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5

Some of the used heavy-tail distributions are: Log-Cauchy and Log-Gamma Lévy Burr and Weibull Mixed normal Here two papers that cover some of them and others: http://ect-pigorsch.mee.uni-bonn.de/data/research/papers/Financial_Economics,_Fat-tailed_Distributions.pdf http://www.rff.org/RFF/Documents/RFF-DP-11-19-REV.pdf


3

Arithmetic returns allow for easier cross-sectional aggregation and log returns allow for easier time-aggregation. The reason people use log returns (for equities) is that they are approximately invariant and hence easier to work with in estimating distributions. Meucci does better justice in describing invariance here. The basic idea (again, for equities) ...


2

The most common transformations you see for these three variables on credit desks is to compute "returns" on the credit variables. So, rather than taking the straight daily differences $\Delta s_t$ of swap spreads and $\Delta H_t$ of the high yield index (by which I assume here you mean on-the-run CDX HY), practitioners will transform to $\frac{\Delta ...


2

Edited Comments: Sharpe Ratio covers both future and historical time frames (as @Freddy points out). Referencing the "Geometric Return and Portoflio Analysis", for the historical calculation, you want to make as few assumptions as possible (in my opinion). Let $m_i \triangleq$ the monthly return for period $i$ and $r_t \triangleq$ annual return, for ...


1

The answer depends on what model you assume for the underlying. The situation, that the underlying can become negative also occures for interest rate spreads and even for interest rates. Here some people use absolute changes, that is $X_{i} - X_{i-1}$ instead of relative changes $\frac{X_{i} - X_{i-1}}{X_{i-1}}$ or (which is almost the same as relative ...


1

I think you need to exactly define which ratio you are talking about. For example the ex-post Sharpe ratio's components are all well known. You have your realized returns, risk free returns (or whatever other benchmark you define your excess returns against) and realized volatility of returns. For realized asset returns you should not use log returns but ...


1

I am a bit confused about your question in that you say at one point that you want to explain the relationship between credit spreads and equity prices. Is that what you really want to know? Why? I thought you already have empirical evidence that supports the relationship between the two? Or are you after something else? Anyway, I would actually recommend ...


1

It looks like 1 and 2 are different portfolios of companies. 1 is a portfolio of dual-listed companies, and 2 is a portfolio of everything in the "market". Once you have constructed these these portfolios, let's say you put the returns for every time step into a vector, call it r, then the average return would be mean(r). You need some clarification as ...



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