Sunday, June 24, 2018

Are Collateralized Loan Obligations the New Debt Bombs?

Last year, in a post entitled Credit Derivatives-Is This Time Different we wrote about credit derivatives and their potential impact on the markets. Since then, they have started attracting more and more attention. For example, Bloomberg recently reported that collateralized loan obligations (CLO), a type of complex credit derivatives, are becoming a favorite financing vehicle for corporate America.

...Investors haven’t been able to get enough of the repackaged corporate loans known as collateralized loan obligations. That intense demand, is allowing the managers that put these securities together to sell off pieces of CLOs that by law they previously had to hang on to. These sales are the crest of what could be a $7 billion wave of such deals. Read more

credit derivatives US High Yield Credit Spreads

As reported by the Washington Post, money raised from these CLOs is used to finance corporate stock buybacks and dividend payouts.

The most significant and troubling aspect of this buyback boom, however, is that despite record corporate profits and cash flow, at least a third of the shares are being repurchased with borrowed money, bringing the corporate debt to an all-time high, not only in an absolute sense but also in relation to profits, assets and the overall size of the economy.

In recent years, moreover, a greater part of corporate borrowing has come in the form of bank loans that are quickly packaged into securities known as CLOs, or collateralized loan obligations, which are sliced and diced and sold off to sophisticated investors just as home loans were during the mortgage bubble. Bloomberg News recently reported that pension funds and insurance companies, particularly those in Japan, can’t get enough of the CLOs because of the higher yields that they offer. Wells Fargo estimates that a record $150 billion will be issued this year, roughly double last year’s issuance. And as happened with the late-cycle home mortgages in 2007 and 2008, analysts are noticing a marked decline in the quality of loans in the CLO packages, with three-quarters of them now without the standard covenants designed to reduce the chance of default. Read more

But how risky are these collateralized loan obligations?

In the current market environment, it’s difficult to evaluate the riskiness of these CLOs. First of all, Value at Risk (VaR), a popular risk measure used by many financial institutions to quantify the risks and manage economic capital, has been developed and tested in a low-interest rate and low-volatility environment. This makes the VaR  vulnerable to future change in the market environment.

Second, in the calculation of VaR for a credit derivative portfolio, we would have to determine the probabilities of default (PD) and loss given default (LGD) of the borrowers. Both of these quantities are difficult to estimate. Furthermore, the correlation between PD and LGD is not constant and will likely increase during a market stress.

All of these factors make the VaR less accurate.  Consequently, managing the risks of a CLO portfolio is a non-trivial task. A slight change in the market environment can lead to damaging consequences.

Post Source Here: Are Collateralized Loan Obligations the New Debt Bombs?

Saturday, May 19, 2018

Do Properly Anticipated Prices Fluctuate Randomly? Evidence from VIX Futures Markets

According to Marketwatch, Goldman Sachs strategists just issued a warning regarding the volatility index, VIX,

Goldman analysts Rocky Fishman and John Marshall said that the VIX, which uses options bets on the S&P 500 to reflect expected volatility over the coming 30 days, has been hovering at or below 13, marking its lowest level since around January (though it is tipping up in Monday trade). Its current level takes the gauge of implied volatility, which tends to rise when stocks fall and vice versa, well below its historic average at about 19.5 since the fear index ripped higher in February.

Goldman argues that the 5-day intraday swings of the S&P 500 have been out of whack with the price of the cost of a one-month straddle on the index. A straddle is an options bet that allows an investor to profit from a sharp move in an asset, but without wagering on the specific direction of that expected move. In other words, it is an inherent bet on volatility. A straddle can be structured by buying a put option, which confers the owner the right but not the obligation to sell an asset at a given time and price, and a call option, which offers the comparable right to buy an underlying asset, at the same expiration date and strike price. Read more

volatility trading strategies VIX predictable
Volatility Index VIX as of May 18 2018

But is the volatility index predictable? How about VIX futures and ETFs?

A recent research article raised some interesting questions,

The VIX index is not traded on the spot market. Hence, in contrast to other futures markets, the VIX futures contract and spot index are not linked by a no-arbitrage condition. We examine (a) whether predictability in the VIX index carries over to the futures market, and (b) whether there is independent time series predictability in VIX futures prices.

The answer is no.

The answer to both questions is no. Samuelson (1965) was right: VIX futures prices properly anticipate predictability in volatility, and are themselves unpredictable. Read more

But then why do we trade VIX futures and ETFs?

We think that the reasons might be:
  • Trading the spot VIX is difficult,
  • When trading VIX futures and ETFs, we exchange the predictability of the spot index for a little extra return stemming from the volatility risk premium.


Tuesday, May 15, 2018

Overnight Index Swap Discounting

The overnight index swap (OIS) has come into the spotlight recently, due to the widening of the Libor-OIS spread. For example, the Economist recently reported:

WATCHING financial markets can be like watching a horror film. A character walks into the darkness alone. A floorboard creaks. The latest spooky sign is the spread between the three-month dollar London interbank offered rate (LIBOR) and the overnight index swap (OIS) rate. It usually hovers at around 0.1%, but has recently climbed to 0.6% (see chart). As it widens, bankers are bracing for a jump scare.

To see why, consider what each rate represents. LIBOR is the rate that banks charge other banks for unsecured loans. The OIS rate measures expectations for the federal funds rate, which is set by the central bank. As LIBOR rises above the OIS rate, that suggests banks fear it is getting riskier to lend to each other. (The gap was 3.65 percentage points in the depths of the crisis, after Lehman Brothers filed for bankruptcy.) Read more

[caption id="attachment_459" align="aligncenter" width="628"]Overnight Index Swap Discounting Libor-OIS spread as at May 2, 2018. Source: Bloomberg[/caption]

What exactly is an overnight index swap?

An overnight index swap is a fixed/floating interest rate swap that involves the exchange of the overnight rate compounded over a specified term and a fixed rate. The floating leg of the swap is related to an index of an overnight reference rate, for example Canadian Overnight Repo Rate Average (CORRA) in Canada or Fed Funds rate in the US.

Usually, for swaps with maturities of 1 year or less there is only one payment. Beyond the tenor of 1 year, there are multiple payments at regular intervals. At the inception of the swap, the par swap rate makes the value of swap zero. That is, the net present value (NPV) of the fixed leg equals the NPV of the floating leg,

Interest rate swap derivative valuation

where N denotes the notional amount of the swap,

Ri-1,i is the forward OIS rate,

Zi is the discount factor at time ti

is the daily accrual factor, and

 sK is the par swap rate of a swap with maturity tK.

The OIS discount factors (DF) are often used to value interest rate derivatives that require a posting of collateral.  The OIS discount factor curve is built by bootstrapping from the short maturity and long maturity overnight index swap rates in order of increasing maturity.  The processes for backing out the discount factors from the short and long maturity swap rates are, however, different.

In the short end of the curve, given that there is only 1 payment, the discount factor is calculated based on the spot rates. At the long end of the curve, the DF curve is determined as follows,

  • Payment dates are generated at each 6 months (or a year, depending on the currency) from the time zero up to 30 years,
  • Par swap rates are determined at each payment date. To obtain the par swap rates for the payment dates where there are no swap quotes, one linearly interpolates the par swap rates in order to complete the long end of the swap curve,
  • Using the par swap rates at each payment date, discount factors are obtained by solving a recursive equation.

This is just an introduction to OIS discounting. The process for building an OIS discount curve involves many technical details. We are happy to answer your questions.

Post Source Here: Overnight Index Swap Discounting

Saturday, May 5, 2018

Can a Horse Racing System be Applied to the Stock Markets?

Bill Benter is one of the most profitable professional gamblers in the world. According to Wikipedia

William Benter was born and raised in Pittsburgh, Pennsylvania.[2] As he grew up, he wanted to use his mathematical talents to make a profit so immediately after finishing a university physics degree in 1977,[3] he went to the blackjack tables in Las Vegas and used his skills to count cards. He came across the book, Beat the Dealer, by Edward O. Thorp, which helped him improve his methods.[4] Seven years later, he was banned from most of Vegas’ strip’s casinos.[2]

Benter then met with Alan Woods, a like-minded gambler whose expertise in horse racing complemented his own in computers. The two became racing partners and in 1984, moved to Hong Kong.[3] Starting with a mere US$150,000 (equivalent to US$353,331 in 2017), the pair relied on their mathematical skill to create a formula for choosing race winners.[2]

Using his statistical model, Benter identified factors that could lead to successful race predictions. He found that some came out as more important than others.[5] Benter later worked with Robert Moore.

Benter is a visiting professor at the Southampton Management School[6] as part of the Centre for Risk Research and a fellow of the Royal Statistical Society.[7]

Bloomberg recently published an interesting story about his career, 

Benter grew up in a Pittsburgh idyll called Pleasant Hills. He was a diligent student and an Eagle Scout, and he began to study physics in college. His parents had always given him freedom—on vacations, he’d hitchhiked across Europe to Egypt and driven through Russia—and in 1979, at age 22, he put their faith to the test. He left school, boarded a Greyhound bus, and went to play cards in Las Vegas.

Benter had been enraptured by Beat the Dealer, a 1962 book by math professor Edward Thorp that describes how to overcome the house’s advantage in blackjack. Thorp is credited with inventing the system known as card counting: Keep track of the number of high cards dealt, then bet big when it’s likely that high cards are about to fall. It takes concentration, and lots of hands, to turn a tiny advantage into a profit, but it works.

Thorp’s book was a beacon for shy young men with a gift for mathematics and a yearning for a more interesting life. When Benter got to Las Vegas, he worked at a 7-Eleven for $3 an hour and took his wages to budget casinos. The Western—with its dollar cocktails and shabby patrons getting drunk at 10 a.m.—and the faded El Cortez were his turf. He didn’t mind the scruff. It thrilled him to see scientific principles play out in real life, and he liked the hedonistic city’s eccentric characters. It was the era of peak disco, with Donna Summer and Chic’s Le Freak all over the radio. On a good day, Benter might win only about $40, but he’d found his m├ętier—and some new friends. Fellow Thorp acolytes were easy to spot on casino floors, tending to be conspicuously focused and sober. Like them, Benter was a complete nerd. He had a small beard, wore tweedy jackets, and talked a lot about probability theory. Read more

But can a winning horse racing system be applied to the stock markets? Benter himself provided an answer in this video


Monday, April 30, 2018

VIX Mean Reversion After a Volatility Spike

In a previous post, we showed that the spot volatility index, VIX, has a strong mean reverting tendency. In this follow-up installment we’re going to further investigate the mean reverting properties of the VIX. Our primary goal is to use this study in order to aid options traders in positioning and/or hedging their portfolios.

To do so, we first calculate the returns of the VIX index. We then determine the quantiles of the return distribution. The table below summarizes the results.

Quantile 50% 75% 85% 95%
Volatility spike -0.31% 3.23% 5.68% 10.83%

We next calculate the returns of the VIX after a significant volatility spike. We choose round-number spikes of 3% and 6%, which roughly correspond to the 75% and 85% quantiles, respectively. Finally, we count the numbers of occurrences of negative VIX returns, i.e. instances where it decreases to below its initial value before the spike.

Tables below present the numbers of occurrences 1, 5, 10 and 20 days out. As in a previous study, we divide the volatility environment into 2 regimes: low (VIX<=20) and high (VIX>20). We used data from January 1990 to December 2017.

VIX spike > 3%
Days out All cases VIX<=20 VIX>20
1 56.1% 54.9% 58.1%
5 59.7% 58.4% 61.8%
10 60.3% 57.0% 65.8%
20 61.6% 57.0% 69.5%


VIX spike > 6%
Days out All cases VIX<=20 VIX>20
1 58.2% 56.9% 60.3%
5 62.5% 62.0% 63.3%
10 64.0% 61.7% 67.6%
20 65.9% 61.4% 73.2%

We observe the followings,

  • The greater the spike, the stronger the mean reversion. For example, for all volatility regimes (“all cases”), 10 days after the initial spike of 3%, the VIX decreases 60% of the time, while after a 6% volatility spike it decreases 64% of the time,
  • The mean reversion is stronger in the high volatility regime. For example, after a volatility spike of 3%, if the VIX was initially low (<20), then after 10 days it reverts 57% of the time, while if it was high (>20) it reverts 66% of the time,
  • The longer the time frame (days out), the stronger the mean reversion.

The implication of this study is that

  • After a volatility spike, the risk of a long volatility position, especially if VIX options are involved, increases. We would better off reducing our vega exposure or consider taking profits, at least partially,
  • If we don’t have a position prior to a spike, we then can take advantage of its quick mean reversion by using bounded-risk options positions.

Source Here: VIX Mean Reversion After a Volatility Spike