## Volatility Tracker: Skewed Returns

Volatility Tracker for the week of August 24, 2009

‘Reflation’ is the name of the conceptual cure for the cognitive dissonance experienced by any rational observer of this market. Equities returned to short-term overbought status this week [4] and options are relatively fairly priced [6]. At 16%, the 21-day realized volatility of the S&P 500 is as low as it’s been since the financial crisis began, though it would be folly to try to call a bottom in volatility, or a top in price.

I haven’t discussed the daily return distributions very much in the past, but they are a helpful way to get an alternative look at recent price action. Notice that, over the last three months, daily returns for the S&P 500 have not been normally distributed. [9] In statistical jargon, we can say that the distribution is leptokurtic (kurtosis = 0.46) – indicating a greater number of values around the mean – and negatively skewed, since the left tail is longer and more of the distribution is located on the right side. For an example of a population with slightly negative kurtosis, look at the recent distribution of returns for USO, the oil ETF. [18]

The long view on oil volatility I discussed last week has held up nicely so far. At Monday’s open, the USO Aug 35 straddle was about $1.70, suggesting about a 5% move in the ETF by expiration; on Friday it closed up 6.11% on the week, and the straddle closed at about $3.20, for an 88% return on risk. While the purpose of this letter is explicitly not to make investment recommendations, outcomes like this one highlight the value that volatility-based trades can bring to a portfolio.

CFE delisted VXD futures on August 13, so I have removed that chart from [7].

1. Comment. Highlights items of note in the data below along with our short-term volatility bias and any trading theses. The Expected Daily Move table displays the de-annualized price and percentage change in each underlying asset as implied by its volatility index, within one standard deviation. The Forward Bias table displays my bias for the movement of the price and implied volatility of several assets for the coming week.

2. Weekly Change. Tracks the weekly percentage change in the assets listed and in their implied volatility indexes.

3. Implied Volatility Indexes. A one year chart of the implied volatility indexes for the S&P 500, gold, oil, and USD/EUR. Indexes for the Nasdaq 100 and Russell 2000 are omitted because of their tight correlation with VIX.

4. S&P 500 Price and Bollinger Bands. Tracks daily closing prices in SPX with an overlay of one and two standard deviation 50-day bands.

5. S&P 500 Implied and Realized Volatility. Tracks the 21-, 60-, and 90-day realized (or “historical”) volatility of the index and the21-day lagged CBOE Implied Volatility Index (”VIX”). Realized volatility is displayed as the annualized standard deviation of lognormal returns over the period specified, and may be thought of as a backward-looking measurement of price behavior. Implied volatility is the annualized standard deviation of returns implied by option prices, and may be thought of as a forward-looking measurement of expected price behavior.

6. S&P 500 Implied/Realized Volatility Ratio. Tracks the ratio of 21-day lagged implied volatility (IV) to 21-day realized volatility (RV). This ratio asks how well IV from one month ago predicted the RV over the next 21 trading days (roughly, 30 calendar days). When IV correctly anticipates RV over the period, the ratio will hover near 1; we regard the area near 0.9 –1.2 as normal, given the persistence of a volatility risk premium in equity market derivatives. A ratio less (greater) than 1 indicates that the price behavior of the underlying asset was more (less) volatile than anticipated.

7. Volatility Futures Term Structure. Tracks the Friday closing prices of the Volatility Futures complex (VIX, RVX) for the two weeks prior, along with the spot levels for reference.

8. VIX Premium Ratio. Tracks the ratio of rolling three-month (VXV) to one-month (VIX) implied volatility. Periods in which one-month readings persist at an extreme premium or discount to three-month levels have tended to coincide with major market moves.

9.S&P 500 Daily Return Distribution (3 month). Histogram plotting the frequency of daily percentage returns over the prior 63 trading days.

10. Implied Correlation Index. Reflects the market-capitalization weighted average correlation of the 50 largest components of the S&P 500.

11. Gold Price and Bollinger Bands. Tracks daily closing prices in GLD with an overlay of one and two standard deviation 50-day bands.

12. Gold Implied and Realized Volatility. Tracks the 21-, 60-, and 90-day realized (or “historical”) volatility of the ETF and the 21-day lagged CBOE Gold Volatility Index (”GVZ”).

13. Gold Implied/Realized Volatility Ratio. See #6 above; given the novelty of the VIX-style gold volatility index (GVZ) and the characteristics of the underlying, we do not yet have a range we regard as normal.

14.Gold Daily Return Distribution (3 month). See #9 above.

15-18. Oil charts correspond to 11-14 above.

Sun, Aug 23, 2009 | Jared Woodard

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