Tag Info

9

I'm not sure about the "CAPM formula" that you are referring to. I assume you are referring to the estimated coefficient of a regression of a security on a market portfolio. That is to say $$\beta_{security,market} = \frac{\sigma_{security,market}}{\sigma^2_{market}}$$ The idiosyncratic risk is the portion of risk unexplained ...

7

I found this paper: Conditional value-at-risk for general loss distributions by Rockafellar and Uraysev http://dx.doi.org/10.1016/S0378-4266(02)00271-6 which says CVaR is coherent for general loss distributions, including discrete distributions. I think that I was confused by other authors who were also confused with the definitions of CVaR. In particular, ...

6

Each shop will differ - there is no widely used, unified framework shared across firms. Competitive advantages vary across shops, which ultimately reflect the biases/characteristics of the particular shop. Some will be far more mathematically sophisticated/inclined than others. Some maintain strong aversion to quantiative techniques such as risk models. ...

6

$VaR^\alpha$ is not a coherent risk measure because it fails sub-additivity (a coherent risk measure is monotonic, sub-additive, positive homogenous, and translation invariant). The expectation operator $E[\cdot]$ is linear, so it meets sub-additivity, as well as the other three properties, so $CVaR$ is a coherent risk measure.

5

Step 1: Get your data from SQL into R -> http://www.r-bloggers.com/?s=SQL Step 2: Run your analysis/optimizations like -> http://www.r-bloggers.com/portfolio-optimization-in-r-part-1/ or http://blog.streeteye.com/blog/2012/01/portfolio-optimization-and-efficient-frontiers-in-r/ or via RMetrics: ...

5

I know you're really looking for some empirical work on this topic, but I think the following theoretical paper puts your question into proper perspective.* Risk-Based Asset Allocation: A New Answer to an Old Question by Wai Lee, JPM 2011. Overall, he finds that supposedly risk-based approaches to portfolio construction are really making implicit ...

4

Conditional VaR (CVaR), which is also called Expected Shortfall, is a coherent risk measure (although being derived from a non-coherent one, namely VaR). See this paper: Expected Shortfall: a natural coherent alternative to Value at Risk from Carlo Acerbi and Dirk Tasche http://www.bis.org/bcbs/ca/acertasc.pdf EDIT: I just saw that you emphasized ...

4

"Factor loading" is a somewhat ambiguous phrase -- it could refer to the factors in a linear model (e.g. the beta in CAPM or extended linear stock models), the factors of principal component analysis, etc. If you could provide a reference to the exact example/paper it would be clearer. In credit, however, a likely interpretation is the loadings of different ...

4

They are not mutually exclusive. PCA and clustering are similar but used for different purposes. You could use PCA to whittle down 10 risk factors to say 4 uncorrelated factors, and you could combine securities with different FACTORS into different clusters with offsetting returns and variance characteristics. However, when you say you want to derive risk ...

4

Great question. We would expect 3rd party risk providers to have specialized expertise (robust regression techniques, factor research, data cleansing etc.). We might grant them these advantages but still find weakness in the product design. Let's start off with the different uses of risk models and the procedure or metric which is maximized to solve for ...

4

Autocorrelation of returns can be used as a proxy measure for liquidity of the asset. The degree of serial correlation in an asset’s returns can be viewed as a proxy for the magnitude of the frictions, and illiquidity is one of the most common forms of such frictions. A strongly liquid asset should reveal no serial autocorrelation. You can perhaps build ...

4

Most of the credit risk models are some derivative of survival models. Cox Proportional Hazard is one of the early and more popular models, Kaplan-Meier and Logrank tests are others you may have heard of. There are a few ways to go from here. The simplest is to model the sample as binomial with one population as current and the other as in default. A ...

4

I would use the identity that Total Variance = Systematic Variance + Unsystematic Variance. Therefore, you can calculate systematic variance via: Systematic Risk = beta * std(x), so , Systematic Variance = (Systematic Risk)^2, and then you can rearrange the identity above to get: Unsystematic Variance = Total Variance - Systematic Variance, or if you want ...

3

There are a lot of code in Eric Zivots recent class in computational finance. http://spark-public.s3.amazonaws.com/compfinance/R%20code/portfolio.r http://spark-public.s3.amazonaws.com/compfinance/R%20code/testport.r http://spark-public.s3.amazonaws.com/compfinance/R%20code/rollingPortfolios.r Also, you can google some slides in his class where he ...

3

No specific history. I'm not aware who introduced this measure initially. Most probably it came up as an example in the research papers on coherent risk measure. All names make sense to some extent: Expected shortfall - as it's an expectation of losses Conditional Value at Risk - as it can be written as $E[X |X >VaR_α(X)]$, i.e. conditional expectation ...

3

First of all, usually these models are heavily adapted to a specific country (even for Europe), real estate class (housing, commercial) and market (secondary, primary). In general I would say it's very hard to directly apply standard quantitative tools (like MC) from finance for real estate market. The models I've seen were not heavily quantitative. The ...

3

Danielsson and Macrae suggest that portfolio optimization should be based on simple models. I interpret that to mean using something like Ledoit-Wolf (as opposed to most commercial models). In that case doing it yourself is not at all laborious assuming you have return data. A link to Danielsson and Macrae (worth reading if you haven't seen it) is in ...

3

A simple top-down shortcut calculation : Set annualized alpha = compounded alpha = 1 + a1 + a2 + a1*a2 + ... = $\Pi$ (1 + $\alpha_t$) Set annualized return from factors = compounded factor return = $\Pi$ (1 + $factorReturn_t$) Interaction Term contribution is then = Compounded Security Return - Compounded alpha - Compounded factor return Therfore the ...

3

I've played around with both schemes, but not for portfolio optimization. I used PCA on some interest rate models. That turned into a Partial Least Squares scheme, then into some non-linear thing. I wasn't impressed with the results. My Cluster Analysis scheme morphed into a classification scheme, and it turned out that the K-Nearest-Neighbor method ...

2

There is a brief discussion of the two modelling frameworks in An Introduction to Economic Capital by Mohan Bhatia in the "Insurance Risk" chapter. To pull a quote from the "Solvency II versus Basel II" section of that chapter: Like the regulatory approach to internal models in Basel II, Solvency II aims to bring the internal modelling approaches ...

2

I recommend the book The Basel II Risk Parameters. This book is primarily a collection of articles on the development, validation and stress testing of the risk parameters. The good thing about this book is that it provides an overview of the methodologies used which should be easy to follow for an experienced credit risk professional. However, it does not ...

2

Couple points for your consideration: At the time of order execution: You are most likely a liquidity taker and thus are rendered a service by those that provide liquidity and you compete for taking liquidity with other takers in the market. As such you need to have a firm grasp at the market impact of your order. Liquidity can be extremely dynamic even ...

2

I have also seen (in rough decreasing importance order): Mean excess loss, Tail conditional expectation and the variant C.T.E., Tail mean, Mean shortfall... AVaR doesn't seem as common as the other three you mentioned. Acerbi&Tasche 2002 discuss the difference between CVaR and ES. In practice there's little mention on reasons for each choice and ...

2

as vanguard2k points out the prolem is dealt with e.g. in Scaling portfolio volatility and calculating risk contributions in the presence of serial cross-correlations and references therein. It turns out that correlations are lowered while lag one cross-correlations increase. E.g. you can probably see a correlation of Japan today to US yesterday due to the ...

2

This can for example be seen in modern portfolio theory (Harry Markowitz, William Sharpe) As an example consider a two asset portfolio with a full investment constraint ($w_1+w_2=1$) so we can write the proportion in asset 1 as $w_1=w$ and in asset 2 as $1-w$ The expected portfolio return $E[R_p]=wE[R_1]+(1-w)E[R_2]$ And variance $\sigma_p^2 = ... 1 For corporate credit portfolios, sector, rating, and maturity are the usual suspects that go into the credit portion of risk model structure, which usually also have interest rates and liquidity pieces. This book is slightly outdated but will give you a good general introduction. 1 Your idea of using the empirical (historical) distribution makes the most sense for risk management. For one thing, it ensures you are working with real-world probabilities, whereas obtaining a distribution from an option pricing model (say by fitting Heston to the VIX options) would put you in risk-neutral probability space. For another, the common ... 1 I am not confident that I understand specifically what you are asking, but I hope this helps: What are theoretical approaches to model and answer this question? This question is rather broad. I will say that in comparing a random collection of purchases and sales of securities, with only the time between the transactions as varying among different ... 1 First you need to define what you need a risk measure for. It is usually to take a decision, so you have an operational criterion that defines your risk. You should go back at this point and see what is the impact of a change of distribution on it. Just say for instance that you need a risk measure to take decisions according to a Sharpe ratio and define it ... 1 There is a relationship:$ \log \delta^{-1} = \frac{\sqrt{Var[r(t)]}}{\sqrt{p(1-p)}}$Which relates the jump size to the volatility of short rate and risk neutral jump probability. The vol of short rate is chosen to be const in basic model, could be time-varying, but makes things complicated. To solve for$\delta\$ you do need the vol of short rate given ...

Only top voted, non community-wiki answers of a minimum length are eligible