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Recent members
Burns Statistics wrote a new blog post titled The scaling of Expected Shortfall
Getting Expected Shortfall given the standard deviation or Value at Risk. Previously There have been a few posts about Value at Risk and Expected Shortfall. Properties of the stable distribution were discussed. Scaling One way of thinking of Expected Shortfall is that it is just some number times the standard deviation, or some other number times the Value at Risk. Those numbers, of course, depend on the distribution that is being assumed. t distribution Figures 1 through 4 show scalings for t distributions with degrees of freedom from 3 to 20. Figure 1: 95% Expected Shortfall relative to...
4 days ago
Burns Statistics wrote a new blog post titled Introduction to stable distributions for finance
A few basics about the stable distribution. Previously “The distribution of financial returns made simple” satirized ideas about the statistical distribution of returns, including the stable distribution. Origin As “A tale of two returns” points out, the log return of a long period of time is the sum of the log returns of the shorter periods within the long period. If: non-overlapping time periods produced statistically independent returns returns over the same time span had the same distribution (IID in textbook lingo), then returns would have a stable distribution. The...
10 days ago
Burns Statistics wrote a new blog post titled Value at Risk and Expected Shortfall, and other upcoming events
Highlighted Value at Risk and Expected Shortfall A two-day course exploring Value at Risk and Expected Shortfall, and their role in risk management. 2013 June 25 & 26, London. Lead by Patrick Burns. Details at the CFP Events site. New Events Thalesians — San Francisco 2013 June 5. Jesse Davis on “Risk Model Imposed Manager-to-Manager Correlation” Details on the Thalesian website. Thalesians — London 2013 June 12 Lajos Gergely Gyurko on “Modelling and measuring slippage”. Details on the Thalesian website. Advanced Statistical Methods in Credit Risk 2013...
16 days ago
Burns Statistics wrote a new blog post titled The low volatility anomaly and CAPM
A look at a paper that explores possible assumption failures of CAPM that would explain the low volatility anomaly. Previously We’ve talked about CAPM before, in particular: 4 and a half myths about beta in finance There has also been substantial talk about low volatility investing. The paper The paper is “Explanations for the Volatility Effect: An Overview Based on the CAPM Assumptions” by David Blitz, Eric Falkenstein and Pim Van Vliet. A quote: One of our findings is that not just one or two, but at least four out of the five CAPM assumptions are involved with the...
17 days ago
Burns Statistics wrote a new blog post titled Value at Risk with exponential smoothing
More accurate than historical, simpler than garch. Previously We’ve discussed exponential smoothing in “Exponential decay models”. The same portfolios were submitted to the same sort of analysis in “A look at historical Value at Risk”. Issue Markets experience volatility clustering. As the previous post makes clear, historical VaR suffers dramatically from this. An alternative is to use garch, the down-side of which is that it adds (some) complexity. A middle ground is to use exponential smoothing: it captures quite a lot of the volatility clustering with a...
23 days ago
Burns Statistics wrote a new blog post titled Implied alpha and minimum variance
Under the covers of strange bedfellows. Previously The idea of implied alpha was introduced in “Implied alpha — almost wordless”. In a comment to that post Jeff noticed that the optimal portfolio given for the example is ever so close to the minimum variance portfolio. That is because there is a problem with the example (though it sort of doesn’t matter). It uses a risk aversion of 2.5 (which would be a risk aversion of 5 in some people’s minds). That is a moderate risk aversion. Except that the variance and the expected returns are scaled to percent. This...
31 days ago
Burns Statistics wrote a new blog post titled US market portrait 2013 week 20
US large cap market returns. Fine print The data are from Yahoo Almost all of the S&P 500 stocks are used (as implied by Wikipedia on 2013 January 5 — see the R commands to scrape the data) The initial post was “Replacing market indices” The R code is in marketportrait_funs.R — you are free to use these functions however you like
33 days ago
Burns Statistics wrote a new blog post titled US market portrait 2013 week 19
US large cap market returns. Fine print The data are from Yahoo Almost all of the S&P 500 stocks are used (as implied by Wikipedia on 2013 January 5 — see the R commands to scrape the data) The initial post was “Replacing market indices” The R code is in marketportrait_funs.R — you are free to use these functions however you like
40 days ago
Burns Statistics wrote a new blog post titled US market portrait 2013 week 18
US large cap market returns. Fine print The data are from Yahoo Almost all of the S&P 500 stocks are used (as implied by Wikipedia on 2013 January 5 — see the R commands to scrape the data) The initial post was “Replacing market indices” The R code is in marketportrait_funs.R — you are free to use these functions however you like
47 days ago
Burns Statistics wrote a new blog post titled Slouching towards simulating investment skill
When investment skill is simulated, it is often presented as if it is obvious how to do it. Maybe I’m wrong, but I don’t think it’s obvious. Previously In “Simple tests of predicted returns” we saw that prediction quality need not look like what you would find in a textbook. For example, there was a case where there was no predictive power on the low values, but good prediction for high values. Data 443 large cap US equities are used. The variance matrix is estimated using the daily returns during 2011 (via a Ledoit-Wolf shrinkage model). Both long-only and...
52 days ago
Burns Statistics wrote a new blog post titled garch and the distribution of returns
Using garch to learn a little about the distribution of returns. Previously There are posts on garch — in particular: A practical introduction to garch modeling The components garch model in the rugarch package garch and long tails There has also been discussion of the distribution of returns, including a satire called “The distribution of financial returns made simple”. Question Volatility clustering affects the distribution of returns — the high volatility periods make the returns look longer tailed than if we take the volatility clustering into account. The...
59 days ago
Burns Statistics wrote a new blog post titled Stock-picking opportunity and the ratio of variabilities
How good is the current opportunity to pick stocks relative to the past? Idea The more stocks act differently from each other relative to how volatile they are, the more opportunity there is to benefit by selecting stocks. This post looks at a particular way of investigating that idea. Data Daily (log) returns of 442 large cap US stocks with histories back to the start of 2004 were used. The ratio Consider a window of returns over a certain period and of a certain universe of assets. We can get a measure of the variability of these returns in two ways: find the standard deviation across...
66 days ago
Burns Statistics wrote a new blog post titled Expected returns of an investment mandate
What to expect from fund managers who follow your investment mandate. You hope that the fund managers that you hire have skill. But markets are noisy so it is hard to tell skill from luck. It is impossible to tell skill from luck if you don’t know what luck looks like. Here we draw pictures of what luck looks like for past periods of time. The technique is to create a large number of portfolios that obey the rules of the mandate but are otherwise random, and then draw the distribution of their returns. Crude example Suppose the mandate is: The universe is the equities in the S&P...
73 days ago
Burns Statistics wrote a new blog post titled Alternative equity indices and random portfolios
A study has come out of Cass Business School that investigates a number of ways of building equity indices. Andrew Clare, Nicholas Motson and Stephen Thomas, of course, include market capitalization weighting. A number of schemes that fall under the name of “smart beta” are also included. They compare the indices not only among themselves but to a cohort of random portfolios. When I say “random portfolio”, I mean that there are constraints to be obeyed. But the only constraints that the random portfolios in the paper obey is that the weights are non-negative and...
76 days ago
Burns Statistics wrote a new blog post titled US market portrait 2013 week 13
US large cap market returns. Fine print The data are from Yahoo Almost all of the S&P 500 stocks are used (as implied by Wikipedia on 2013 January 5 — see the R commands to scrape the data) The initial post was “Replacing market indices” The R code is in marketportrait_funs.R
81 days ago
Burns Statistics wrote a new blog post titled Variability of garch predictions
How variable are garch predictions? Previously There have been several posts on garch, in particular: A practical introduction to garch modeling The components garch model in the rugarch package Both of these posts speak about the two common prediction targets: prediction (of volatility) at the individual times (usually days) term structure prediction — the average volatility from the start to the time in question It will be the latter that is investigated here. Data and models Daily log returns of the S&P 500 are used as the example. The latest data is from 2013 March 14....
95 days ago
Burns Statistics wrote a new blog post titled Upcoming events
Highlighted LondonR is soon — see the “Previously Announced” section. New Events Thirsty Quants 2013 March 21, London. Some thirsty quants will be going for a drink on the 21st of March as of 18.30 at the Lamb Tavern in Leadenhall Market. http://www.lambtavernleadenhall.com/ Rethinking the Economics of Pensions 2013 March 21 & 22 in London. Description and details. CambR 2013 March 25. Andrius Druzinis presenting about interactive visualisations and GUIs with Shiny and Adrian Alexa who will talk about specific problems he (and many others) need to solve in R, code...
98 days ago
Burns Statistics wrote a new blog post titled Predicted correlations and portfolio optimization
What effect do predicted correlations have when optimizing trades? Background A concern about optimization that is not one of “The top 7 portfolio optimization problems” is that correlations spike during a crisis which is when you most want optimization to work. This post looks at a small piece of that question. It wonders if increasing predicted correlations will improve the optimization experience during a crisis (when correlations do rise). Data and portfolios The universe is 443 large cap US stocks. We act as if we are optimizing as of 2008 August 29. 250 days of returns...
107 days ago
Burns Statistics wrote a new blog post titled Portfolio tests of predicted returns
Exploring the quality of predictions using random portfolios and optimization. Previously “Simple tests of predicted returns” showed a few ways to look at expected returns at the asset level. Here we move to the portfolio level. The previous post focused on correlation. Win Vector Blog points out that gauging prediction quality using correlation can be misleading (because correlation picks the best center for each variable but the center will be fixed in prediction). Data and model The universe is 443 large cap US stocks that have data back to the beginning of 2004. The daily...
115 days ago
Burns Statistics wrote a new blog post titled US market portrait 2013 week 7
US large cap market returns. Fine print The data are from Yahoo Almost all of the S&P 500 stocks are used (as implied by Wikipedia on 2013 January 5 — see the R commands to scrape the data) The initial post was “Replacing market indices” The R code is in marketportrait_funs.R
124 days ago
