Price As Well As Volatility Inward The Peachy Crash
I made the next cool graph terminal week. (Well, I retrieve it's cool):
The dark job is the VIX volatility index. You tin retrieve of it every bit a marketplace forecast of volatility over the adjacent month. It starts at well-nigh 25, reflecting a 25% per twelvemonth measure departure of stock returns. In the fiscal crisis, it shoots upwards to 80%. Yes, 80% annualized measure deviation. Then it tails dorsum ane time again alongside to a greater extent than or less other trammel inward early on 2010. (The VIX tracks realized volatility almost perfectly inward this episode, thence it's non well-nigh volatility endangerment premiums.)
The bluish job is the cumulated supply on the Fama-French full stock marketplace index. (Data from Ken French's website.) If y'all had a dollar inward the marketplace inward Jan 2008, it shows y'all the pct gain or loss through time. (The grade of the S&P500 shows almost precisely the same pattern.) That's also pretty dramatic: y'all lose one-half your coin past times March 2009, earlier the marketplace recovers.
The negative correlation betwixt these ii lines is striking. Yes, we've known for a long fourth dimension that lower prices are associated alongside higher volatility, but it's non ofttimes that y'all reckon such a hitting correlation.
What create nosotros brand of it? It seems to revive the thought that hateful returns as well as volatility are related. If volatility goes up, as well as thence hateful returns must larn upwards too, thence that the average investor keeps asset the marketplace portfolio. The entirely way for hateful returns to larn upwards is for the cost to decline. You tin almost blame the autumn inward prices on the ascension inward volatility.
The challenge is to larn the numbers to add together up. The measure portfolio allotment dominion says
Variance is volatility squared, thence if volatility goes from twenty to 80, the denominator rises past times a element of 80^2/20^2= 16! If y'all convey all your coin inward stocks, part = 1, nosotros require the hateful also to ascension past times a element of 16; say from 6% to nearly 100%. Did participants await the entire 50% stock marketplace refuse to live on reversed inward half dozen months? I've written well-nigh time-varying expected returns, but fifty-fifty for me a marketplace endangerment premium of +100% seems similar a lot.
I retrieve the response is, this is the incorrect equation. It's fourth dimension to larn serious well-nigh Merton portfolio theory for long-lived investors. The existent (Merton) portfolio theory adds to the terminal equation
So, something well-nigh this term must live on screaming "get in" to counteract the terminal equation's advice to "get out." Why create people attention well-nigh volatility risk? ("aversion") Why does this term vary strongly over time?
Something inward this lawsuit seems to live on crying to explicate "state variable risk" inward an intuitive way, but doing thence is only out of my reach. (I've been puzzling well-nigh this for a while, reckon p. 1082 of "Discount Rates". )
Of course, volatility is non the ultimate "state variable," as well as agreement the crusade of stock prices volition eventually agency nosotros require to dig deeper to underlying events.
Context: I was discussing ii overnice papers at the NBER asset pricing meetings: "Volatility, the Macroeconomy as well as Asset Prices, by Ravi Bansal, Dana Kiku, Ivan Shaliastovich, as well as Amir Yaron, and "An Intertemporal CAPM alongside Stochastic Volatility" past times John Y. Campbell, Stefano Giglio, Christopher Polk, as well as Robert Turley. Both papers explore time-varying volatility as well as endeavor to response this puzzle. (Google for latest versions of the papers.)
Cambpbell et. al. also debate that the value final result (higher returns for value stocks than increase stocks) is explained past times value stock's style to motility alongside changes inward volatility. That's why I included the value stock cumulative supply inward the graph.
Update
Pedro Santa-Clara sent this graph:
It shows a overnice correlation betwixt the VIX as well as the earnings/price ratio. In turn, the earnings/price ratio is ane of the best supply forecsaters. So, conditional hateful as well as conditional variance of returns create motility together.
That's nice, every bit it sometimes seems that volatility as well as hateful supply wander off inward unlike directions, inward response to unlike acre variables, as well as at unlike frequencies. H5N1 united persuasion of the ii moments is essential.
But don't larn also exited. The graph for sure does non document a constant Sharpe ratio, or fifty-fifty a constant hateful to variance ratio. The earnings yield corresponds roughly 1 to 1 ("roughly" agency betwixt 1 to 1 as well as 1 to 3) alongside one-year expected returns, thence you're seeing expected returns vary roughly from four to vii percent. The VIX is moving orders of maginitude more. So one-year Sharpe ratios as well as mean/variance ratios are nonetheless moving a lot over time! But mayhap nosotros tin coalesce the acre variables somewhat, as well as notice mutual factors inward conditional hateful as well as variance.
The dark job is the VIX volatility index. You tin retrieve of it every bit a marketplace forecast of volatility over the adjacent month. It starts at well-nigh 25, reflecting a 25% per twelvemonth measure departure of stock returns. In the fiscal crisis, it shoots upwards to 80%. Yes, 80% annualized measure deviation. Then it tails dorsum ane time again alongside to a greater extent than or less other trammel inward early on 2010. (The VIX tracks realized volatility almost perfectly inward this episode, thence it's non well-nigh volatility endangerment premiums.)
The bluish job is the cumulated supply on the Fama-French full stock marketplace index. (Data from Ken French's website.) If y'all had a dollar inward the marketplace inward Jan 2008, it shows y'all the pct gain or loss through time. (The grade of the S&P500 shows almost precisely the same pattern.) That's also pretty dramatic: y'all lose one-half your coin past times March 2009, earlier the marketplace recovers.
The negative correlation betwixt these ii lines is striking. Yes, we've known for a long fourth dimension that lower prices are associated alongside higher volatility, but it's non ofttimes that y'all reckon such a hitting correlation.
What create nosotros brand of it? It seems to revive the thought that hateful returns as well as volatility are related. If volatility goes up, as well as thence hateful returns must larn upwards too, thence that the average investor keeps asset the marketplace portfolio. The entirely way for hateful returns to larn upwards is for the cost to decline. You tin almost blame the autumn inward prices on the ascension inward volatility.
The challenge is to larn the numbers to add together up. The measure portfolio allotment dominion says
part inward risky assets = 1/(risk aversion) x hateful supply / variance of return
Variance is volatility squared, thence if volatility goes from twenty to 80, the denominator rises past times a element of 80^2/20^2= 16! If y'all convey all your coin inward stocks, part = 1, nosotros require the hateful also to ascension past times a element of 16; say from 6% to nearly 100%. Did participants await the entire 50% stock marketplace refuse to live on reversed inward half dozen months? I've written well-nigh time-varying expected returns, but fifty-fifty for me a marketplace endangerment premium of +100% seems similar a lot.
I retrieve the response is, this is the incorrect equation. It's fourth dimension to larn serious well-nigh Merton portfolio theory for long-lived investors. The existent (Merton) portfolio theory adds to the terminal equation
... + (aversion to volatility risk) x (covariance of supply alongside changes inward volatility)
So, something well-nigh this term must live on screaming "get in" to counteract the terminal equation's advice to "get out." Why create people attention well-nigh volatility risk? ("aversion") Why does this term vary strongly over time?
Something inward this lawsuit seems to live on crying to explicate "state variable risk" inward an intuitive way, but doing thence is only out of my reach. (I've been puzzling well-nigh this for a while, reckon p. 1082 of "Discount Rates". )
Of course, volatility is non the ultimate "state variable," as well as agreement the crusade of stock prices volition eventually agency nosotros require to dig deeper to underlying events.
Context: I was discussing ii overnice papers at the NBER asset pricing meetings: "Volatility, the Macroeconomy as well as Asset Prices, by Ravi Bansal, Dana Kiku, Ivan Shaliastovich, as well as Amir Yaron, and "An Intertemporal CAPM alongside Stochastic Volatility" past times John Y. Campbell, Stefano Giglio, Christopher Polk, as well as Robert Turley. Both papers explore time-varying volatility as well as endeavor to response this puzzle. (Google for latest versions of the papers.)
Cambpbell et. al. also debate that the value final result (higher returns for value stocks than increase stocks) is explained past times value stock's style to motility alongside changes inward volatility. That's why I included the value stock cumulative supply inward the graph.
Update
Pedro Santa-Clara sent this graph:
That's nice, every bit it sometimes seems that volatility as well as hateful supply wander off inward unlike directions, inward response to unlike acre variables, as well as at unlike frequencies. H5N1 united persuasion of the ii moments is essential.
But don't larn also exited. The graph for sure does non document a constant Sharpe ratio, or fifty-fifty a constant hateful to variance ratio. The earnings yield corresponds roughly 1 to 1 ("roughly" agency betwixt 1 to 1 as well as 1 to 3) alongside one-year expected returns, thence you're seeing expected returns vary roughly from four to vii percent. The VIX is moving orders of maginitude more. So one-year Sharpe ratios as well as mean/variance ratios are nonetheless moving a lot over time! But mayhap nosotros tin coalesce the acre variables somewhat, as well as notice mutual factors inward conditional hateful as well as variance.
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