the basics of Implied Volatility

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the basics of implied Volatility

About VSTOXX ® and VIX ® Short- and Mid-Term Futures Indices

Volatility is a complex investment tool and is aimed at sophisticated investors

who understand the way volatility works as an investment and the risk involved

in so doing. You should not invest in any volatility related instrument unless

you understand the risks involved in such investments (taking independent

professional advice as you deem appropriate), and you are capable of assuming

such risks.

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* The investor fee is the Annual Fee times the applicable closing indicative value times the applicable daily index factor, calculated on a daily basis in the following manner: The investor fee on the inception date will equal zero. On each subsequent calendar day until maturity or early redemption, the investor fee will be equal to the Annual Fee times the closing indicative value on the immediately preceding calendar day times the daily index factor on that day (or, if such day is not an index business day, one) divided by 365.

This document provides a basic introduction to the concept of volatility and some of its implications for an investor. The document focuses particularly on the implications for equity markets and outlines the basics of the benchmark equity market volatility indices. however, the document is an introduction and does not attempt to detail all the applications and risks of volatility.

OPINIONS SUBJECT TO CHANGE

All opinions and estimates are given as of the date hereof and are subject to change. Barclays is not obligated to inform you of any

change to such opinions or estimates. Barclays will not be liable for any use you make of any opinion or estimate provided.

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WHAT IS VOlATIlITy?

The diagram below shows the hypothetical price movement of two assets over a period of time. Note that both assets have had the same return ending the period at a price of 1.25.

however, the paths taken to get to this point are significantly different. Asset 1 has had significant positive and negative swings in its growth over the term, whilst Asset 2 has had a stable growth over the term.

FIGUrE 1

hypothetical price moVement

The measure of the stability (or more accurately instability) of growth in financial assets is known as volatility. Assets such as emerging market equities, which can be subject to significant swings in growth, are said to have a high volatility.

Assets such as short dated, low credit risk government bonds, which traditionally tend to have smaller swings in growth, are said to have a low volatility. Note that volatility is not a measure of directional performance (consider the example above), but it is often used as a measure of financial risk. Thus typically assets which exhibit high volatility are considered to be more risky than assets with a lower volatility.

in addition, volatility for a given asset is unlikely to remain constant. For example, during periods of economic uncertainty equities tend to be more volatile as new information helps investors to significantly re-assess future growth prospects (either positively or negatively). similarly, during periods of stability equities tend to be less volatile as new information tends to lead to minor adjustments of future growth prospects.

WHAT ArE THE TyPES OF VOlATIlITy?

There are two types of volatility which may be considered for any asset. The first is a backward looking measure of how volatile the returns of the asset have been historically. This volatility is known as realised volatility and can be calculated using the formula for the standard deviation of returns.

The second type of volatility is forward looking, and is a measure of what the market expects the realised volatility to be in the future. As this “expected volatility” is defined by market participants’ expectation of how the asset will behave in the future, it cannot be calculated using a formula.

Fortunately, there is a reasonable proxy measure that can be derived from market parameters and this is known as implied volatility.

Time 1.50

1.25

1

0.75

0.50

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HOW IS IMPlIEd VOlATIlITy dErIVEd?

There are a set of traded financial instruments called

‘option contracts’, e.g. put options and call options, whose value has been shown to be a function of expected volatility. Furthermore, whilst there is no perfect valuation model for these contracts, there is a generally accepted one. Using this model it is possible to “reverse engineer”

the expected volatility assumption that would be required such that the model would show a value of the prevailing market price. This expected volatility assumption is known as implied volatility. For further information, please take independent professional advice as you deem appropriate.

PrOPErTIES OF IMPlIEd VOlATIlITy

implied volatility is a measure of market sentiment as it is a measure of instability of future returns, and is sometimes referred to as the “fear gauge”.

however, this market sentiment is based on existing imperfect knowledge and assumptions about future growth.

As a consequence, it can be very sensitive to news and information flows which may affect the future returns in a market. For example:

An earnings report which is worse than expected is likely to have a negative effect on the value of the equity markets. however, the news may also increase uncertainty in respect of potential future earnings. This uncertainty often translates into an increase in implied volatility.

An earnings report in line with or better than expectation is likely to have a positive and stabilising effect on the value of equity markets. This stability may translate into a decrease in implied volatility.

Furthermore, implied volatility tends to change more sharply than the underlying equity markets. in particular, during periods when equity markets fall significantly, implied volatility tends to increase sharply, often by much more than the percentage fall in the equity market.

These properties mean than implied volatility can have a strong negative correlation with equity markets, particularly during periods of negative returns, see Figure 2.

FIGUrE 2

index performance

These figures refer to past performance. Past performance is not a reliable indicator of future results.

source: Bloomberg, Barclays capital. 3

rd

Jan 2000 – 31

st

Oct 2011

implied volatility (represented here by the VsTOXX index) has tended to decline or remain stable in periods of equity market growth. however, it tends to “spike” in times of market distress.

WHAT ArE THE BENCHMArk VOlATIlITy MEASUrES?

There are currently two popular measures of implied volatility in equity markets:

Vix: which is a measure of the implied volatility of the s&P 500

®

, the Us equity market benchmark index.

Vstoxx: which is a measure of the implied volatility of the Euro sTOXX 50

®

, the European equity market benchmark index.

These measures of implied volatility are calculations, but cannot be traded directly. however, listed futures contracts do exist that allow professional investors to trade on this basis.

Usual application of the model

Volatility

Theoretical Value

market Price

implied

Volatility other known

variables

other known variables

„reversed engineered“

application of the model

a+b+c+d=

d+c+b+a=

Euro sTOXX 50 index (lhs) VsTOXX (Rhs) 6,000

5,000 4,000 3,000 2,000 1,000 0

90 80 70 60 50 40 30 20 10 0

JAN 00 JAN 01

JAN 02 JAN 03 JAN 04 JAN 05 JAN 06 JAN 07

JAN 08 JAN 09 JAN 10 JAN 11

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lISTEd FUTUrES CONTrACT

A futures contract is a standardised contract which amounts to an agreement to buy or sell a specified asset of standardised quantity and quality at a specified future date at a price agreed today (the futures price). For example:

if an investor were to agree to “buy” one futures contract entitling them to 100 shares of XYZ plc with an expiration date in december 2011 paying £ 350, then following the contracts expiration, they would be obliged to accept delivery of 100 XYZ Plc shares and pay £ 350.

if an investor were to agree to “sell” one futures contract worth 100 shares of XYZ Plc with an expiration date in december 2011 at £ 350, following the contracts expiration, they would be obliged to deliver 100 XYZ Plc shares to the “buyer” of the contract and receive £ 350.

WHAT ArE THE VOlATIlITy INdICES?

An investor who would like to maintain a continuous exposure to implied volatility could face some practical issues. if an investor wishes to maintain exposure to a futures position past the expiry date of the futures contract they currently hold, they must sell it prior to its expiry date and purchase a futures contract with a delivery date further in the future (often the next succeeding futures contract). This is known as “rolling” from one future to another.

Fortunately, a number of index providers now calculate volatility indices using futures contracts on the basis of rolling from one future to another as described above. The most popular are:

standard & Poor’s ViX family of indices linked to the ViX

sTOXX ltd.’s VsTOXX family of indices linked to the VsTOXX

in both cases the index sponsors offer two types of indices,

namely a short term futures index and a mid-term futures

index. The details of how the indices are calculated by

the index sponsors are beyond the scope of this note (For

details on how these indices are calculated please contact

the index calculators, either standard and Poor’s or sTOXX

ltd., directly). however, the basic methodology used is

summarised on the following page.

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SHOrT-TErM FUTUrES INdEX:

The short-term futures index follows a strategy of systematically rolling futures each day to maintain an

“average” 1-month position, see Figure 3.

At the end of each month, the index has 100% exposure to the following month’s futures contract (known as the

“front month” contract).

Each subsequent day, a proportion of the front month contract is sold and the second month contract is bought.

FIGUrE 3

short-term futures rolling mechanism

This daily rolling continues such that by the end of the month, the index no longer has any exposure to that front month contract and is fully exposed to the second month contract (which subsequently becomes the new front month contract when the existing front month contract expires).

MId-TErM FUTUrES INdEX:

The mid-term futures index follows a strategy of systematically rolling futures each day to maintain an

“average” 5-month position, see Figure 4.

At the end of each month, the index has equal exposure to the 4

th

, 5

th

and 6

th

month futures contracts.

Each subsequent day, a proportion of the index’s exposure to the 4

th

month contract is sold and the 7

th

month contract is bought.

FIGUrE 4

mid-term futures rolling mechanism

This daily rolling continues such that by the end of the month, the index is fully exposed in equal proportions to 5

th

and 6

th

and 7

th

month futures contracts (which, once the existing 4

th

month futures contract expires, now become the new 4

th

, 5

th

and 6

th

month futures contracts respectively).

october

october november 100% invested

in the march future

march future

July august

Over each roll period, allocation is systematically shifted from the 4

th

month contract to the 7

th

month contract

June september July october august november

august september

september october

FEB mAR APR mAY

FEB mAR APR mAY

april future

april future may future

may future

June future

June future 100% invested

in the June future 100% invested

in the may future 100% invested

in the april future

source: Barclays capital

source: Barclays capital

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Another aspect of these indices is that they are often quoted as “excess return” or “total return” indices. An index that tracks the return generated by rolling the future contract is known as an excess return index. however, excess return indices do not take into account that an investor having futures exposure would usually be holding the notional amount in cash. Total return indices look to adjust for this by calculating the value of the index as the excess return plus an interest amount.

most index tracking investments relate to the total return indices as these are the best index proxies to a fully committed cash investment with continuous exposure to implied volatility.

IMPlIEd VOlATIlITy BlOOMBErG TICkEr

ViX Total Return index ViX index

ViX short-Term Total Return index sPVXsTR index ViX mid-Term Total Return index sPVXmTR index

VsTOXX Total Return index V2X index

VsTOXX short-Term Total Return index VsT1mT index VsTOXX mid-Term Total Return index VmT5mT index

dO THE VOlATIlITy INdICES HAVE A

“rOll yIEld” SIMIlAr TO THAT OF THE COMMOdITy INdICES?

The ViX and VsTOXX family of indices do rely on the rolling of futures contracts, and therefore do have the potential to experience a roll yield. like the commodity indices, the roll yield can be either positive or negative.

however, unlike commodity indices, the rolling does not arise from a single roll of the futures contract close to its expiration

WHAT IS A “rOll yIEld”?

1

Usually the price of the applicable futures contract will not be the same as the current prevailing level of either the ViX or VsTOXX index, (known as the ‘spot price’).

however, over time, as the term to expiry of the futures contract shortens, the price of any given futures contract will converge towards the spot price. Thus an investor, rolling a future, i.e. buying a future, holding it for some time and then selling it to buy a longer dated future, will experience either a profit or a loss even if the spot price has remained unchanged. The return generated by the rolling of the future is known as the “roll yield”.

The roll yield can be negative or positive:

negative roll yield

if the spot price is lower than the futures contract price, then all else being equal, the futures price will decrease over time towards the spot price. in this scenario, the roll yield will be negative, and an index, or an investor, will experience a negative return.

positive roll yield

if the spot price is higher than the futures contract price, then all else being equal, the futures price will increase over time towards the spot price. in this scenario, the roll yield will be positive, and an index, or an investor, will experience a positive return.

1

Please see the document “The Basics of commodities” for more information on

the roll yield, available on the iPath website www.iPathETN.eu

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WHy INVEST IN IMPlIEd VOlATIlITy?

The properties of implied volatility outlined above highlight the tendency of implied volatility to:

increase in times of uncertainty usually associated with declining equity markets and decrease in times of certainty usually associated with stable or increasing equity markets, i.e. implied volatility tends to be negatively correlated to equity market growth, and

As a result investors could use an implied volatility investment to:

take a directional view on uncertainty:

investors may have an outright view on the direction of volatility. For example, an investor who believes that the forthcoming market environment is likely to have high levels of uncertainty could invest in an asset that gives exposure to one of the implied volatility indices.

however, such an investment may have a negative return if implied volatility remains stable or even decreases, for example if the market outlook remains the same or becomes more stable.

FIGUrE 5

diVersification effect

change more sharply than the underlying equity markets, particularly during sharp falls in the equity market.

diversify the portfolio

While diversification may not necessarily protect against all market risk, the historically negative correlation between implied volatility and equities may help stabilise returns of an equity portfolio. Although it can be counterintuitive, but adding some implied volatility, whose returns can be very volatile, can lower the overall volatility of a diversified equity portfolio (see case study below).

however, it is important to remember that diversification is not a panacea for all risk. For example, the magnitude of the implied volatility move is difficult to predict and therefore an investment may not fully offset any losses in the equity portfolio. Please note that you should not invest in any volatility related investment unless you understand the risks involved in such investments (taking independent professional advice as you deem appropriate), and you are capable of assuming such risks.

These figures refer to past performance. Past performance is not a reliable indicator of future results.

source: Bloomberg, Barclays capital. 18

th

Oct 2005 – 31

st

Oct 2011

Basket (90% sX5T + 10% VsT1mT) sX5T index

case study: using implied Volatility as a diVersification tool within a european equity portfolio

it is important to note that during stable markets, an investment in implied Volatility may suffer losses as market participants feel a greater

sense of certainty in the markets. in these scenarios, an allocation to implied Volatility within an equity portfolio may reduce any positive

returns earned through the allocation to equities.

including implied Volatility as part of an investment portfolio may helpt to reduce

losses during turbulent markets and enhance the long term returns.

150 140 130 120 110 100 90 80 70 60

OcT 2005 OcT 2006 OcT 2007 OcT 2008 OcT 2009 OcT 2010 OcT 2011

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WHAT ArE SOME OF THE rISkS THAT SHOUld BE CONSIdErEd?

investable implied volatility investments are proxies for expected volatility

When investing in implied volatility investments it is

important to remember that these are proxies for the market

“expected” volatility. Furthermore, the ViX and VsTOXX implied volatility refer to the Us equity markets and large cap European equity markets respectively, so may not reflect change in uncertainty in other regional markets, for example the UK equity market, or small cap European equities.

the performance of implied volatility and implied volatility indices is unpredictable

implied volatility is in itself inherently volatile and may be affected by numerous factors including liquidity, supply and demand, market activity, regulatory intervention, civil action, natural disaster and other geopolitical circumstances. You should regard implied volatility linked products as high risk.

investable implied volatility indices are subject to the roll yield most implied volatility investments will be referenced to implied volatility indices. As mentioned earlier, these investments are likely to be subject to a roll yield effect. This effect may be positive or negative and can lead to significant divergence, either positive or negative, between the return of the indices and the theoretical level of the current implied volatility.

an implied volatility index may be substituted in certain circumstances

investments linked to implied volatility indices will usually have the right to substitute the index in certain circumstances. such action may negatively affect the value and performance of the investment. Furthermore, the investments are not guaranteed by an exchange and they do not confer any ownership of any exchange traded contracts.

the policies of the relevant index sponsor

The policies of the sponsor of the relevant volatility index and

changes that affect the composition and valuation of the

relevant volatility index could affect the amount payable on

investment, linked to a volatility index and its market value.

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WHICH IMPlIEd VOlATIlITy INdEX COUld BE USEd?

The popular indices are proxies for two of the main world equity markets and should be used as such:

ViX family of indices for the Us equity market and

VsTOXX family of indices for the European equity markets Furthermore, relative to the mid term indices, the short term indices tend to have a higher degree of sensitivity to implied volatility, but also tend to have a higher degree of roll yield.

As a result the short term indices tend to be used as a tool for taking short-term directional views, whilst the mid-term indices tend to be used as diversification tools.

Please note that negative roll yields could adversely affect the value of an index and, accordingly, decrease any payment investors might receive at maturity or upon redemption of an investment in a product linked to such an index.

HOW dO I INVEST IN IMPlIEd VOlATIlITy?

There are several ways of investing in implied volatility, but below is a brief summary of some common strategies for gaining exposure:

Option strategies: some sophisticated investors may be able to implement various option strategies to extract the exact implied volatility required. however, this is not cost effective or practical other than for the more sophisticated institutional investors.

Futures contracts: managed futures eliminate the operational burden of managing an options strategy, but are best suited for institutional investors with the resources to meet investment minimums and manage derivatives contracts.

Volatility funds: some hedge funds implement various futures or options strategies. however, some of the funds may not be regulated in the relevant jurisdiction and may not be appropriate for a less sophisticated investor.

Exchange traded products: A range of exchange traded volatility products are available. These are often in the form of notes or certificates. They provide an effective and easy to use investment, although the investor may be exposed to the issuer’s credit risk.

You should not invest in any volatility related investment

unless you understand the risks involved of such investments

(taking independent professional advice as you deem

appropriate), and you are capable of assuming such risks.

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Barclays has issued iPath

®

Exchange Traded Notes (ETNs) designed to provide investors with a new way to access this difficult- to-reach market. iPath

®

ETNs provide investors with convenient access to the returns of key implied volatility indices (less an investor fee), and may be one of the most convenient and cost effective means yet of gaining exposure. Please consult your financial adviser before considering an investment in iPath

®

ETNs.

An investment in iPath

®

ETNs involves risks, including possible loss of principal. in addition, iPath

®

ETNs do not pay any coupon.

For a description of the main risks, see “The Basics of iPath ETNs” and the “Risk Factors” in the applicable prospectus.

Please refer to www.iPathETN.eu

iPATH

®

EXCHANGE TrAdEd NOTES (ETNs)

iPATH

®

AlTErNATIVE ETNs

tickersymbol annual

fee* isin

iPath

®

VsTOXX

®

short -Term Futures™ ETN VsXX GY / VsXX lN VsXX im

0.89%

0.89%

dE000Bc2KTT9 dE000Bc2KZY6

iPath

®

VsTOXX

®

mid -Term Futures™ ETN VsXY GY / VsXY lN VsXY im

0.89%

0.89%

dE000Bc2KYE1

dE000Bc2K050

iPath

®

s&P 500 ViX short -Term Futures™ ETN VXis GY / VXis lN 0.89% dE000Bc1c7Q6

iPath

®

s&P 500 ViX mid -Term Futures™ ETN VXim GY / VXim lN 0.89% dE000Bc1c7R4

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subsequent formal agreement which will be set out in binding transaction documents and which is subject to internal approvals.

This dOcUmENT dOEs NOT ANd cANNOT disclOsE All POssiBlE RisKs RElATiNG TO ThE PROdUcT. Before investing, you must satisfy yourself that you fully understand the Product and the risks of investing in it.

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Barclays is not responsible for the accuracy or completeness of information stated to be obtained or derived from third party sources or statistical services.

if you on-sell any Product described herein, you will comply with all applicable regulations, and to the extent required you will fully disclose any fees or commissions received or paid by you in connection with such Product.

YOU ARE REsPONsiBlE FOR cOmPlYiNG WiTh ANY APPlicABlE lAWs ANd REGUlATiONs iF YOU OFFER, sEll, REsEll OR dEliVER ThE PROdUcT OR disTRiBUTE ANY OFFERiNG mATERiAl RElATiNG TO sUch PROdUcT TO ThE PUBlic iN ANY JURisdicTiON.

The EURO sTOXX 50

®

index, EURO sTOXX 50

®

Volatility index (the

“VsTOXX index”) and the EURO sTOXX 50

®

Volatility short-Term Futures Total Return™ index and the trademarks used in the index name are the intellectual property of sTOXX limited, Zurich, switzerland and/or its licensors. The indices are used under license from sTOXX. The securities based on the index are in no way sponsored, endorsed, sold or promoted by sTOXX and/or its licensors and neither sTOXX nor its licensors shall have any liability with respect thereto.

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®

”, “s&P

®

” “Gsci

®

”, “s&P Gsci

®

”, “s&P Gsci

®

index”, “s&P Gsci

®

index Total Return” and “s&P Gsci

®

commodity index” are trademarks or service marks of The mcGraw- hill companies, inc and have been licensed for use by Barclays Bank Plc in connection with the securities.

The s&P Gsci

®

index, the s&P Gsci

®

index Total Return, the s&P Gsci

®

Energy index Total Return, and s&P Gsci

®

commodity index are not owned, endorsed, or approved by or associated with Goldman sachs & co. or its affiliated companies. The securities are not sponsored, endorsed, sold or promoted by standard & Poor’s, a division of the mcGraw-hill companies, inc. or any of its affiliates (“standard & Poor’s). standard & Poor’s does not make any representation or warranty, express or implied, to the owners of the securities or any member of the public regarding the advisability of investing in securities generally or in the securities particularly or the ability of the s&P Gsci

®

index or any of its subindices to track general commodity market performance.

“standard & Poor’s

®

”, “s&P

®

”, “s&P 500

®

”, “standard & Poor’s 500™”,

“s&P 500 ViX short -Term Futures™” and “s&P 500 ViX mid - Term Futures™” are trademarks of standard & Poor’s, a division of The mcGraw- hill companies, inc. and have been licensed for use by Barclays. “ViX

®

” is a registered trademark of the chicago Board Options Exchange, incorporated and has been licensed for use by s&P. The securities are not sponsored, endorsed, sold or promoted by standard & Poor’s or cBOE and standard & Poor’s and cBOE make no representation regarding the advisability of investing in the securities.

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No part of this document may be reproduced, distributed or transmitted without Barclays written permission.

FINd yOUr iPATH www.ipathETN.eu

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References

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