like USD) or gold

And it is cheap in almost all valuation metrics

Overall, emerging markets investors will be cautious. Irrespective of the softness of data from the US, I do not think we are going to see any stop in taper from the Fed, unless the data is real bad. So staying cautious is always a good idea, but I think no need to go massive short. IMF Direct Blog has a very interesting recent piece out on EM economies (The Trillion Dollar Question). India has probably a much better positions among other emerging market economies with much lower levels of external debt and debt to GDP ratio (although am sure these calculation excludes India's need for oil import, which is more or less inelastic to price, and hence should be treated as obligation and should be added to external debt for most economic purposes). Plus there is a good chance of an upside after the elections in May

I only wonder will that upside come too early and will the market correct after the election results are out

Inflation Trends in Developed Economies

Across developed economies, food inflation and housing related inflation remains contained (even in UK!!). Energy related components have been on a downward trend as well.

UK CPI Harmonized  - In recent time, UK HICP has been mostly dominated by housing, education and eat-out costs. Food and beverages inflation has been steadily decreasing, and the rest totally subdued

US CPI (Urban Consumer)  - Similar story in the US. CPI mostly propped up by Housing, and Health Care components. F&B going down steadily. Rest negligible

Germany CPI  - In Germany, Housing against is a significant component. Followed by food and beverages and recreation.

Euro-Area MUICP - Euro Area MUICP contraction has been way below ECB target. The major propping up component for other regions, i.e. Housing , seems to give in in case of Euro Area

Japan CPI (Nationwide) - The recent spike in inflation in Japan mostly driven by import and energy related cost. More closely linked to yen depreciation and Fukushima closure than a case of consumer demand driven one

As most recovering markets nears the unemployment rate thresholds of the central banks, inflation will once again become the focus. And any divination based on past data continues to make a case for “Low for Long”. We have seen little evidence of strong productivity growth. In UK, actually improvement in unemployment has been accompanied by fall in productivity. And consumer credit growth remains weak. Without gain in productivity, there will be little wage pressure to drive demand-driven inflation. However, we think the surprise , if any, can come from the US.

The Job Of A Central Banker

I have always said the ECB under Draghi has been a markedly different institute. But it still remains ECB, central bank to a disparate bunch of nations. Back in 2011 and 2012, when the US economy kind of hit the bottom, the Fed did not relent because it was stabilized. It chased with all-in QE to bridge the output gap. In Eurozone, the ECB admits the very high output gap and unemplyment rate. But still fails to act, as "medium to long term inflation expectation" remains "well anchored" 

The ECB perhaps suffers from too much of its own credibility. Ever since it took over the charge from the revered Bundesbank, the inflation expectation remained well anchored. Much in line with Goodhart's Law

 In a world where inflation is well anchored, is it anymore valid to have it as a policy target? Unlike the Fed and others, the ECB does not have any dual mandate. So legally it is bound to target price stability at the expense of everything else. But what about that generation that will be lost because their grandpas demanded price stability. What about human costs 

Any central banker at Draghi's place would be personally motivated to act. If he gets it right he will be a hero. If he gets it wrong, well, all other central bankers doing it anyways. And no, I dont expect any deflation in the Euro area. Unlike Japan in late 90s, inflation is more of a global phenomenon these days. So perhaps in the long run, whether the ECB acts or not will have no or limited impact on the Euro zone inflation  and inflation expectation. But the impact on the lives of thousands of unemployed or under-employed will be profound

Extracting Volatility Smile from Historical Data for Swaption Market

For options markets in general, comparing ATM volatility with the historical realized volatility is one of the most popular and extensively used methods of relative value trading, especially in the shorter‐dated options space. The realized volatility, with appropriate time scaling, can be directly compared to the ATM implied volatility, irrespective of the level in the underlying or change thereof, for analyzing relative richness and cheapness. This follows directly from the concept of continuous delta‐hedging

However, for someone interested in the relative richness of options away from the ATM strike, things are difficult, to say the least. While from the quoted options prices it is still possible to extract implied volatilities at a given strike (by inverting a pricing formula, for example Black‐Scholes), coming up with a comparable realized volatility number is not straight‐forward. Computing standard deviation from historical returns (or changes) provide only one estimate, irrespective of the strike of the option. And as we mentioned earlier, that estimate is most applicable for ATM strike

One rigorous method of computing the applicable volatility for OTM options from historical price information is to use the concept of break‐even volatility. Break‐even volatility can be construed as the value of the volatility parameter in a pricing formula where if we buy an OTM option at that value and delta‐hedge, net expected PnL should be zero. This expectation can be computed using historical price information over appropriate time period (i.e. as a simple average of different historical delta‐hedging back‐tests, or some similar methodology). But as it is obvious, this requires considerable amount of computation effort, for running enough number of back‐tests to be able to compute the expected value

One approximate way‐out is to exploit the historical distribution information and use that to directly price a given option at any strike. Then the value of volatility parameter can be backed out by inverting the pricing engine. This can be compared, then, with the option price implied value at that particular strike and one can make an estimate of relative richness from these numbers. Following is an approach to develop a method for this process

For Swaption market, the market standard is to use normal basis points volatility. Hence we start with historical change in the underlying swap rates over a chosen interval (daily or weekly), scaled up appropriately depending on the option expiry. From this, a simple Gaussian Kernel Density can be extracted. This is basically for smoothing the realized histograms of changes. The distribution is then given by

where K is the standard normal density function. However, before we use this distribution we impose two conditions

The first ensures that it is centered around the current ATM forward level (F). That is, the expected value of underlying is always equal to the current ATM forward, irrespective of historical levels. The second condition ensures that the currently priced‐in uncertainty is maintained. Strictly speaking, this is not a required condition. However, since we are primarily interested in developing a methodology for skew comparison, this condition becomes useful. Also, it can be construed that the level of uncertainties currently priced‐in contains important forward‐looking information, and dropping this may result in significant under/over‐pricing of OTM options depending on implied variance and variance of the recent realized changes in the underlying. We enforce this condition by first extracting the complete implied
distribution from options prices and then setting the variances of this implied and the historical distribution equal. The other method is to force the implied volatility at the ATMF strike equal. The former is preferred as it is model independent

Note that to further improve the method one can add another condition that requires the entropy distance (Kullback‐Leibler distance) between the historical distribution and the implied distribution to be minimized. This corresponds to the requirement that the difference in total information (or reduction in uncertainty) between the two distribution is not very significant. We skip this stage specifically to maintain the frequent bi‐modal distributions observed in swap rates in recent times and avoid parameterization. In essence, this allows us to extract information from the shape of the historical distribution, while maintaining the overall central tendency and uncertainty (as measured by variance). This is very useful for implementing distributional arbitrage.

Finally, the historical distribution, thus obtained, can be used to price an option from the first principle

Where, C is the price of a call, N is an appropriate numeraire (DV01 of the underlying swap), E denotes the expectation operator, F is the underlying rate, and K is the strike

This method is useful for looking at the relative richness of collars and strangles (w.r.t. straddle) for shorter maturities (including midcurve options) and for implementing distributional arbitrage (shape of the distribution). However, the underlying assumption here, which is similar to the original realized vs. implied volatility method, is that historical returns have useful information about future outcomes

Macro Views Series: 2014 Points to Ponder

Views and observation for the coming year, as usual, without any forecasts!

• 2014 Points to Ponder Adobe PDF, 286KB

Past Sell-Off Dynamics

Beta during the sell-off for different swap tenors, fixing the dynamics of the 10y point as pure normal (BETA = 1) - for past selloff episodes in EUR and USD.

Different swap tenor reponse to a 1BP move in 10Y during these sell-offs (in BPS MOVE), as implied by the above BETAs.

Historically, the front end for USD has shown much lower beta (meaning more log-nomrality w.r.t. 10y rate) compared to Euro, perhaps due to a better pricing of fed expectation and less surprises in rate hikes (Notice how the Mid 08 oil shock was surprise for both the markets but for EUR was considerably stronger). In fact the strong and persistent correlation between front end slope for EUR we have now is only a recent phenomenon in the sell-off in 2013 (one of the major difference between the 2010 sell-off and the current sell-off). Whereas this has been common in USD in 2013 of course, and also during most of the past sell-off.

Projecting this in to future, the recent correlation of front end slopes with the belly (e.g. 1s3s vs 5y) will be stronger in USD than EUR, and I expect EUR to lead the first reversal of this correlation (provided we are not heading towards very different rates levels in EUR and USD) For directional trades this provides a good way to position for bearish (bullish) rates, by going long (short) the slope in USD vs EUR. Also for a contrarian trade, an OTM flattener in EUR vs USD in a good hedge for inflation suprises, (assuming ECB's reaction function is unchanged)

SABR Skew Dynamics & Beta | Part II

In original SABR model, the beta has two distinct roles - 1) it determines the back-bone of the atmvol vs atm and 2) it contributes to beta skew (and beta smile) in a way that is independent of the vanna smile (the smile driven by correlation parameter).

However, in most common implementations of SABR, this is NOT the case. The traders in rates are familiar in normal bps vols. So the ATM vols are input in terms of normal bps vols (as opposed to the ALPHA parameter, the ATM vol in correct beta).

Because of the implementation, the beta COMPLETELY looses its first role (the modeled back-bone). Instead of determining the the dynamics in terms of the back-bone, beta switches to play its role in determining the skew dynamics as mentioned in below mail - which will not be seen in a true implementation 

On the 2nd role as well, the implementation introduces a twist. The main point in implementation is, as opposed to parameterizing the model in terms of ALPHA (local vol in the correct blend), CORREL. VOLVOL and BETA, it parameterizes in terms of ATMVOL (vol in normal blend), CORREL, VOLVOL and BETA. in a generic model the interplay between beta skew and correl skew depends on two parameters - BETA and CORREL*LAMBDA - where LAMBDA is ratio of VOLVOL/ALPHA. So while the general rule is that a instead of decreasing the correlation (more negative) one can increase the beta to match a skew, this has impact on far OTM strikes.

As one increases the beta, the local-vol (at the correct blend) falls drastically, This drastically changes the LAMBDA ratio. This introduces a very different smile (curvature) effect at far OTM strikes This shows 1y10y smile for 1) correl =0, beta = 0.35 (blue) vs 2) correl=0.55, beta =1 (green). As can be seen the curvature on the far OTM sides is very different. We match the skew in 2nd case by setting beta =1 and increasing the correl. However this changes the local vol and the LAMBDA ratio. This introdcues difference in smiles in the far OTM strikes Typically, matching skews by changing beta or correl is NOT equivalent. One difference is obviously the change in the dynamics (which will impact hedges) mentioned in the previous post on this. The other difference, as illustrated above, a change in OTM smile