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29

I would offer the distinctions are i) pure statistical approach, ii) equilibrium based approach, and iii) empirical approach. The statistical approach includes data mining. Its techniques originate in statistics and machine learning. In its extreme there is no a priori theoretical structure imposed on asset returns. Factor structure might be identified thru ...


13

I think you have the correct dichotomy here. Things started in the late 1980s and through the 1990s with analytical approaches particularly to derivative pricing (as in "hey, let's create yet another exotic option we can sell to the buy side"). The risk modelling "fashion" of the 1990s (when regulated entities such as banks needed to beef up reporting) ...


11

Increased volatility (high VIX) signifies more risk. To keep their portfolio in line with their risk preferences, market participants deleverage. Since long positions outweigh short positions in the market as a whole, deleveraging entails a lot of selling and less buying. The relative increase in selling causes downward pressure on stocks.


10

Equity returns have persistent negative skewness and excess kurtosis[1] over longer periods. So yes you're right: a majority of the daily returns is positive and small and a minority of the returns is negative and larger. This can be quite extreme, for example Black Monday. I don't have the data right now but you can get returns on major indices freely. ...


8

Technically, yes, the VIX is a measure of implied volatility. But practically speaking, it is a measure of market uncertainty: when market participants are uncertain of the future, they buy options to protect their positions, driving up option premiums and increasing implied volatility. The broader market hates uncertainty, however, so that same uncertainty ...


6

the Commodity Traders report is the most useful for this, it lets you deduce large and small players on the stock index futures. This is only released weekly by the CFTC Otherwise you can use volume:price divergence and average volume moving average to further deduce whats happening. Finally you can use level 2's to get a feel for the speed of orders and ...


6

VIX is mechanically determined from the price of S&P500 call and put options. So if the demands for S&P500 calls/puts rise, then the prices rise, then the implied vol from these options rises. During a down market there's a lot of demand for portfolio protection. If you're diversified, then S&P500 puts are good protection, so the prices for puts ...


5

The term 'rule of thumb' is ambiguous here. Because I don't think there are any rule of thumb, you just need to do the number crunching. However there are some stable characteristic through time linked to correlation. For instance it is a common fact that the hierarchy of correlation within different market is relatively stable. US equities are less ...


5

So my first answer was off base. For some reason I was thinking first moment (idiosyncratic returns), but he's looking for second moment (idiosyncratic volatility). There is a line of research on the returns to portfolios sorted on idiosyncratic volatility and I was hoping that there were descriptive statistics that said "fraction $\rho$ of stock/portfolio ...


5

I just want to give a qualitative assessment to your question: Volatility of a market is different than the volatility of a stock. Similarly like Copeland and Antikarov (2001) say that "...the volatility of a gold mine is different than the volatility of a gold..." If you want to quantitatively compute the percentage of a stock's volatility affected by ...


5

Richardh is spot on. The price of the VIX option is a weighted sum of put (strikes < forward) and call (strikes > forward) options on the S&P 500. The weights are proportional to 1/strike^2. As the S&P goes down the out of the money puts become more valuable and those have the highest weights. I will leave arguments about the market as a whole to ...


5

By definition, the average investor holds the market portfolio. Risk aversion can be measured as the slope (i.e. ratio of expected returns to volatility) on the efficient frontier. Therefore, the risk aversion of the average investor assuming the S&P500 is the proxy for the market portfolio is the expected returns of the S&P 500 divided by the ...


5

Your question will be very difficult to answer, at least for equities. The best you can probably do in terms of accurate information are research reports from organizations like Tabb. You can look at positioning of players from 13F reports, meaning you can see which players have large positions in a certain equity. You may not be able to discern why, ...


5

Is your question more about approaches taken on the buy side vs. sell side? If so, you may want to read Attilio Meucci's paper, P vs. Q, on this topic. He breaks down the dichotomy as derivatives pricing (the "Q" world), which uses a lot of very sophisticated modeling involving Ito calculus and PDEs, and portfolio management (the "P" world), which makes ...


5

SMM stands for single-month mortality and CPR stands for constant (or conditional) prepayment rate. They're both units of voluntary prepayment rates ($CPR = 1-(1-SMM)^{12}$). They could be based on either estimated or actual prepayments. Where to get actual MBS prepayment data will depend on what type(s) of MBS pools you're modeling (e.g. agency, ...


4

I think there is a result that some generalizations of the Vickrey auction to two sided trading do not have balanced budgets: i.e. require additional incentives from the market maker. It occurs as a consequence of avoiding any participant's price being dependent on their own input. The "Vickrey" approach would be to make someone's price equal to the ...


4

One idea - borrowing from Google's 2nd Price auction model, which uses Vickery, for prioritizing rank of ads on their search page would be to determine a strictly monotonic increasing function $f(*)$, which applied to $u1 = (o1 - r1)$ and $u2 = (o2-r2)$ results in $o1*f(u1) \geq o2*f(u2)$ iff $o1 \geq o2$. The winner in this case would pay: $o2*f(u2) / ...


4

One way of thinking about the problem is with a statistical factor model. Consider the two cases: You have more assets than time points In this case if you accept enough factors, then there is no idiosyncratic risk. But there will be idiosyncratic risk if you restrict the number of factors. You have more time points than assets In this case even if ...


4

Take the CAPM regression (it's not exactly correct, but it's instructional) $$(R_i - R_f) = \alpha_i + \beta_i (R_{mkt} - R_f) + \epsilon_i$$ The author is saying that these days the $(R_{mkt} - R_f)$ term is driving all returns and that the $\alpha_i$ and $\epsilon_i$ terms are not significantly different than zero because all returns are correlated. ...


4

To avoid confusion, this only applies to most equity/index option. In a return distribution, there's a measurement called skewness which measures the asymmetry of upside and downside. Let's define that as 30d Put Premium/ 30d Call Premium. It's already priced in because most of the time, skew > 1. However, if you trade commodities or companies that might ...


4

This is known as a 'crossed' book, the exchange will attempt to uncross the book at the price at which the maximum amount of volume can trade. In your example at the price of 42 there's only 3533 amount of buying quantity, and there are more than enough sellers to cover this. At a price of 40, there's now 3533+425 buying quantity willing to trade, and still ...


3

An Axioma research paper from August 2011, Using Multiple Risk Models for Superior Portfolio Management… A Practice Not Just For Quants, answers exactly your question, I believe. Note the graphs at the top of page 8. They compare their medium-horizon fundamental and statistical factor models from January 2008 to January 2009. At the start of the period, ...


3

Suppose that you have a model of returns, and a representative agent whose form of utility function you have specified right off the bat. This RA can be constructed, under conditions, from a population that is defined to have heterogeneous utility objectives. This is the problem of aggregation, and it's treated in every good asset pricing theory text (e.g. ...


3

The blog post "A slice of S&P 500 skewness history" http://www.portfolioprobe.com/2012/01/16/a-slice-of-sp-500-skewness-history/ has a bit of data on this question. It appears that log returns might have some negative skew, but symmetry is a possibility.


3

Bootvis accurately describes the math - Skew plus Kurtosis. What's interesting is that many of the efficient market theorists (example: Eugene Fama) observed this phenomenon too. I consider two intuitive reasons for this: 1) Behavioral - According to prospect theory, the mental benefit of gaining a dollar is lower than the fear of losing a dollar. This ...


3

As Tal Fishman and chrisaycock said in their comments, you need to have a possible economic gain (or a physical delivery) coming from the underlying (in your example a rock band) that motivates the investor to acquire shares. What you suggest has already been done in France, through the website MyMajorCompany.com where you can buy a "share" of artists ...


3

There are two excellent choices for implementing prediction markets: (1) Use book orders that stand until filled, just as intrade.com does. (2) Use an automated market maker (like Robin Hanson's) that stands ready to make trades. The book orders model is very simple to implement, but can suffer from very wide Bid/Ask spreads. And, it can be tough to bet ...


2

Answering this question is impossible without making many significant assumptions regarding risk preferences, utility functions, a model of returns, etc. One way to measure the risk aversion of the representative investor is to compare the market's expected return to expected volatility. When applied to the allocation decision between equity and fixed ...


2

A proper analysis of whether idiosyncratic returns exist requires a "joint hypothesis" test. In other words, an equilbirum risk factor model must be assumed to test that the intercept across stocks is not statistically different from zero. You can use the GRS statistic to test the joint hypothesis that the idiosyncratic returns are zero. The CAPM test as ...



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