Volatility Asset Class

Prima Capital. | 303.573.7315 | 303.573.7362 fax | www.primacapital.com

VO L AT I L I T Y A S A N A S S E T C L A S S

By Cliff Stanton CFA, Chief Investment Officer, Prima Capital

The Potential of the VIX as a Hedging Tool and the Shortcomings of VIX Exchange Traded Notes

“…the only thing we have to fear is fear itself.” – Franklin D. Roosevelt

That famous phrase was uttered in the midst of a banking crisis in 1933; a situation not entirely unlike the one

investors faced in 2008. A recounting of the events of 2008 would be highly redundant at this point, but the

experience of 2008 allows us to twist President Roosevelt’s statement into an interesting question. If the only

thing to fear is fear itself, can fear in turn be a good defense against fear? Enter the VIX.

The Chicago Board Options Exchange (CBOE) Market Volatility Index, or VIX, was conceived in 1993 by

Professor Robert E. Whaley of Duke University to provide a benchmark of expected short term volatility.

According to the CBOE,

“VIX measures 30-day expected volatility of the S&P 500 Index. The components of VIX are near-

and next-term put and call options, usually in the first and second S&P 500 Index (SPX) contract

months.”

As we will demonstrate, the value of volatility itself lies in the fact that it is negatively correlated to the returns

of the equity market, and becomes increasingly so as market declines accelerate. As a result, long exposure to

volatility could provide increasing levels of portfolio protection exactly when investors are most in need of such

protection. Another way to think about this is that because most investors are net long equities, they are

implicitly short volatility, and therefore hedging that exposure may be prudent.

The theoretical knowledge and empirical understanding of implied volatility, as defined by the VIX, was put

into play in 2004 when VIX futures began trading, followed in 2006 by the creation of options on the VIX1.

More recently, in 2009 Barclays Capital launched exchange traded notes that track VIX futures contracts2. The

development of exchange traded notes (“ETNs”) on the VIX has special relevance for the private wealth

management industry. While institutional investors regularly utilize derivative instruments, the ability of

financial advisors to use futures, options or swaps is often greatly limited, if not precluded, when working with

high net worth individuals. The reasons vary, but include a host of operational considerations, a lack of

familiarity with derivatives at the advisor level, and/or reluctance of individual investors to allocate capital to

1 Prior to 2004 options strategies and variance swaps had been utilized to capture exposure to volatility.

2 Symbols: VXX and VXZ

Volatility as an Asset Class /17

Prima Capital | 303.573.7315 | 303.573.7362 fax | www.primacapital.com

“exotic” structures. The availability of an exchange traded note solves these problems, although as we will see,

not without introducing other issues.

Our evaluation of these ETNs and the volatility index on which they are based attempted to answer the

following questions:

1. What is the nature of equity volatility?

2. What are the characteristics of the VIX and does it adequately capture true volatility?

3. Are the VIX futures and related ETNs in turn able to harness the qualities of the VIX, or is something lost

in translation?

4. What would an allocation to volatility as an asset class bring to a diversified portfolio?

But before we begin to address these questions, we must delineate the primary difference between volatility and

other asset classes. Unlike a share of stock, a bond, or an ounce of gold, volatility has no intrinsic value. As

such, over time the expected return to this mean reverting measure will be equal to the cost of attaining

exposure. In other words, long term exposure to volatility is simply a cost, a drag on portfolio performance. For

the truly long term investor, who isn’t negatively impacted by short term volatility, there is no reason to bear

such a cost, but for the rest of us, volatility may prove useful.

What is the nature of equity volatility?

The following chart demonstrates a few interesting features of volatility. For one, the downside is truncated.

Unlike other assets, volatility cannot go to zero, and over the past three decades, it has spent little time below

10%. In addition, volatility is not normally distributed; it has exceedingly fat tails, as indicated by high kurtosis

(i.e. peakedness of the distribution). Finally, it is itself highly volatile and positively skewed, making long

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S&P 500: Actual 30‐Day Annualized Volatility(source: S&P)

Mean = 13.2%

Median = 11.4%Maximum = 90.8%

Minimum = 2.7%Skewness = 3.9Kurtosis = 26.1Volatility = 124.9% (annualized)



exposure to volatility quite beneficial to investors.

As indicated, the prior chart shows actual 30-day volatility, selected in order to correspond to 30-day implied

volatility as measured by the VIX. Additionally, a review of the return distribution of the S&P 500 is

informative. From the chart below we see that daily returns for the S&P 500 are also non-normal, that is, fat

tails exist (even if the scale prevents us from seeing them). But unlike 30-day volatility, this distribution is

negatively skewed. Further, the maximum daily loss has been roughly twice the size of the maximum daily gain;

something to keep in mind as we take a look at the VIX in the next section of this paper.

What are the characteristics of the VIX and does it adequately capture true volatility?

It is impossible to invest in volatility directly, and therefore, the prior analysis of the volatility of the S&P 500 is

helpful as a backdrop, but not particularly useful in practice. The VIX gets us one step closer to investing in

volatility, but in and of itself the VIX suffers from the same problem, one cannot invest directly in the VIX; it is

not a tradable index. Before exploring products that attempt to generate returns dependent on the VIX, we need

to determine whether the VIX itself does a good job of capturing the positive hedging characteristics of actual

volatility.

To do that, we should consider the transmission mechanism by which equity volatility impacts the VIX. Whaley

(2008) and Siegel (2007) both touch on this mechanism. And that is, when equity markets are falling, the

demand for both out-of-the-money and at-the-money put options increases, driving up the price of those

options, and concurrently, implied volatility. Siegel also points out that arbitrageurs who sell puts, must also sell

stocks in order to hedge their position and remain delta neutral. The more puts they sell, the more stocks they

sell, which may exacerbate a selloff and increase the negative correlation between implied volatility and equities.

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S&P 500: Daily % Change Jan. 1950 ‐ Feb. 2010(source: Standard & Poors)

Maximum = 11.6%

Minimum = ‐20.5%Skewness = ‐0.7

Kurtosis = 22.8 Volatility = 15.3% (annualized)



The following charts show the closing level and the daily return distribution, respectively, of the VIX going back

to 1990. As is the case with actual volatility, the series is mean reverting, the downside is truncated, the

distribution is non-normal and it is positively skewed.

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CBOE Spot VIX: Daily % Change Jan. 1990 ‐ Feb. 2010

Maximum = 64.2% Minimum = ‐25.9%Skewness = 1.22Kurtosis = 7.54 Volatility = 95.9% (annualized)

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CBOE Volatility Index (VIX)(Daily Closing Levels)

Mean = 20.3Median = 18.8Maximum = 80.9Minimum = 9.3



While considering the return distribution of the daily changes of the VIX, recall the return profile of the S&P

500 that was presented earlier3. The best single day for the S&P 500 going back to 1950 was +11.6%, and its

worst one day loss, suffered in October of 1987 on Black Monday, was -20.5%. While the worst one day loss

on the VIX is similar in magnitude at -25.9%, the best single day for the VIX was +64.2%. The return profile

for the VIX is indeed asymmetrical, and that asymmetry can be demonstrated by comparing 30-day returns on

the S&P 500 to 30-day returns on the VIX.

The slope of the line is steepest when the S&P 500 is deep in the red, but flattens out as equities post positive

returns. What does this tell us? When it is most needed, that is, when the equity markets are falling

dramatically, the delta, or rate of change on the VIX is the greatest. This type of profile allows for a small

commitment of capital to provide meaningful protection to a portfolio, which we will explore later.

But let’s continue with the question of whether the VIX captures actual volatility in a meaningful way. As

option traders are acutely aware, implied volatility is almost always higher than actual subsequent volatility, up

until the moment when actual volatility spikes. It is for this reason that selling naked options has been likened to

picking up nickels in front of a steam roller – it works and it’s easy right up until the moment when you get run

over. Small win…small win…small win…big loss, is not an attractive return profile for most investors.

3 Please note that the time periods of these two return distributions differ, as the S&P 500 data goes back

to 1950 whereas the VIX data begins in 1990.

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VIX M

onthly % Chg

S&P 500 Monthly % Chg

Monthly % Change in the S&P 500 vs. VIX Jan. 1990 ‐ Feb. 2010



While implied volatility is almost always higher than actual subsequent 30-day volatility (see above), the

correlation between the two series is high at 0.73. But if we are considering using VIX exposure as a hedge, we

aren’t particularly concerned with the ability of the VIX to forecast future volatility (and that’s not a question

that a simple correlation analysis can answer in any event). What we are concerned with is both the correlation

and sensitivity between the daily changes in the S&P 500 and the daily changes in the VIX. By regressing the

VIX on the price changes of the S&P 500 we calculated the following statistics4 on both a daily and monthly

basis.

S&P

500vs. Correlation

Bull

Correlation

Bear

Correlation Beta

Bull

Beta

Bear

Beta

Up

Capture

Down

Capture

VIX

(daily) -0.7 -0.4 -0.6 -3.5 -2.2 -3.9 -388% -434%

VIX

(monthly) -0.6 -0.2 -0.5 -2.6 -0.9 -3.0 -215% -361%

4 The time period over which the calculations were made is from January 1990 through February 2010.

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S&P 500: Implied vs. Actual Subsequent Volatility(source: S&P, CBOE and Prima Capital)

VIX Actual 30‐Day Vol



As you can see, these statistics confirm what we’ve already been discussing, i.e. that the return profile to the VIX

is quite different in up markets than it is in down markets. The correlation statistics become more negative

during down markets and the beta statistics increase, and the down market capture ratios are greater than the

up market capture ratios. These relationships are exactly what we’d like to see in a hedging vehicle.

There is one final point that we’d like to make regarding the VIX and its mean reverting ways. Our regression

analysis revealed that the strongest linkage between the starting point on the VIX and subsequent returns was

around the five year mark. Meaning that if an investor was able to invest in spot VIX, and held that position for

five years, the return to that investor would be largely dictated by the beginning level of volatility. This can be

thought of in similar terms to the relationship between the starting valuation level for the equity market and

subsequent equity returns. To demonstrate this point, we constructed the following table, indicating the level of

the VIX at that time a hypothetical investment would have been made, and the subsequent 5-year return on that

investment.

SPX VIX Closing Level at Time of

Investment

Average Subsequent 5-Yr Annualized

Return

<11.96 16.0%

11.96-16.96 10.9%

16.96-21.96 0.3%

21.96-26.96 -7.9%

26.96-31.96 -10.5%

>31.96 -11.0%

The takeaway from this is that the payoff to volatility is greatest when it is in effect cheapest, that is, when

market participants are complacent and risk seeking. Once the markets are in the midst of a selloff and market

participants are scared stiff, the expected payoff to VIX exposure at that point turns negative. Yet another

instance where being contrarian pays off.



Are the VIX futures and related ETNs in turn able to harness the qualities of the VIX, or is something lost in

translation?

Thus far we’ve been able to make the case that volatility as an asset class has attractive features that could allow

it to be an effective hedge against negative equity outcomes. Further, we’ve shown that while the VIX is

intended to reflect expectations of future near term volatility, it does more than an adequate job of capturing

changes to actual volatility as those changes occur. The question remaining is whether futures based on the

VIX, and in turn the ETNs, will convey similar advantages to investors.

One problem at this point in time is the lack of history on which to make a meaningful analysis. The Barclay’s

ETNs were launched in January of 2009, providing little more than a year of data. Even so, the ETNs are based

on futures contracts and futures have been trading on the VIX since late 2004. As such, we begin with an

analysis of those futures contracts.

Like all futures contracts, a term structure exists for VIX futures. That term structure is typically in contango5

when volatility is stable or low, and moves to backwardation6 when volatility is high. The term structure of the

VIX as of March 31, 2010 is shown below7, a time when volatility was subdued and the futures were in

contango. During such periods, rolling the futures contracts results in a significantly negative “roll yield”.

Specifically, buying higher priced, longer dated futures contracts and selling them at lower prices as they

approach maturity, rolling the proceeds into yet another longer dated futures contract, results in a loss.

5 Contango is a term used in the futures market to describe an upward sloping forward curve.

6 Backwardation is a term used in the futures market to describe a downward sloping forward curve.

7 Source: CBOE

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VIX Futures Term Structure as of March 31, 2010



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VIX Futures Term Structure as of October 15, 2008

However, in times of high volatility, such as that witnessed in October of 2008, the term structure will likely be

in backwardation. As such there will be a positive roll yield earned by investors, as contracts are rolled forward.

This concept of roll yield adds to the story developed earlier about the starting level on the VIX and subsequent

returns, and these two aspects work against one another. In times of high volatility, the roll yield is positive, but

the expected return on the VIX turns negative. In contrast, when volatility is low, the expected return is positive,

but the roll yield is negative, and maintaining such a position becomes expensive.

To explore what that cost might look like over time we considered a hypothetical portfolio consisting of spot

VIX versus a portfolio consisting of VIX futures contracts. Barclays Capital provided an index series

representing a hypothetical VIX futures portfolio managed on the same basis as the iPath S&P 500 VIX Short

Term Futures ETN (ticker: VXX; gross of fees). The following chart shows the value of these two hypothetical

portfolios.



It is at this point that our story, which had been quite promising, starts to fall apart. As a reminder, an investor

cannot invest in spot VIX, so the theoretical portfolio value indicated above is merely a reference against which

we can judge the efficacy of a futures portfolio in capturing the theoretical returns to spot VIX. Having said

that, a constant futures position fails miserably in delivering the returns produced by spot VIX. Over the time

period indicated, the annualized return to spot VIX was almost 17%, whereas the futures portfolio generated

an annualized return of approximately -22%. That differential, almost 40% annualized, is primarily due to the

roll yield. It is also impacted by a difference in the time periods utilized in calculating the two series, as the VIX

reflects implied volatility in the near term and next term options contracts, while the futures on the VIX are

priced off of future expectations for implied volatility. As an example, a 3-month VIX futures contract is

measuring what the expected implied volatility on the S&P 500 Index will be in three months time. This time

discrepancy is the reason that VIX futures exhibit lower volatility than spot VIX.

In defense of the cost of rolling futures contracts, Barclays points out that roll yield can be likened to the theta

(time decay) of put options, and claims that the roll yield is lower than the implied realized premium in put

options. Further, because of the term structure of VIX futures, Barclays offers two different ETNs. The short

term VIX ETN (VXX) is based on the 1 and 2 month futures contracts, whereas the medium term VIX ETN

(VXZ) is based on the 4-7 month futures contracts, both of which are managed with a daily roll methodology.

Because the mid range of the term structure is flatter, roll costs are minimized, and in a low volatility

environment when the roll yield is in contango, investors are better off in VXZ. The downside to VXZ is lower

beta relative to VIX. Barclays calculates that the highest beta of VIX futures relative to actual VIX is in the 1-

month and 2-month contracts, and turns out to be about 0.5 and 0.35, respectively. That beta decreases with

maturity, and so VXX is best when volatility spikes.

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Growth of $100: Spot VIX vs. VIX Futures Portfolio

Hypothetical Futures Portfolio Spot VIX



Due to the issues explored above, the return profile for VXX and VXZ will differ materially from the VIX.

Consider the daily change in the price of VXX relative to the daily change in VIX since inception of the ETNs,

graphed below.

As you can see, the daily differential is typically large, and in fact the average differential is 2.5% on an absolute

basis. Further, as discussed previously, the beta of VXX to VIX is far below 1.0. Our calculation of the beta of

VXX to VIX on a daily basis is 0.47. Even so, VXX is highly correlated to VIX; the correlation between the

daily price changes is around 0.86.

What can we conclude from this analysis? It is clear that while the VIX itself has attractive characteristics that

make it a highly effective hedging tool, the futures contracts, and ETNs in turn, are far less compelling for

investors wishing to take a buy and hold approach to what is effectively portfolio insurance. Holding the

position long term not only results in a direct cost of 89 basis points for the ETNs, but more importantly, a

materially negative roll cost.

Our first thought as to how to deal with this issue was to come up with a simple trading strategy based on the

level of the VIX when a position was initiated. For example, one could take a full position in VXX or VXZ

when volatility was near 1-standard deviation below the mean, virtually ensuring a positive expected return to

volatility given its mean reverting tendencies. That position could be pared as VIX reached its mean, and then

exited at 1-standard deviation above the mean, at a time when expected returns are negative. However, as

discussed earlier, the term structure of the VIX results in the highest roll costs during periods of low volatility,

and while volatility is mean reverting, it can take years for that to occur, all the while placing a significant drag

on an investor’s portfolio. More intricate trading models based on much shorter time frames could work,

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VXX iPath ETN vs. VIX: Daily Price Change Differential



although that detracts significantly from the use of these types of products within the private wealth

management industry. Alternatively, positions could be added whenever an advisor believes that the likelihood

of a volatility spike is increasing, such as around major macro events, and that would be highly effective, but

unfortunately, not all major market crises have an observable ramp-up ex-ante. Advisors wishing to utilize

these ETNs are necessarily going to be injecting significant timing risk into their use. Ultimately, we do not

believe that they are appropriate for buy and hold investors, even though they do react quite nicely when truly

needed.

What would an allocation to volatility as an asset class bring to a diversified portfolio?

While we’ve concluded that an investment in the VIX through ETNs is too costly to be practical as a strategic

allocation to a portfolio, we decided to explore what an investment in spot VIX could add to a portfolio, if that

could be achieved. Ours is an ever changing industry and more optimal ways of harnessing the VIX may come

along.

Every asset added to a portfolio should serve at least one of two purposes, return enhancement or risk

reduction. Those descriptors are relative, meaning that the role that an asset plays is relative to another asset.

Strategies employing hedging techniques more often than not provide risk reduction to an equity heavy

portfolio, but typically provide return enhancement as well to a fixed income heavy portfolio. Many strategies

employed by hedge funds (and increasingly hedge fund like mutual funds) attempt to reduce systematic risk (e.g.

equity risk, credit risk, interest rate risk) within their own portfolio, but do not directly offset those very same

risks contained elsewhere in an investor’s portfolio. For example, an equity market neutral fund may not

introduce any equity beta into a portfolio, but it doesn’t offset the equity beta that comes from a large cap

growth manager in the portfolio. In order to protect a portfolio against large losses in times of market stress, an

investor needs a direct hedge, i.e. an asset that is negatively correlated to other assets in the portfolio. Volatility,

as mentioned previously, is just such an asset.

We constructed a series of efficient frontiers using forward looking return and risk expectations. Our goal is to

be as realistic as possible about the risk and return characteristics of this hypothetical VIX position, and we

understand that exposure to any asset comes with a cost. In this case, for simplicity sake, we assumed that the

return expectation to the VIX was -0.89%, which mirrors the explicit cost to the VIX ETNs (but importantly,

ignores the roll cost described earlier). Even with a negative expected return, inclusion of the VIX improves

efficiency. What you can see below is that an efficient frontier constructed solely with a basic set of asset classes,

i.e. domestic stocks, bonds and cash, can be improved by adding a VIX position. That improved upon efficient

frontier pushes out even farther when constructed using a complete asset class set (which includes a variety of

assets from domestic stocks, to emerging market debt to bank loans, in addition to the VIX). You can also see

that a small allocation to the VIX can have a big impact. The portfolio labeled BG&I, which is a balanced

growth and income portfolio, has an expected return of 6.85% with expected volatility of 10.5%. A 3.5%

allocation to the VIX at the expense of the equity exposure (i.e. BG&I + 3.5% VIX) decreases expected return

by 30 basis points, but decreases risk by 216 basis points; a valuable tradeoff.



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Expected Return

Risk

The Efficient Frontier(Calculated with 5‐Year Forward Looking Estimates)

Complete Asset Class Set Basic Asset Class Set + VIX Naïve Portfolios

Basic Asset Class Set BG&I BG&I + 3.5% VIX

50% Equity / 40% Bonds / 10% VIX

55% Equity / 40% Bonds / 5% VIX

60% Equity / 40% Bonds

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End of Horizon Value at Risk (5%) Within Horizon Value at Risk (5%)

$109,381

$146,935

$95,282

$134,280

$66,376

$101,587

Value at Risk for a $1 Million Portfolio Over a 1‐Year Horizon

60/40 BG&I BG&I + 3.5% VIX

We also looked at what inclusion of the VIX would mean to Value at Risk8 and loss probability, comparing a

basic 60/40 portfolio with the same BG&I and BG&I + 3.5% VIX portfolios identified on the efficient frontier.

8 VaR – The maximum likely loss over the indicated time period at the 95% confidence level.



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Probability of a Loss of 5% or Greater Over a 1‐Year Horizon

60/40 BG&I BG&I + 3.5% VIX

Again, inclusion of the VIX, with only a small allocation of capital, has a noticeable impact. What is most

striking is the decrease in the probability of a loss of 5% or greater over a 1-year horizon (on a continuous

basis). A 60/40 portfolio has a 46% chance of a loss of 5% or more, whereas the BG&I + 3.5% VIX has only

a 28% chance of such a loss.

Conclusion

Volatility as an asset class is compelling. It is negatively correlated to the returns to the equity markets, and

becomes increasingly so as market declines accelerate. As a result, long exposure to volatility could provide

increasing levels of portfolio protection exactly when investors are most in need of such protection. The

convexity provided by volatility means that a relatively small allocation of capital can provide meaningful

protection.

However, as we demonstrated, the benefit to volatility erodes as we transfer its characteristics from actual

volatility, to implied volatility, to futures on implied volatility, and finally, to ETNs based on the futures on

implied volatility. In the end, what appeared to be a powerful diversifying tool for strategic asset allocators,

ends up being appropriate only to express shorter term views on volatility.

What other options does an investor have? The use of dedicated short managers can certainly be effective in

mitigating total equity risk, and many hedge fund of fund managers do just that. However, the return profile

tends to be more linear with the return to the equity market. That is, a 4% decline in the S&P 500 would likely

result in a return of 4% to a dedicated short manager with at least enough skill to offset fees. But the

asymmetric return profile of the VIX cannot be matched by short managers.



Another possibility is of course equity options. But Szado (2009) demonstrated that VIX calls provide a more

efficient means of diversification than S&P puts. Further, Jacob and Rasiel (2009) made the following

observations about buying options:

“Options have exposure not just to volatility, but also to market direction. To maintain directional

neutrality requires frequent updating of a delta hedge position on the underlying asset.”

“Options are a wasting asset…Therefore, options cannot be included as an asset in a buy-and-hold

portfolio.”

Finally, what about hedge funds in general? We advocate the inclusion of hedging strategies in a portfolio, to

complement long-only equity and fixed income managers. However, as mentioned previously, while many

strategies employed by hedge funds attempt to reduce systematic risk (e.g. equity risk, credit risk, interest rate

risk) within their own portfolios, that risk reduction does not directly offset those very same risks contained

elsewhere in an investor’s portfolio. Equity beta coming from the large cap growth manager is not offset by the

hedged equity position within a convertible arbitrage strategy.

Given our findings regarding the VIX ETNs, as well as the limitations of other potential investments as true

hedges against market crises, we are forced to conclude that the search for the holy grail of hedging for

strategically allocated portfolios must continue. In the absence of a perfect hedging vehicle, investors should

continue to rely on tried and true measures of risk mitigation. First and foremost, know what you are investing

in and why; thoroughly evaluate the risk and return characteristics of each investment, and properly balance

those characteristics in order to achieve the desired results. Be realistic in forecasting return expectations, and

recognize that risk management isn’t simply about the probability of being wrong, but the magnitude of the loss

if you are wrong. Second, diversify broadly. Go beyond the naïve approach, which can be greatly improved

upon through proper portfolio construction in which asset allocation and manager selection are utilized as

separate and distinct tools to solve different problems. Investors utilizing these principals have been well served

over time (2008 notwithstanding), and will likely reap the rewards of doing so in the future.



References

Barclays Capital. 2009. “Trading Equity Volatility with S&P 500 VIX Short Term & Mid-Term Futures

Indices.” Institutional Investor Presentation

Darnell, Max. 2009. “What Volatility Tells Us about Diversification and Risk Management.” CFA Institute

Conference Proceeding: Asset and Risk Allocation (Philadelphia 2009)

Deshpande, Maneesh and Rohit Bhatia. 2010. “Understanding VIX ETNs.” Barclays Capital Conference Call

Presentation

Evans, Mark and Raymond Chan. 2010. “Managing the Left Tail: A Framework for Market Risk

Management.” Goldman Sachs Asset Management Conference Call Presentation

Goldstein, Daniel G. and Nassim Nicholas Taleb. 2007. “We Don't Quite Know What We are Talking About

When We Talk About Volatility.” The Journal of Portfolio Management, vol. 33, no. 4: 84-86.

Jacob, Jai and Emma Rasiel, PhD. 2009. “Index Volatility Futures in Asset Allocation: A Hedging

Framework.” http://www.lazardnet.com/lam/global/investment_research.html

Kritzman, Mark. 2009. “Managing Assets in Turbulent Markets.” CFA Institute Conference Proceeding: Asset

Allocation for Private Clients (Atlanta 2008)

Lustig, Michael. 2007. “Using Derivatives to Enhance Returns and Manage Risk.” CFA Institute Conference

Proceeding: Fixed Income Management (San Francisco 2006)

Moran, Matthew T. 2004. “Taking a Ride on the Volatile Side.” The Journal of Indexes, October/November

2004

Moran, Matthew T. and Srikant Dash. 2007. "VIX Futures and Options: Pricing and Using Volatility Products

to Manage Downside Risk and Improve Efficiency in Equity Portfolios." The Journal of Trading, Summer

2007: 96-105.

Nossman, Marcus and Anders Wilhelmsson. 2009. “Is the VIX Futures Market Able to Predict the VIX Index?

A Test of the Expectation Hypothesis.” The Journal of Alternative Investments, Fall 2009: 54-67.

Siegel, Jeremy J. 2007. Stocks for the Long Run. 4th Edition. New York: McGraw-Hill

Szado, Edward. 2009. “VIX Futures and Options – A Case Study of Portfolio Diversification During the 2008

Financial Crisis.” The Journal of Alternative Investments, Fall 2009: 68 - 85.

Whaley, Robert E. 2008. “Understanding VIX.” Available at SSRN: http://ssrn.com/abstract=1296743



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