An index is a
statistical measure which describes the changes in a p?rtf?li? ?f st?cks ?f a
specific secti?n ?f market. It is thus a mathematical ?bject used by invest?rs
and financial managers t? describe and c?mpare specific features ?f a market.

Mr. Charles D?w
created the first index ever in May ?f 1896 and the m?st widely kn?wn until n?w.
N?wadays it is kn?wn as the D?w J?nes Industrial Average1
(ticker symb?l “DJIA”). Since 1896 many ?ther indices have been created f?r
example S&P 100, S&P 500, Nasdaq C?mp?site index etc. ?ther types ?f
indices are capitalisati?n indices2,
fixed inc?me indices3,
residential pr?perty indices4,
sect?r indices5,
strategy indices6
and v?latility indices, which are analyzed in detail in the next paragraphs.

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1.2 V?latility Indices and the VIX index

V?latility
indices measure the market’s expectati?n ?f v?latility based ?n the prices ?f ?pti?ns.
The m?st widely used v?latility indices is the VIX index ?f Chicag? B?ard ?pti?n
Exchange (CB?E).

The VIX index
is m?re ?r less, like the Nasdaq C?mp?site index. Their maj?r difference is
that the VIX measures v?latility, that is the unexpected m?ves either up ?r d?wn
?f an index, and n?t price. The VIX index (v?latility index) was created in
1993 by the CB?E. The index is an instant measure ?f implied market v?latility.
It is calculated by using the mean ?f real time S 500 ?pti?ns (SPX).

When Whaley
first intr?duced the VIX index he had tw? things in mind (R?bert E. Whaley ,2008).
The first ?ne was that, the index had t? bec?me a benchmark ?f implied sh?rt-term
(30- days) market v?latility. He als? wanted t? make the c?mparis?n between the
then- current level ?f VIX with the hist?rical ?nes, s? the minute by minute
values were c?mputed using index ?pti?n prices ?f 1986. The ch?ice ?f this
specific date was n?t rand?m. 1987 was the peri?d ?f the w?rst st?ck market
crash since the Great Depressi?n, the w?rst depressi?n that the w?rld had ever
faced until then. This was particularly imp?rtant since invent?rs were able t?
d?cument the level ?f market anxiety during a very difficult peri?d f?r the ec?n?my.
The sec?nd reas?n f?r the creati?n ?f the index was the intenti?n ?f pr?viding
an index which c?uld be used as an underline asset, f?r futures and ?pti?ns c?ntracts
?n v?latility. The imp?rtance ?f such trading assets was rec?gnized s??n after
they were first launched (futures May 2004 and ?pti?ns February 2006).

1.3The “Invest?r Fear Gauge”

The VIX index
is als? called “invest?rs fear gauge” (Whaley,2008). It has been named like
that because, as already menti?ned, it is f?rward l??king and sh?ws what market
expects f?r the 30-days v?latility. The index became p?pular because many
invest?rs want t? hedge their investments. Invest?rs can buy puts ?n the index
in ?rder t? av?id l?ses fr?m a p?tential dr?p in the price. The Figures 1, 2
and 3 sh?w the negative c?rrelati?n between the prices ?f the index and the
prices ?f S 500). S?, as invest?rs became m?re w?rried ab?ut the p?tential
prices decreases they ask f?r m?re puts s? they push the put prices up. The
increase ?f the prices ?f puts increase the implied v?latility (ceteris
paribus)7
s? the price ?f the index is increased as well. The VIX is thus an index that
reflects the price ?f the p?rtf?li? insurance (invest?rs fear gauge).

1 ?he Dow Jones Industrial
Average (DJIA) contains 30 of the largest and most influential companies in the
U.S.

2 Capitalisation indices
represent the sum of the market capitalisations of the companies making up the
index (www.asx.com.au)

3 Fixed income indices measure the
performance of the bond market and the short-term money market. (www.asx.com.au)

4 Property indices are similar to other
asset performance indices in that they measure changes in the market value of
the asset class in question, in this case residential property. (www.asx.com.au)

5 Sector indices enable investors to
benchmark the performance of a particular stock market sector or industry.
(www.asx.com.au)

6 Strategy indices track the performance
of a particular investment strategy (www.asx.com.au)

7 The price of the put is an
increasing function of implied volatility and as a result “1-1” function.