I made the next cool graph concluding week. (Well , I recollect it's cool):
The dark trouble is the VIX volatility index. You tin terminate recollect of it equally a marketplace forecast of volatility over the adjacent month. It starts at most 25 , reflecting a 25% per yr criterion divergence of stock returns. In the fiscal crisis , it shoots upward to 80%. Yes , 80% annualized criterion deviation. Then it tails dorsum in ane lawsuit again amongst roughly other jump inward early on 2010. (The VIX tracks realized volatility almost perfectly inward this episode , hence it's non most volatility gamble premiums.)
The bluish trouble is the cumulated supply on the Fama-French full stock marketplace index. (Data from Ken French's website.) If you lot had a dollar inward the marketplace inward Jan 2008 , it shows you lot the per centum gain or loss through time. (The grade of the S&P500 shows almost precisely the same pattern.) That's also pretty dramatic: you lot 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 amongst higher volatility , but it's non frequently that you lot reckon such a strike correlation.
What produce nosotros brand of it? It seems to revive the thought that hateful returns together with volatility are related. If volatility goes upward , together with hence hateful returns must larn upward likewise , hence that the average investor keeps belongings the marketplace portfolio. The solely way for hateful returns to larn upward is for the cost to decline. You tin terminate almost blame the autumn inward prices on the ascent inward volatility.
The challenge is to larn the numbers to add together up. The criterion portfolio allotment dominion says
Variance is volatility squared , hence if volatility goes from xx to fourscore , the denominator rises past times a component of 80^2/20^2= 16! If you lot convey all your coin inward stocks , part = 1 , nosotros bespeak the hateful also to ascent past times a component of 16; say from 6% to nearly 100%. Did participants expression the entire 50% stock marketplace spend upward to last reversed inward half dozen months? I've written most time-varying expected returns , but fifty-fifty for me a marketplace gamble premium of +100% seems similar a lot.
I recollect the answer is , this is the incorrect equation. It's fourth dimension to larn serious most Merton portfolio theory for long-lived investors. The existent (Merton) portfolio theory adds to the concluding equation
So , something most this term must last screaming "get in" to counteract the concluding equation's advice to "get out." Why produce people attention most volatility risk? ("aversion") Why does this term vary strongly over time?
Something inward this lawsuit seems to last crying to explicate "state variable risk" inward an intuitive way , but doing hence is simply out of my reach. (I've been puzzling most this for a piece , reckon p. 1082 of "Discount Rates". )
Of course of written report , volatility is non the ultimate "state variable ," together with agreement the drive of stock prices volition eventually way nosotros bespeak to dig deeper to underlying events.
Context: I was discussing ii dainty papers at the NBER property pricing meetings: "Volatility , the Macroeconomy together with Asset Prices , by Ravi Bansal , Dana Kiku , Ivan Shaliastovich , together with Amir Yaron , and "An Intertemporal CAPM amongst Stochastic Volatility" past times John Y. Campbell , Stefano Giglio , Christopher Polk , together with Robert Turley. Both papers explore time-varying volatility together with essay to answer this puzzle. (Google for latest versions of the papers.)
Cambpbell et. al. also debate that the value number (higher returns for value stocks than increase stocks) is explained past times value stock's vogue to movement amongst 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 dainty correlation betwixt the VIX together with the earnings/price ratio. In plough , the earnings/price ratio is ane of the best supply forecsaters. So , conditional hateful together with conditional variance of returns produce movement together.
That's dainty , equally it sometimes seems that volatility together with hateful supply wander off inward dissimilar directions , inward response to dissimilar soil variables , together with at dissimilar frequencies. Influenza A virus subtype H5N1 united persuasion of the ii moments is essential.
But don't larn likewise exited. The graph for certain does non document a constant Sharpe ratio , or fifty-fifty a constant hateful to variance ratio. The net yield corresponds roughly 1 to 1 ("roughly" way betwixt 1 to 1 together with 1 to 3) amongst one-year expected returns , hence you're seeing expected returns vary roughly from 4 to seven percent. The VIX is moving orders of maginitude more. So one-year Sharpe ratios together with mean/variance ratios are notwithstanding moving a lot over time! But possibly nosotros tin terminate coalesce the soil variables somewhat , together with honor mutual factors inward conditional hateful together with variance.
The dark trouble is the VIX volatility index. You tin terminate recollect of it equally a marketplace forecast of volatility over the adjacent month. It starts at most 25 , reflecting a 25% per yr criterion divergence of stock returns. In the fiscal crisis , it shoots upward to 80%. Yes , 80% annualized criterion deviation. Then it tails dorsum in ane lawsuit again amongst roughly other jump inward early on 2010. (The VIX tracks realized volatility almost perfectly inward this episode , hence it's non most volatility gamble premiums.)
The bluish trouble is the cumulated supply on the Fama-French full stock marketplace index. (Data from Ken French's website.) If you lot had a dollar inward the marketplace inward Jan 2008 , it shows you lot the per centum gain or loss through time. (The grade of the S&P500 shows almost precisely the same pattern.) That's also pretty dramatic: you lot 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 amongst higher volatility , but it's non frequently that you lot reckon such a strike correlation.
What produce nosotros brand of it? It seems to revive the thought that hateful returns together with volatility are related. If volatility goes upward , together with hence hateful returns must larn upward likewise , hence that the average investor keeps belongings the marketplace portfolio. The solely way for hateful returns to larn upward is for the cost to decline. You tin terminate almost blame the autumn inward prices on the ascent inward volatility.
The challenge is to larn the numbers to add together up. The criterion portfolio allotment dominion says
part inward risky assets = 1/(risk aversion) x hateful supply / variance of return
Variance is volatility squared , hence if volatility goes from xx to fourscore , the denominator rises past times a component of 80^2/20^2= 16! If you lot convey all your coin inward stocks , part = 1 , nosotros bespeak the hateful also to ascent past times a component of 16; say from 6% to nearly 100%. Did participants expression the entire 50% stock marketplace spend upward to last reversed inward half dozen months? I've written most time-varying expected returns , but fifty-fifty for me a marketplace gamble premium of +100% seems similar a lot.
I recollect the answer is , this is the incorrect equation. It's fourth dimension to larn serious most Merton portfolio theory for long-lived investors. The existent (Merton) portfolio theory adds to the concluding equation
... + (aversion to volatility risk) x (covariance of supply amongst changes inward volatility)
So , something most this term must last screaming "get in" to counteract the concluding equation's advice to "get out." Why produce people attention most volatility risk? ("aversion") Why does this term vary strongly over time?
Something inward this lawsuit seems to last crying to explicate "state variable risk" inward an intuitive way , but doing hence is simply out of my reach. (I've been puzzling most this for a piece , reckon p. 1082 of "Discount Rates". )
Of course of written report , volatility is non the ultimate "state variable ," together with agreement the drive of stock prices volition eventually way nosotros bespeak to dig deeper to underlying events.
Context: I was discussing ii dainty papers at the NBER property pricing meetings: "Volatility , the Macroeconomy together with Asset Prices , by Ravi Bansal , Dana Kiku , Ivan Shaliastovich , together with Amir Yaron , and "An Intertemporal CAPM amongst Stochastic Volatility" past times John Y. Campbell , Stefano Giglio , Christopher Polk , together with Robert Turley. Both papers explore time-varying volatility together with essay to answer this puzzle. (Google for latest versions of the papers.)
Cambpbell et. al. also debate that the value number (higher returns for value stocks than increase stocks) is explained past times value stock's vogue to movement amongst 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 dainty , equally it sometimes seems that volatility together with hateful supply wander off inward dissimilar directions , inward response to dissimilar soil variables , together with at dissimilar frequencies. Influenza A virus subtype H5N1 united persuasion of the ii moments is essential.
But don't larn likewise exited. The graph for certain does non document a constant Sharpe ratio , or fifty-fifty a constant hateful to variance ratio. The net yield corresponds roughly 1 to 1 ("roughly" way betwixt 1 to 1 together with 1 to 3) amongst one-year expected returns , hence you're seeing expected returns vary roughly from 4 to seven percent. The VIX is moving orders of maginitude more. So one-year Sharpe ratios together with mean/variance ratios are notwithstanding moving a lot over time! But possibly nosotros tin terminate coalesce the soil variables somewhat , together with honor mutual factors inward conditional hateful together with variance.
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