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Wednesday, April 12, 2017

Low Bond Volatility Not Surprising

Chart: 10-year Treasury Historical Volatility

The low levels of implied volatility in the bond market has attracted a fair amount of commentary. Although it seems reasonable to believe that volatility selling strategies have reduced market volatility, there's no fundamental reason to expect a big reversal (outside of another crisis).

I will immediately note that I am not particularly in tune with what is happening in the nooks and crannies of the fixed income volatility market; I am just attempting to give a simple explanation of the fundamental forces that result in low volatility. Additionally, this should not be construed as investment advice. Although there are good reasons to be complacent about fixed income volatility, it can only go one way in a crisis.

The chart above shows the realised (historical volatility) of the 10-year Treasury (using the Fed H.15 data). As can be seen, the 50-day volatility is near a record low -- which is unusual for a tightening cycle. This reality has to be kept in mind when discussing the low levels of implied volatility: implied volatility is supposed to be an unbiased estimator for realised volatility. If traders kept implied volatility higher than realised, it would be easy to lock in a pseudo-arbitrage profits, with very little risk (and balance sheet exposure). Therefore, we should not be surprised that implied volatility is low.

There is an interesting feedback loop between the options market and the bond market. If investors are selling a lot of options (volatility), then this has the effect of helping suppress realised volatility (which benefits investors who sell volatility). How this effect works is probably not obvious; I will now sketch how it works.

In order to discuss volatility without taking a view on the direction of bond yields, we need to buy a straddle (a put and a call). (My working assumption for this article is that the reader knows what a put and a call are.) If we just buy a put (or a call), we are positioning for a move in interest rates in one direction or another, which takes the focus away from the effects of volatility. If we buy a straddle, we just want rates to move in either direction.

It must be kept in mind that the options market is zero sum; for every seller, there is a buyer. If both side of options trade hedged in a similar fashion, there would be little net effect on the bond market. In order for the feedback loop to kick in, we need asymmetric behaviour.
  • The seller of the straddle does not delta-hedge (discussed below).
  • The buyer of straddle delta-hedges the risk.
This is what we would expect to happen if there was a net imbalance of investors who wanted to sell volatility; the market is only balanced out by drawing in other investors who think implied volatility is too low, but do not want to be exposed to directional risks.

Actions of the Straddle Buyer

Let's assume that the bond yield starts at 2%, and the strike of the straddle is at 2% as well (it is at-the-money).* The directional risk of the call and put cancel out, and so the buyer has no directional exposure. The buyer wants to remain with no directional risk, so she follows a delta-hedging strategy.
  • The next day, the bond yield rises to 2.10% (and hence, the price falls). The call option leg of the straddle loses money, and the put option leg gains money. The behaviour of options which are close to at-the-money tells us that the put option gains money faster than the call option loses money. As a result, at 2.10%, the position now has a net short exposure to bonds: it makes more money if bond yields rise by 1 basis point than if it falls by 1 basis point. In order to hedge out this undesired directional position, the straddle buyer would buy a small position in the bond to return to a net neutral position.
  • The following day, the yield drops back to 2.00%. Both the put and call are at-the-money again, and so once again, the straddle has a neutral interest rate sensitivity. However, the previously bought bond position now unbalances the portfolio. The straddle buyer will thus sell the piece of the bond that was bought the previous day.
The profitability of the straddle buyer is determined by two factors.
  1. There will have been a profit on the sold bond position; it was bought at 2.10%, and sold at 2.00%. (Yield down, price up!) The size of these profit was determined by the size of the move in yields; if the bond had only gone from 2.00% -> 2.05% -> 2.00%, the profits would have been (roughly) halved.
  2. The straddle is now two days closer to expiry. It's time value would have dropped (assuming unchanged implied volatility). If the option originally has two days to expiry, the straddle expired worthless.
In summary, the net profit of the straddle buyer depends upon the relationship between realised volatility and the cost of the option (implied volatility). 

For our discussion here, the key point is that the straddle buyer acts in a stabilising fashion for the bond market: when the bond yield rose, she bought, and then she sold when the yield fell.

Straddle Seller

If the straddle seller delta-hedged as well, the transactions would mirror that of the buyer. This would have no net effect on the bond market. However, this is probably not what most volatility sellers want to do. Instead, the seller does not hedge.

In order to lose money over the life the straddle, the bond yield has to move far enough away from the straddle strike so as to generate a capital loss that is greater than the received premium for the straddle. The scenario above makes the straddle seller happy, as the bond yield is back where it started from, and two days have ticked away from the life of the straddle.

Therefore, in order to get the straddle seller worried, yields have to move strongly in one direction or another; it is not enough to just jump around around a certain level.

In other words, if bond yields range trade, unhedged volatility sellers laugh all the way to the bank.

However, things get ugly if yields start to move, and the straddle seller wants to get risk under control. In this case, the seller needs to act in a fashion that accentuates market movements: selling when prices fall, or buying when prices rise.

Can We Hit a Volatility Crisis?

Chart: 3-month USD eurodollar historical vol

Although a crisis driven by volatility hedging in interest rates is possible, the obvious difficulty is that it will be hard to move yields away from where forwards lie. The chart above shows the historical volatility of the 3-month eurodollar rate, on a 24-month window. This volatility is driven entirely by Fed policy and the LIBOR spread, and is not affected by delta hedging. As one would suspect, it has been extremely low in recent years. Even though the Fed started hiking in December 2015, the realised volatility is still below almost the entire pre-Financial Crisis history.

The Federal Reserve is dominated by New Keynesians, and they impute great powers to the central bank's ability to guide expectations. The result is that during an expansion, the short rate ends up pretty close to where the forwards priced it to be. This generates a pattern of range-trading -- which means that realised volatility remains low.

There are a great many commentators who are disturbed by this state of events. They believe that the Federal Reserve should act in a erratic fashion, so as to blow up the bond market (by raising term premia?). The apparent logic is that the Fed needs to cause a crisis, in order to prevent a crisis. It may be that personnel changes in the Fed could lead to such an outcome, but I would not hold my breath waiting for that.

Mortgage Market

The mortgage market is always good for generating wonkish-sounding stories about risk in fixed income. The reason why American conventional mortgage-backed securities are good for volatility is that the bulk of them are 30-year amortising instruments, with an embedded call option -- homeowners are largely free to refinance at lower rates. (Such consumer-friendly mortgages do not exist in most other developed countries.)

The result is that the duration of a mortgage-backed security (MBS) drops as yields get lower: we expect borrowers to refinance, and so we effectively end up with a short maturity instrument. If rates then rise, we no longer expect refinancing, and so the effective maturity lengthens. If you are hedging a pool of mortgages, you end up trading in the same direction as market moves. (As should be expected, this is a short volatility position.)

If you are worried about rising yields, the MBS market should not be too much of a concern if implied volatility is low. The low implied volatility means that the discounted odds of a refinancing is already low, and so the effective duration of the MBS is already quite long. This is unlike the situation when mortgage hedging was a big deal in the market, which features large moves into and out of refinancing range for mortgage portfolios. Any mortgage hedging that might occur would be dwarfed by the need for funds to buy bonds to meet actuarial liabilities.

The only real scare story is that we have a big rally in bonds, in which case refinancing might once again matter.

Concluding Remarks

Although it is fun to imagine potential crises, the rates market is probably not going to be the source of problems. As always, the main risks revolve around unsound lending practices.

Technical Appendix

My implied volatility charts show the normal volatility, which measures volatility in a number of basis points per time period (day, month, year). It is calculated by the standard deviation of yield changes over the trading window. An alternative is to express log-normal volatility, where the volatility is expressed as a percentage of the level of yields. (This is similar to how volatility is defined for equity prices.) Fixed income models can have more flexible behaviour, for example lying between these two cases.

In a low rate environment, log-normal volatility is problematic, and so my charts are reasonable. However, people who believe that rates are closer to log-normal in behaviour might argue that the rates volatility is overstated at the beginning of the time period (since the absolute level of yields was higher, and so volatility should be scaled down).

Footnote:

* I am skipping a lot of the details that would be needed for option pricing; I am not even giving the maturity of the bond. Purists would note that what matters is the forward yield, and not the spot yield. The embedded assumption in this example is that the forward and spot yield are the same, which is not that far off most of the time.

(c) Brian Romanchuk 2017

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