By Toby White, CFA, FSADrake University

Finance / Actuarial ScienceIowa Actuarial Education Day

March 27, 2012

OutlineIntroduction to Volatility: Motivations and

Definitions

Volatility v. Return RelationshipsExtreme Volatility in U.S. Equity MarketsWhy has Volatility Increased in Recent Years?Factors Affecting Volatility LevelsUsing Derivatives to Manage Volatility Risk

Conclusion: Predicting Future Volatility

Intro: Why Care about Volatility?Shifts in Volatility may make a diversified

portfolio ‘less diversified.’Arbitrageurs may get it wrong when volatility

becomes too high.Abnormal event-related returns are strongly

impacted by volatility.Both stock and option prices are associated

with changes in volatility.

Definitions of VolatilityHistorical Volatility – based on the s.d. of

continuously compounded stock returns.Idiosyncratic Volatility – based on the s.d. of

residuals from a factor model for returns.Implied Volatility – the volatility level that

would produce an observed option price.VIX (“fear index”) – measures the market’s

volatility expectation over the next 30 days.

Volatility v. Return RelationshipStocks with large sensitivities to market

volatility have lower average returns.Periods of high volatility tend to occur in

bear markets, and periods of low volatility occur in bull markets.

Return dispersion is countercyclical, but is related positively to subsequent market volatility, and tends to lead unemployment.

Explanation for RelationshipIt is no surprise that high-risk stocks do

relatively well in ‘up’ markets, but relatively poorly in ‘down’ markets.

However, the negative effects from ‘down markets’ often dominate the positive effects from ‘up markets.’

This might indicate an inverse relationship between risk (historical volatility) + return.

Can CAPM be salvaged?CAPM states that there is direct relationship

between risk (beta) + return.However, when investor sentiment (and

volatility levels) are high, speculative, high-risk stocks do worse than bond-like stocks.

Empirical data supports a quadratic CAPM rather than a linear model, where returns do rise with risk up to some point, but then fall when volatility is excessive.

Extreme Volatility EventsVolatility Spikes tend to occur during times

of low or insufficient liquidity:

October 19, 1987 (portfolio insurance)

August (2nd half), 1998 (Russian financial crisis)

September 11, 2001 (WTC / markets closed for 4 days)

May 6, 2010 (Flash Crash)

Extreme Volatility EpisodesThe Great DepressionThe Internet BubbleThe Recent Financial Crisis

In 2008: the daily DJIA changes were at least 1% on 134/253 (53%) of all trading days

This compares to a 15.6% avg. (2004-2007)European Debt Crisis / U.S. Treasury

Downgrade (3rd Quarter 2011)

Fatter Tails than ExpectedRisk Modelers were unprepared for 2008,

since volatility had not been this high (and for so long) since the mid-to-late 1930s.

Tail events can be caused by a currency crisis, sovereign bond defaults, large-scale disasters, or other hard-to-predict events.

Tails are fatter now than they were 15-20 years ago due to increased systemic risk.

Discrete Jumps in Stock PricesDiscrete jumps often occur when reported

earnings are different than expectations.Institutional investors now react quite swiftly

to such news, and in similar fashion.Thus, stock price change distributions have

higher kurtosis/fatter tails (v. normal), especially among lightly traded stocks.

Recently, the magnitude of price changes has exceeded what fundamentals dictate.

Why has Volatility Increased?Firm-Specific Factors:

Newly listed firms are younger, riskier, and need a less proven track record (to be listed)

The number of stocks on U.S. exchanges has doubled since 1980, but the average size of the newly listed firms is smaller

Increased Volatility of Firm Fundamentals like EPS and ROE (levels declining, variability up)

More Financial Leverage and Innovation

Why has Volatility Increased?Macro-level Factors:

Increased Equity Weights among institutional investors, who invest in block trades, and get information + form opinions in similar circles

Increasing Prominence of NASDAQ marketTrend of Breaking up ConglomeratesProduct Markets getting more competitiveMore Incentives for Executives to assume risk

and to pursue higher growth rates

Other Factors Affecting VolatilityVolatility tends to be higher for small firms.The variability of interest rates, bond yields

and the amplitude of the business cycle can affect stock and option volatilities.

Behavioral effects (e.g. – ‘follow the herd’ mentality) can impact volatility, as investors tend to overreact to the arrival of new information.

Firms with high market-to-book ratios and firms with high growth strategies tend to have higher firm-specific volatility levels.

Long v. Short Volatility ViewsLong positions are like buying insurance (i.e.

– buying calls or puts) – they mostly lose money but can provide huge payoffs.

Short positions are like selling insurance (i.e. – selling calls or puts) – they mostly gain money but have potentially high loss.

Between 2004-2007, a strong preference existed for ‘short volatility positions’, which contributed to pain in the financial crisis.

Collared StockThis position is created when a long stock

holding is supplemented with a long put and a short call with a higher strike price.

Premium = S + P1 – C2 (where K2 > K1)This manages volatility risk by locking in a

certain volatility level (i.e. – the maximum profit and maximum loss is limited).

Straddle (Purchased / Written)A purchased straddle consists of buying a call

and buying a put with the same strike.Premium = C2 + P2

If one has a ‘long volatility’ view, buying a straddle can exploit this – the more the stock moves in either direction, the better.

If one has a ‘short volatility’ view, writing a straddle can create premium revenues – the less the stock moves, the better.

StrangleSimilar to a Straddle, except now, both the

call and put are out-of-the-money options, so as to reduce initial premium outlay.

Premium = C3 + P1 (K1 < K2 < K3)Compared to a straddle, profits will be lower

(when the stock price moves a lot), but the maximum loss will also be lower (of stock prices do not move at all).

Butterfly SpreadThis position is created when a written

straddle is supplemented with a purchased strangle, thus reducing downside risk.

Premium = (– C2 – P2) + (C3 + P1)This creates a situation where losses are

small (but limited) whenever stock prices move a lot, but gains can still occur if stock prices remain close to K2.

Conclusion: Predicting VolatilityIt is easier to predict future volatility (given past

volatility) than it is to predict future returns (given past returns).

This is because there is considerable serial correlation in volatility measures.

However, volatility levels tend to occur in episodes, so that periods of high volatility are often followed by periods of low volatility, and vice-versa.

In 2012, only 5/58 (8.6%) of all trading days so far have seen the DJIA move by at least 1%, and 4 of the 5 days were ‘up’ days. The Dow is now near its 50-mo. high.

Thank youIowa Actuaries ClubPricewaterhouseCoopersKelley Insurance CenterDrake University

Tom RootLingxiao Li

QUESTIONS?