Divergence Between Credit Default Swap and Equity Volatility

In a previous post, we examined the relationship between the Credit Default Swap (CDS) and equity volatility, and argued that there is a strong correlation between them.  But like any relationship in financial markets, this one can break down and divergence can happen.

For instance, last month we noticed that CDS in Asia and Australia tightened considerably with respect to their US counterparts. Bloomberg actually reported:

Credit-default swaps on the bonds of every Asian emerging market except for South Korea have tumbled this year, outperforming debt risk for the U.K. and for France, which has jumped amid the presidential election campaign. Inflows into developing Asian bond markets have also swelled in 2017 as investors bet the world’s fastest-growing region will be able to better withstand the volatility and outflows unleashed by a tightening Federal Reserve.

“Emerging Asia scores relatively well on both macro as well as political stability and is likely to remain an attractive region to invest in for the foreseeable future,” said Anders Faergemann, a senior fund manager in London at PineBridge, which manages about $83 billion globally. “The short-term risk is mainly associated with external factors as the markets fear the Fed is behind the curve.” Read more

This tightening of CDS in Asia presented an interesting trade opportunity.  Indeed, Asia Unhedged pointed out:

The difference between emerging market (EM) and US corporate BBB Option-Adjusted Spread is at an all-time low. The difference between EM volatility and VIX is around the average. This chart begs the question: Is there a trade in shorting credit and buying equity? Read more

This means that the EM CDS is relatively low with respect to the US counterpart when taking the volatility differential into account.  The post also suggested going long EM equity and short its CDS.

So this is an example of divergence. But it’s important to note that it happens between the VIX and CDS  differentials, i.e. it represents a dislocation between secondary risks, and not primary risks.

 Article Source Here: Divergence Between Credit Default Swap and Equity Volatility

Pricing Convertible Bonds and Preferred Shares

A convertible bond (or preferred share) is a hybrid security, part debt and part equity. Its valuation is derived from both the level of interest rates and the price of the underlying equity. Several modeling approaches are available to value these complex hybrid securities such as Binomial Tree, Partial Differential Equation and Monte Carlo simulation. One of the earliest approaches was the Binomial Tree model originally developed by Goldman Sachs [1,2] and this model allows for an efficient implementation with high accuracy. The Binomial Tree model is flexible enough to support the implementation of bespoke exotic features such as redemption and conversion by the issuer, lockout periods, conversion and retraction by the share owner etc.

In this post, we will summarize the key steps in valuing a convertible bond using the Binomial Tree approach. Detailed description of the method and examples are provided in references [1,2].

Generally, the value of a convertible bond with embedded features depends on:

• The underlying common stock price
• Volatility of the common stock
• Dividend yield on the common stock
• The risk free interest rate
• The credit worthiness of the preferred share issuer

Within the binomial tree framework, the common stock price at each node is described as

where S₀ is the stock price at the valuation date; u and d are the up and down jump magnitudes. The superscript j refers to the time step and i to the jump. The up and down moves are calculated as

and

where is the stock volatility, and  is the time step.

The risk neutral probability of the up move, u, is

and the probability the down move is 1-p

After building a binomial tree for the common stock price, the convertible bond price is then determined by starting at the end of the stock price tree where the payoff is known with certainty and going backward until the time zero (valuation date). At each node, Pj,i  the value of the convertible is

where m denotes the conversion ratio.

If the bond is callable, the payoff at each node is

The payoff of a putable bond is

Here C and P are the call and put values respectively; r denotes the risk-free rate.

The above equations are the key algorithms in the binomial tree approach. However, there are several considerations that should be addressed due to the complexities of the derivative features

• Credit spreads (credit risk) of the issuers which usually are not constant.
• Interest rates can be stochastic.
• Discount rate ri,j depends on the conversion probability at each node. This is due to the fact that when the common share price is well below the strike, the preferred share behaves like a corporate bond and hence we need to discount with a risky curve. If the share is well above the strike then the preferred behaves like a common stock and the riskless curve need to be used.
• The notice period: the issuer tends to call the bond if the stock price is far enough above the conversion price such that a move below it is unlikely during the notice period. For most accurate results, the valuation would require a call adjustment factor. This factor is empirical and its value could be determined by calibration to stock historical data.

This pricing approach can be implemented in scripting languages such as VBA and Matlab. In the next installment, we will provide a concrete example of pricing a convertible bond. If you have a convertible bond that you want us to use as example, send it to us.

References
[1] Valuing Convertible Bonds as Derivatives, Quantitative Strategies Research Notes, Goldman Sachs, November 1994.
[2] Pricing Convertible Bonds, Kevin B. Connolly, Wiley, 1998.

 The post Pricing Convertible Bonds and Preferred Shares first appeared on Relative Value Arbitrage

Is Volatility Back for Good?

The week ended with high implied volatilities across the board. Eric Lam et al. at Bloomberg wrote:

The calm in stocks worldwide is giving way to concern, with investors in Europe and the U.S. rushing to hedge against declines and a Credit Suisse Group AG index flashing a warning as the list of economic and political obstacles grows.

There’s no shortage of potential concerns. Tensions over North Korea’s nuclear program have intensified days after the U.S. fired missiles at a Syrian airfield. There’s uncertainty over the outcome of the French election, with the first round scheduled for April 23, and in Britain doubts are emerging on whether the economy can withstand the political shocks the Brexit negotiations will bring. Read more

So it seems that investors are very concerned with the uncertainties these days.

Interestingly, just about 10 days ago, Joe Mallen et al. of Helios Quantitative Research presented an interesting chart that showed a divergence between the index of economic policy uncertainty and the VIX. The authors then concluded that most investors have become desensitized to the news headlines:

It seems most investors over the years have simply become desensitized to the volume of squawking news headlines.  In more recent days, despite economic policy stories that usually cause market trepidation – such as healthcare reform (or lack thereof), the debt ceiling debate, and short term interest rate hikes to name a few – the US equity market has trended to very low levels of volatility. So, why do some investors say this environment feels so volatile, but traditional measures of volatility remain historically low?  Read more

So currently are investors oversensitive?
After the French election, will we be back to the low volatility environment again?

Is It a Good Time to Go Long Volatility?

Last week, in the post entitled

This ETF Helps Investors Hedge Market Risks

we discussed how it’s important to hedge against a market downturn, and pointed out some strategies for doing it.

Yesterday, Brian Chappatta reported that some big portfolio managers already started buying volatility

Some of the world’s biggest bond managers have been waiting for this moment. Rather than ponder the sustainability of the reflation trade and its implication for yields, investors including Rick Rieder at BlackRock Inc. and Bob Michele at J.P. Morgan Asset Management say they’ve been betting that price swings will grow more dramatic in the days and months ahead. That’s already borne fruit this week, with the CBOE/CBOT index of 10-year Treasury note volatility, known by its ticker TYVIX, jumping to the highest closing level since February. Read more

On the research side,  Chrilly Donninger timely published a paper on how to protect a portfolio from a tail risk event:

Protecting an equity market portfolio with VIX-Futures eats not only the kurtosis but also the profits of the portfolio. Being constantly VIX-Futures long is too expensive Therefore one has to find an  appropriate timing strategy.  This working paper presents a Hidden-Markov-Model which not only has  a reasonable tail-risk-protection but even improves the overall return of the SPY. The strategy is – at  least in the historic simulation – close to what is called in German an “eierlegende Wollmilchsau” (“egg-laying wool-milk-sow”). Read more

Are You Betting on Terminal Distribution or Volatility Dynamics?

In volatility space, many investors don’t know exactly what they’re betting on. Briefly, with options, they can bet on:

1. Terminal distribution of returns
2. Dynamics of the volatility

Today, we noticed an article by Alex on Valuewalk that discussed these 2 types of options trade. It concluded:

The key takeaway here is:
Traders who don’t hedge delta rely on the trend of the underlying more than its volatility to profit.
Traders who do hedge delta rely on the volatility of the underlying more than its trend.

It usually doesn’t make sense to hedge your delta unless you have a professional commission structure. This is why so few do it. All those hedging trades rack up commissions. And the execution of those hedges requires a lot of screen time or advanced software than can do it automatically.

So if you’re not delta hedging, a better question to ask yourself before placing an option trade is:
Do I believe the underlying will trend or consolidate over the life of the option?

If your answer to that question is “I think the underlying will trend”, you should buy optionality. The underlying will trend away from the strike price and you’ll make money on the option you purchased.

If your answer to that question is “I think the underlying will consolidate”, you should sell optionality. The underlying will stay close to the strike price and you’ll collect the premium from the option you sold.
Read more

We agree with some points in the article. However, we note that:

-Even if an investor does not rehedge, i.e. he’s betting on the terminal distribution, the volatility when he enters the trade does matter. It’s the price that he pays for his option and it determines his final payout.
-The article did not discuss the long term expectancy of these types of bet which is important to know when putting on a new trade.

Market Correlations Started to Break Down

Last week, we noticed that the volatility term structure was inverted on a low reading. In fact, Crystal Kim wrote:

Under normal circumstances, VIX futures curve upward. It's entirely logical -- the longer dated futures trade at a premium to shorter-dated futures. An inversion, as seen yesterday, suggests that the market expects more volatility in the short-term than the long-term.

The reason behind the volatility bid: upcoming elections in France. "The April VIX futures are bid ahead of the French elections, since they will settle into a 30-day VIX that captures both rounds of voting," he says. "The U.S. options market is finally starting to care about the French elections." The first round is set for April 23. If no one wins the majority, a run-off between the top two will take place on May 7. Read more

 
Vix futures term structure as of Apr 12, 2017. Source: Vixcentral.com

But these days  anomalies are happening not just in the volatility space.  As pointed out by Kathleen Brooks  yesterday, the CDS market is also acting out of sync.

On the one hand there is a smell of caution in the air, but on the other, capital is not yet moving away from risky assets.

The US corporate high yield spread should be used to time market moves rather than risk sentiment indicators. The US corporate high yield spread has a significant negative weekly correlation with the S&P 500 at -60% for the last two years. If this correlation is to hold, then we would expect the S&P 500 to continue to rally if the US corporate high yield spread continues to narrow, and vice versa. Read more

And finally today forex.com observed a breakdown in correlations

At the start of 2017 the correlation between the S&P 500 and the high yield corporate spread was -53%. This seems normal as you would expect these products to move inversely to each other: as the S&P 500 rises, high yield debt falls and vice versa. However at the start of April this correlation had reversed to 33%, so now the S&P 500 and the high yield debt spread move together a third of the time. This suggests that 33% of the time when the S&P 500 falls, so too does the price of credit for high risk US corporations. Usually you would expect the opposite to occur. Read more

Last and not least, these articles also gave a warning of an imminent market correction.

Another Look at Prepayment Risk of Mortgage-Backed Securities

Yesterday the Federal Reserve Chair Janet Yellen said at a University of Michigan event that the Fed planned to raise short-term interest rates.

“I think we have a healthy economy now … but it’s been a long time coming,” Yellen said.
Yellen said the current unemployment rate of 4.5% is “even a little bit below” what Yellen and her other colleagues at the Fed would consider “full employment.” She said inflation is “reasonably close” to the Fed’s stated goal of two percent. Read more

In a previous post, we argued that rate hikes will increase volatility through hedging of prepayment options embedded in mortgage-backed securities.

Recently, Mark Robinson presented another argument:

Analysis from SocGen published during the fourth quarter of 2016 points to a 2.6 per cent return on 10-year notes (the equivalent rate for the UK was 1.7 per cent). This reflects the general view that US equity valuations are stretched based on underlying earnings. If we accept that once investments in riskier assets such as equities are deemed relatively expensive to government-backed debt, then stocks could be subject to bigger price swings with increased frequency. Read more

This means  that when interest rate rises, equities  will appear to be expensive relative to government-backed bonds, hence they will be susceptible to selling, thus causing an increase in volatility.

Regardless of the argument, with a rising rate, one might think that it’s risky to invest in fixed-income securities.  However, Tim Mullaney  recently reported that:

Gundlach, CEO of DoubleLine Capital, is betting that the best way to play the coming rate hikes is by holding lots of mortgages

But how about prepayment risk?

“Gundlach doesn’t see prepayment risk as particularly high right now, but if prepayments spike, there’s a risk of losses for the fund.” Read more

Good investment decision sometimes seems counterintuitive.  And if this is true, then prepayment risk will not be a threat to market volatility. Let’s see how this plays out.

Originally Published Here: Another Look at Prepayment Risk of Mortgage-Backed Securities

Where Has the Volatility Gone-Part Trois

Yesterday we published a note regarding the debate about ETFs and their impact on the current low volatility environment

WhereHas the Volatility Gone-Part Deux

To add to the “against camp”, Zerohedge just published a post, citing Eric Peters, the CIO of One River Asset Management:

“The people who are indexing now are the same ones who were selling in 2009,” continued VICE, agitated. “I just spoke at a conference filled for wealth advisors from all the major players. They say the same thing - today’s buyers are not long-term investors.” They’re guys who put $1mm into index ETFs.

“When they lose 6%-7% and decide to sell, who will be on the other side of those trades?” And the stocks that will be savaged worst will be the ones that lagged the indexes on the way up. “It reminds me of 2000, when people piled into the QQQs.”

“I don’t know when the next major crisis will hit, no one does,” admitted VICE. “But I do know that even in the next normal correction, the market’s losses will be amplified enormously by this move away from active management.”

Read more

This means that ETF actually increases the market volatility, especially during a downturn.

Where Has the Volatility Gone-Part Deux

Last week, we asked a question “Do ETFs really cause the low volatility” in this post

Where Has the Volatility Gone?

Today, CNBC released another article on the same topic. This time, the article features opposing points of view from notable researchers. Some experts agree that the rise of ETFs has caused the volatility to decline

“There’s no one resounding answer to [why we’ve seen] this low volatility,” Repetto, who covers the brokers and exchanges, said Tuesday on CNBC”s “Trading Nation.” But the growth of assets in exchange-traded funds, which largely track indexes, “has had some impact.”
Repetto pointed out that the first quarter of 2017 was the least volatile quarter for the S&P 500 in decades — which is just one among a host of stats showing how anomalous the lack of market movement has been.

While some disagree:

“To a large extent, I disagree that low volatility is being caused by ETFs,” Meziani, the author of three books about exchange-traded funds, told CNBC in a Thursday phone interview.
Read more

Volatility Trading Strategies, a Comparison of Volatility Risk Premium and Roll Yield Strategies

Volatility trading strategies

In previous posts, we presented 2 volatility trading strategies: one strategy is based on the volatility risk premium (VRP) and the other on the volatility term structure, or roll yield (RY).  In this post we present a detailed comparison of these 2 strategies and analyze their recent performance.

The first strategy (VRP) is based on the volatility risk premium.  The trading rules are as follows [1]:

Buy (or Cover) VXX  if VIX index <= 5D average of 10D HV of SP500

Sell (or Short) VXX  if VIX index > 5D average of 10D HV of SP500

The second strategy (RY) is based on the contango/backwardation state of the volatility term structure. The trading rules are as follows:

Buy (or Cover) VXX if 5-Day Moving Average of VIX/VXV >=1 (i.e. backwardation)

Sell (or Short) VXX if 5-Day Moving Average of  VIX/VXV  < 1 (i.e. contango)

Table below presents the backtested results from January 2009 to December 2016. The starting capital is $10000 and is fully invested in each trade (different position sizing scheme will yield different ending values for the portfolios. But the percentage return of each trade remains the same)

	RY	VRP
Initial capital	10000	10000
Ending capital	179297.46	323309.02
Net Profit	169297.46	313309.02
Net Profit %	1692.97%	3133.09%
Exposure %	99.47%	99.19%
Net Risk Adjusted Return %	1702.07%	3158.54%
Annual Return %	44.22%	55.43%
Risk Adjusted Return %	44.46%	55.88%
Max. system % drawdown	-50.07%	-79.47%
Number of trades trades	32	55
Winners	15 (46.88 %)	38 (69.09 %)

We observe that RY produced less trades, has a lower annualized return, but less drawdown than VRP. The graph below depicts the portfolio equities for the 2 strategies.

Portfolio equity for the VRP and RY strategies

It is seen from the graph that VRP suffered a big loss during the selloff of Aug 2015, while RY performed much better. In the next section we will investigate the reasons behind the drawdown.

 

Performance during August 2015

The graph below depicts the 10-day HV of SP500 (blue solid line), its 5-day moving average (blue dashed line), the VIX index (red solid line) and its 5-day moving average (red dashed line) during July and August 2015. As we can see, an entry signal to go short was generated on July 21 (red arrow). The trade stayed short until an exit signal was triggered on Aug 31 (blue arrow).  The system exited the trade with a large loss.

10-day Historical Volatility and VIX

The reason why the system stayed in the trade while SP500 was going down is that during that period, the VIX was always higher than 5D MA of 10D HV.  This means that 10D HV was not a good approximate for the actual volatility during this highly volatile period. Recall that the expectation value of the future realized volatility is not observable. This drawdown provides a clear example that estimating actual volatility is not a trivial task.

By contrast, the RY strategy was more responsive to the change in market condition. It went long during the Aug selloff (blue arrow in the graph below) and exited the trade with a gain. The responsiveness is due to the fact that both VIX and VXV used to generate trading signals are observable. The graph below shows VIX/VXV ratio (black line) and its 5D moving average (red line).

VIX/VXV ratio

In summary, we prefer the RY strategy because of its responsiveness and lower drawdown. Both variables used in this strategy are observable. The VRP, despite being based on a good ground, suffers from a drawback that one of its variables is not observable. To improve it, one should come up with a better estimate for the expectation value of the future realized volatility.  This task is, however, not trivial.

References
[1] T Cooper, Easy Volatility Investing, SSRN, 2013

Article source here:  Volatility Trading Strategies, a Comparison of Volatility Risk Premium and Roll Yield Strategies