Volatility Effects

Reward goes with risk, and volatility represents risk. Therefore, volatility means reward; investors/traders get paid for riding roller coasters. Right? These blog entries relate to volatility effects.

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Lessons Learned from Attacking CAPM

How diverse are the beliefs of experts on the Capital Asset Pricing Model (CAPM)? In his November paper entitled “CAPM: The Model and 233 Comments about It”, Pablo Fernandez reproduces 52 largely disagreeing and 181 largely agreeing comments solicited from professors, finance professionals and Ph.D. students regarding his prior paper entitled “CAPM: an Absurd Model” (summarized in “Forget CAPM Beta?”). The range of beliefs in the comments is extreme, from

“I was shocked at how horrible your paper is. It is without a doubt the worst excuse for an academic study I have ever seen (and believe me that is saying a lot).”


“I totally agree with the absurdity of CAPM model.”

After reflecting on the body of comments, he concludes that: Keep Reading

VXX and XIV Returns by Day of the Week

Do the returns of iPath S&P 500 VIX Short-term Futures ETN (VXX) and VelocityShares Daily Inverse VIX Short-term ETN (XIV) vary systematically across days of the week? To investigate we calculate returns by day of the week for:

  1. VXX over its available sample period.
  2. VXX over its available sample period excluding the day before and the day after holidays (to remove any distorting effects of expected but unusual market closures).
  3. XIV over its available sample period.
  4. VXX over the available sample period of XIV.

Using daily close-to-close returns for VXX during February 2009 through November 2014 and for XIV during December 2010 through November 2014, we find that: Keep Reading

Smart Beta Interactions with Tax-loss Harvesting

Are gains from tax-loss harvesting, the systematic taking of capital losses to offset capital gains, additive to or subtractive from premiums from portfolio tilts toward common factors such as value, size, momentum and volatility (smart beta)? In their October 2014 paper entitled “Factor Tilts after Tax”, Lisa Goldberg and Ran Leshem look at the effects on portfolio performance of combining factor tilts and tax-loss harvesting. They call the incremental return from tax-loss harvesting tax alpha, which (while investor-specific) is typically in the range 1%-2% per year for wealthy investors holding broad capitalization-weighted portfolios. They test six long-only factor tilts based on Barra equity factor models: (1) value (high earnings yield and book-to-market ratio); (2) momentum (high recent past return); (3) value/momentum; (4) small/value; (5) quality (value stocks with low earnings variability, leverage and volatility); and, (6) minimum volatility/value (low volatility with diversification constraint and value tilt). Their overall benchmark is the MSCI All Country World Index (ACWI). Their tax alpha benchmark derives from a strategy that harvests losses in a capitalization-weighted portfolio (no factor tilts) without deviating far from the overall benchmark. The rebalancing interval is monthly for all portfolios. Using monthly returns for stocks in the benchmark index during January 1999 through December 2013, they find that: Keep Reading

Stock Beta Meaningless?

Is the market beta of a stock stable across measurement frequencies and measurement intervals? In their October 2014 paper entitled “Which Is the Right ‘Market Beta’?: 1,385 US Companies and 147 Betas/Company in a Single Date”, Jose Paulo Carelli, Pablo Fernandez, Isabel Fernandez Acín and Alberto Ortiz present calculations of 147 betas relative to the S&P 500 Index for each of the S&P 1500 stocks with at least five years of return data on March 31, 2014. They calculate different betas based on monthly, weekly or daily returns over past intervals of one to five years. They then look at the dispersion of each stock’s beta and beta ranking across calculation methods (see the chart below for an example). In assessing dispersion, they focus on the difference between maximum and minimum values by stock. Using daily, weekly and monthly returns for 1,385 stocks and the S&P 500 Index during April 2009 through March 2014, they find that: Keep Reading

Stock Market Returns after Extreme Up and Down Days

What happens after extreme up days and extreme down days for the U.S. stock market? To investigate, we define extreme up and extreme down days as those with daily returns at least X standard deviations above or below the mean (average) return over the past four years (the U.S. political cycle, about 1,000 trading days). Focusing on three standard deviations, we then look at average returns the next day (close-to-close and open-to-close), the next five trading days, the next 21 trading days (about a month) and the next 63 trading days (about a quarter). We also look at correlations between extreme day returns and future returns. Using daily closes for the S&P 500 Index since January 1950 and daily opens since January 1962, both through mid-October 2014, we find that: Keep Reading

Expected Volatility of Stock Market Volatility as a Predictor

S&P 500 Index options data imply expected S&P 500 Index volatility (VIX) over the next month. In turn, VIX futures options data imply expected volatility of VIX (VVIX) over the next month. Does VVIX predict stock index option and VIX option returns? In their September 2014 paper entitled “Volatility-of-Volatility Risk”, Darien Huang and Ivan Shaliastovich investigate whether VVIX represents a time-varying risk affecting: (1) S&P 500 Index option returns above and beyond the risk represented by VIX; and (2) VIX futures option returns. They measure risk effects via returns on S&P 500 Index options hedged daily by shorting the S&P 500 Index and VIX futures options hedged daily by shorting VIX futures. Using monthly S&P 500 Index returns, VIX futures returns, VIX, VVIX, S&P 500 Index option prices and VIX option prices during February 2006 through June 2013, they find that: Keep Reading

Comparing Ivy 5 Allocation Strategy Variations

A subscriber requested comparison of four variations of an “Ivy 5″ asset class allocation strategy, as follows:

  1. Ivy 5 EW: Assign equal weight (EW), meaning 20%, to each of the five positions and rebalance annually.
  2. Ivy 5 EW + SMA10: Same as Ivy 5 EW, but take to cash any position for which the asset is below its 10-month simple moving average (SMA10).
  3. Ivy 5 Volatility Cap: Allocate to each position a percentage up to 20% such that the position has an expected annualized volatility of no more than 10% based on daily volatility over the past month, recalculated monthly. If under 20%, allocate the balance of the position to cash.
  4. Ivy 5 Volatility Cap + SMA10: Same as Ivy 5 Volatility Cap, but take completely to cash any position for which the asset is below its SMA10.

The subscriber proposed the following five asset class proxies for testing:

iShares 7-10 Year Treasury Bond (IEF)
SPDR S&P 500 (SPY)
iShares MSCI EAFE Index (EFA)
PowerShares DB Commodity Index Tracking (DBC)

The DBC series in combination with the SMA10 rule are limiting with respect to sample start date and the first return calculations. Using daily and monthly dividend-adjusted closing prices for the five asset class proxies and the yield on 13-week U.S. Treasury bills (T-bills) as a proxy for return on cash during February 2006 through August 2014 (103 months), we find that: Keep Reading

Timing VIX Futures with the Futures-Spot Ratio

Is the return on CBOE S&P 500 Volatility Index (VIX) futures predictable? In his preliminary paper entitled “The Expected Return of Fear”, Ing-Haw Cheng investigates whether the relationship between VIX futures prices and VIX level predicts the return on VIX futures. He focuses on monthly returns to a continuously-invested position in the nearest available VIX futures contract. He considers several different explanations for the behavior of VIX futures prices. Using VIX futures daily settlement prices during March 2004 through July 2014 (125 months), he finds that: Keep Reading

Global Low-volatility Stock Portfolio Performance Predictors

Are there times when investors should avoid low-volatility stocks? In their August 2014 paper entitled “Tactical Timing of Low Volatility Equity Strategies”, Sanne De Boer and James Norman investigate which factors predict the performance of low-volatility stocks relative to a capitalization-weighted index globally since 1980. They focus on two concerns: (1) will low-volatility stocks perform poorly when they are relatively expensive compared to the rest of the market; and, (2) will low-volatility stocks, which tend to pay high dividends, underperform when interest rates rise. Their low-volatility portfolio is a capitalization-weighted collection of country sectors processed quarterly in three steps designed to achieve a balance of low risk and sufficient diversification. They do not account for quarterly portfolio reformation frictions in return calculations. Using weekly data for all country sectors included in the MSCI Developed Markets Index during January 1975 through March 2014, they find that: Keep Reading

Harvesting Volatility Generated by Naive Investors

What is the best way to harvest asset mispricings derived from aggregate overreaction/underreaction by naive investors? In his July 2014 presentation package entitled “Betting On ‘Dumb Volatility’ with ‘Smart Beta'”, Claude Erb examines strategies for exploiting the “dumb volatility” arguably generated by naive investors who buy high and sell low, temporarily driving prices materially above and below fair values. These strategies generally involve periodically rebalancing portfolios to equal weights or some version of fair value weights (smart beta). Using monthly returns for a variety of indexes and funds during December 2004 through June 2014 (since the advent of smart beta research), he finds that: Keep Reading

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