1. Project: VIX index
and CDS spread
National Economics University
Advanced Finance Program intake 50
2011
9/12/2011
Group students:
Nguyễn Thị Thu Hà
Nguyễn Thị Ngọc Hà
Phạm Quang Huy
Quản Thị Hạnh Mai

2. I. Definitions
1. Credit default swap (CDS)
a. Definition:
A credit default swap (CDS) is
a credit derivative contract
between two counterparties. It is
quite similar to a
traditional insurance policy due to
the fact that it obliges the seller of
the CDS to compensate the buyer
in the event of loan default. In
general, this involves an exchange
or "swap" of the defaulted loan
instrument (and with it the right to recover the default loan at some later time) for immediate
money - usually the face value of the loan.
There are two parties taking part in swap agreement. First of all, protection buyers
purchase insurance against the event of default. Then, he agrees with protection sellers to
pay a premium. As a result, in the event of default, the protection seller has to compensate the
protection buyer for the loss.
In CDS, the buyer makes regular premium payments to the seller, the premium
amounts constituting the "spread" charged by the seller to insure against a credit event.
CDS spread = Premium paid by protection buyer to the seller
The premium (spread) is determined by market forces and depends on the expected
default risk of debt issuers. Therefore, CDS spreads are an indicator of the market's current
perception of sovereign risk when the debt issuers are the Governments. Moreover, CDS
spreads also depend on other factors such as market liquidity, counterparty risk and the global
financial environment, in particular country’s interest rates and global risk appetite.
CDS spreads is usually quoted in basis points per annum of the contract’s notional
amount and is paid quarterly. For example, A CDS spread of 339 bps for five-year debt

3. means that default insurance for a notional amount of $1 million costs $ 33,900 per annum;
this premium is paid quarterly (or $ 8,475 per quarter).
Features
There is negative correlation between a company stock price and its CDS spreads. If
the outlook for a company improves and its share price should go up then its CDS spread
should tighten. It can be explained that the company has less probability to default so the
CDS will decline. On the other hand, if company or market’s outlook deteriorates then CDS
spread should widen and its stock price will decline to reflect the bad situation. Thus, it can
be said that the worse the credit rating, the higher the CDS spread. Nevertheless, there is still
a special situation in which the inverse correlation between a company's stock price and CDS
spread breaks down. This is when the companies apply Leveraged buyout (LBO). Frequently
this leads to the company's CDS spread widening due to the extra debt. But at the same time,
the share price increases, since buyers of a company usually end up paying a premium.
How do CDS spreads relate to the probability of default? The simple case
For simplicity, consider a 1-year CDS contract and assume that the total premium is
paid up front.
Let S: CDS spread (premium), p: default probability, R: recovery rate
When two parties enter a CDS trade, S is set so that the value of the swap transaction is zero,
i.e.
S= (1-R) p
S/ (1-R) =p
Example: If the recovery rate is 40%, a spread of 200 bps would translate into an implied
probability of default of 3.3%.
So a spread of 200 basis points is equivalent to the notion that the market is pricing in an
annual chance of about 3% that the issuing government will default.

4. 2. VIX
In 1993, the first VIX, introduced by Prof. Robert Whaley at Vanderbilt
University, was a weighted measure of the implied volatility of eight S&P 100 at-the-money
put and call options. Ten years later, it expanded to use options based on a broader index, the
S&P 500, which allows for a more accurate view of investors' expectations on future market
volatility.
By definition, VIX is the ticker symbol for the Chicago Board Options Exchange
Market Volatility Index, a popular measure of the implied volatility of S&P 500 index
options. The index is calculated using the price of near-term options on S&P 500 index.
Because the value of an option is closely linked to the expected volatility of its underlying
security, options prices can be a useful indicator of investors' expectations of volatility. Thus,
people might call VIX as the "fear index" because a high VIX represents uncertainty about
future prices (over next 30 days period).
The VIX is quoted in percentage points and translates, roughly, to the expected
movement in the S&P 500 index over the next 30-day period, which is then annualized.
Given an example, if the VIX is 15 means an expected annualized change of 15% over the
next 30 days, it then can implies that the index option markets expect the S&P 500 to move
up or down (1.15%)1 / 12 = 1.17% over the next 30-day period.
By taking the weighted average of implied volatility for the Standard and Poor's
Index, this index can point out number of critical things to investor looking at the near future
market.
-A low VIX indicates trader’s confidence with low volatility of market.
-A high VIX indicates indicate that investors expect the value of the S&P 500 to fluctuate
wildly - up, down, or both - in the next 30 days.
In practice, VIX which is greater than 30 are generally implies a large amount
of volatility as a result of investor fear or uncertainty, while value below 20
generally corresponds to less stressful period in the markets.

5. III. VIX in reality
*Sources: Bloomberg and CBOE.
The Volatility Index (VIX) is a key measure of market expectations of near-term
volatility conveyed by S&P 500 stock index option prices. VIX reflect investors' consensus
view of future expected stock market volatility, so during periods of financial stress, which
are often accompanied by steep market declines, VIX tends to rise. As investor fear subsides,
option prices tend to decline, which in turn causes VIX to decline. As you can see the chart
above is the VIX and S&P 500 Indexes in 9 years, from January 2003 to June 2011. It is very
obvious to see in the chart that the VIX index line and the SPX always move in two opposite
direction. In period 2003 to the first half of 2007, the VIX index was around more than 10
and below 20 and fluctuated slightly. It did not suddenly plunge or go up. In these 5 years,
the VIX tended to go down gradually. Corresponding with the VIX, the S&P 500 index had
upward trend since, but also gradually. In general, the economic conditions in 2003- 2007
was quite stable. However, from July 2007, the VIX index started going up, from 12 in May
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VIX and S&P 500 Indexes
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6. 2007 to 25 in July 2007, increased more than 100% in just 2 months. It indicated that
investors’ fear about the stock market was growing up because of something. It continued to
vary in 20 to 30 in next 10 months and suddenly went up twice in August 2008. The fear of
investors was growing up since the market turmoil at that time. The SPX also plunged as the
investor pessimistic about the market. So what had a big affect to investors? I will show you
more clearly by look at the chart in the period 2008-2010.
*Sources: Bloomberg and CBOE.
In 2008 the whole world faced with financial crisis. The crisis was so severe, and the
world financial system was affected. The global financial crisis, brewing for a while, really
started to show its effects in the middle of 2007 and into 2008. Around the world stock
markets have fallen, large financial institutions have collapsed or been bought out, and
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VIX and S&P 500 Indexes
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7. governments in even the wealthiest nations have had to come up with rescue packages to bail
out their financial systems. Because American financial firms followed the Subprime
Mortgage loan which allowed the consumers could borrow money even with substandard
credit rating. It created the housing bubble crisis, and became the global financial crisis. Both
investors and mortgage companies were in trouble. On the 14th September 2008, it came to
light that the financial services firm, Lehman Brothers, would file for bankruptcy after being
denied support by the Federal Reserve Bank. Later the same day, the Bank of America
announced that it would be purchasing Merrill Lynch. On the 16th September, the American
International Group (AIG) suffered due to its credit rating being reduced. Over the next two
weeks, more banks failed and the two remaining banks-Goldman Sachs and Morgan Stanley
converted into 'bank holding companies' so that they had more access to market liquidity.
Due to the above factors, there was major instability on the global stock markets with
major decreases in market value between the 15th and 17th of September 2008. In 17th
September, the VIX index closed at 36.22, increasing more than 6 with 16th
.
In October 2008, the S&P 500 index fell from around nearly 1200 in September to hit
848.92, the lowest in the first 10 months of 2008. At the same time, the VIX also increased
rapidly to 80.06, the highest record until October 2008.
The situation was even worst in November when in 20th
Nov, the SPX index dropped
to 752.44, the lowest in 2008; and the VIX hit the record of 80.86, the highest number in 16
years (from 1995 to 2010) (VIX has 21 years of history).
The double tops in the VIX index in 2 months showed a very obvious message:
investors were losing their confidence about the future of economy. Investors were afraid of
the high volatility of market, not only in U.S but in all over the world. Numerous plans were
put forward with intent to solve the crisis and in the end President George W. Bush and the
Secretary of the Treasury announced a $700 billion financial aid package intended to limit the
damage that the previous few week's events caused. The plan was received well by investors
on Wall Street and around the world. Government gave some simulation packages to improve
the situation, along with other solutions, the stock market recovered in around June 2009. The
VIX index also decreased and became more stable.
Although we only show the VIX index until June 2011, but after that, especially from
August 2011, the debt crisis in U.S and Euro zone emerged which made the big affect to
expectation of investors. The problems that have weighed on investors - The European debt

8. and fear of a new recession in the United States, in addition the under-expected reports about
unemployment, economic growth, hammered the stock market. Traders fear that one of the
continent's heavily indebted economies could default, an event that would ripple through the
global banking system and make it difficult for other European countries to borrow money.
Moreover, the U.S. economic growth is already slowing, and unemployment is stuck above 9
percent. In 9 September 2011, the Standard & Poor's 500 closed down 32, or 2.7 percent, at
1,154. The VIX closed up 4.2 at 38.52 in 9 September. 1
IV. Credit Default Swap Spread
 Market as of 2007
1
Source: finance.yahoo.com
Cboe.com
Bloomberg.com
Chart1: CDS index in 5 years

9. - After U.S. house sales prices peaked in mid-2006 and began their steep decline forthwith,
refinancing became more difficult. As adjustable-rate mortgages began to reset at higher
interest rates, mortgage delinquencies soared, and securities backed with mortgages lost
most of their value. Concerns about the soundness of U.S. credit and financial markets led
to tightening credit around the world and slowing economic growth in the U.S. and
Europe. Initial subprime concerns appeared made CDS spread began its trend of
increasing.
- In the second half of 2007, Bear Stearns, a global investment bank and securities trading
and brokerage experienced difficulties. The most significant outcome was the record of
61 percent drop in net profits due to their hedge fund losses reported on September 21 in
New York Time note. CDS spread was widen during the last quarter of 2007.
- Fed's dramatic action that lowered rates by 50 bps cheered investors, which CDS spread
declined in August and September. However, from the beginning of October, the news
that U.S brokers reported huge losses and write downs, plus the failure of Bear Stearns,
stimulated the growth of CDS spread.
 Market as of 2008
- In March 2008, Bear Stearns went to debacle and eventually led to its forced sale to JP
Morgan. In the days and weeks leading up to Bear’s collapse, the bank’s CDS spread
widened dramatically, indicating a surge of buyer talking out protection on the bank.
- During the middle of 2008, the fears concerning about Lehman, Fannie/Freddie and
monoclines (such as MBIA, Ambac) downgrade continuously raised the spread of CDS.
- On September 7, 2008, the Federal Housing Finance Agency (FHFA) announced that
Fannie Mae and Freddie Mac were being placed into its conservatorship.
- In September 2008, the bankruptcy of Lehman Brothers caused a drastically fluctuation
of CDS spread.
- Also in September, American International Group AIG required a federal bailout because
it had been excessively selling CDS protection without hedging against the possibility
that the reference entities might decline in value, which exposed the insurance giant to
potential losses over $100 billion.
- Lehman Brother auction settled the CDS smoothly.
- In November, DTCC announced that it would release market data on the outstanding
notional of CDS trades on weekly basic, and Intercontinental Exchange was granted to
begin guaranteeing credit default swaps.

10.  Market as of 2010
- Stable due to recover of economy, improvement of investor expectation
- Some fluctuate and still high due to high deficit level of US government budget
 Market as of 2011
- Still high due to Government deficit of Greece, Portugal, and many other countries in
Euro zone and US.
- Lower credit rating for US
V. Correlation and interpretation for VIX index and CDS spread
First of foremost, we will draw the route that our group will go through. To get the
ball rolling, we start by showing the correlation between VIX index and CDS spread in the
short term. Then we will pick up some key events over 6 years from 2007 to 2011, and
finally, we will show everything in long term and draw our conclusion about this relationship.
For all charts we present here, the VIX is the green line and the CDS spread is the orange
one.2
And here is the first technical analysis figure for the most recently 6 months from Apr
to Sep, 2011:
2
All charts were taken snapshot on Bloomberg.com
Chart2: VIX & US. Bank CDS for 6 months Apr – Sep 2011

11. As you can see via the chart, both VIX and CDS are moving quite similar to each
other over 6 months. The trend is fluctuating consistently between the two from Apr to at the
end of July. Significantly, we should focus on the 2 circle in the chart as we marked. As
looked at the violet circle, both VIX and CDS were raised incredibly, almost double
compared to four previous months (approximately 100 points). Indeed, this peak point was on
5 Aug, 2011, this day was considered as the first day in history the US was lowered down
credit rating by S&P. This news impacted a lot on investors and the economy as a whole, not
only US but also any countries which hold the US Government bonds. The VIX was high
also means that other basic indices decreased. That’s true when the DJIA, S&P500,
NASDAQ and other indices in Europe and Asia were so low the past few days. At the same
time, the CDS spread soared from 16.7 to 77.2 points.
The same story is for the second circle, the blue one. At the beginning of Sep, it was
time for US announced its unemployment report. In fact, the unemployment rate keeps level
up from the beginning of 2011 until now, about 9.1% recently. The bad news one more time
affected the market that forced president Obama had to take action. He also announced his
proposal 447 billion USD to create job and social stability. To react to the news, both VIX
and CDS spread immediately responded by the dropping more than 50 points for VIX and 20
points for CDS. As here we also disclose the relationship between the two in one year.
3/29/11 S&P kept
lowering the credit rating
of Greece & Portugal
Chart3: VIX & US. Bank CDS in one year

12. Take a glance over one year, the two indices move closely to each other, except for
the brown circle, the time when S&P lowered credit rating of both Greece (BB-) and Portugal
(BBB-).
Lastly, we will look at the whole picture over 6 years from 2007 to 2011 in order to
draw key conclusion:
In long term, we can see the whole picture it’s the different story compared to the
short run as we concerned above. We can pay attention to the divergence between the two is
bigger and bigger especially after the global financial crisis 2008 – 2009. At this time, the
CDS spread fluctuated significantly due to the bubble of subprime mortgage was burst and it
created the domino effect that spread all over the world. That formed two CDS’s peaks in
these years and also led the VIX soared drastically. Due to the wide gap amongst them, it also
implicates the instability of the economics especially when the confidence of investors is
eroded and the economics is facing with a lot of obstacles such as outstanding public debts,
the unemployment and inflation and so on.
In short, we can draw conclusion that both VIX and CDS could be considered as one
of useful toolkits to forecast the financial crisis, especially via the crisis 2008 – 2009 and the
Chart4: VIX & US. Bank CDS in 5 years

13. national debts issue, the two shows us something in expectation toward the market and near
future. Or in other word, we can say about the relation amongst them is positive correlation.
Even no one what will happen to the market and no unique tool is perfect for forecasting, we
just use VIX and CDS like a referent ones before making any final conclusion.