# Tag Info

9

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) ...

6

If you want to learn more about price pressure, you should look after market impact of metaorders, which is a more adequate term. Because of the microstructure (i.e. the mix of orderbboks dynamics, trading rules, participants behaviours and habits, etc), the more you buy or sell, the more you influence the price an unfavorable way (for your trades). Just ...

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

5

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 $i\... 3 Portfolio returns are analyzed to account for risk factors only to determine what the risk factor contributed to the returns, was it the underlying assets or the skill of the portfolio manager. Fama French model explains the returns in terms of principal component such SMB and HML besides the market related returns from CAPM. These links have more detais ... 3 It looks like 1 and 2 are different portfolios of companies. 1 is a portfolio of dual-listed companies, and 2 is a portfolio of everything in the "market". Once you have constructed these these portfolios, let's say you put the returns for every time step into a vector, call it r, then the average return would be mean(r). You need some clarification as ... 3 The most common transformations you see for these three variables on credit desks is to compute "returns" on the credit variables. So, rather than taking the straight daily differences$\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 s_t}{...

3

There are a few reasons to use factor models. Most importantly, stocks tend to move together. Stated alternately, the first principal component of the securities in a domestic market tends to explain a large share of the variance. If you're concerned with multiple securities (as in portfolio optimization), then you have to account for this or you will ...

2

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 ...

2

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 ...

2

Another important reason for using risk-adjusted returns is to disentangle "skill" from "risk-taking". Think of a equation for a fund's performance like: $r_{i,t}-r_f=\alpha_i+\epsilon_{i,t}$ where $\alpha_i$ gives you the average excess return of fund $i$. Alpha is often interpreted as measure of a managers' skill in timing the market and selecting ...

2

It depends on what makes more economic sense: If you are calculating CAGR for FX (which is traded effectively 24/7) strategy returns for instance, it would seem fair to use 365.25 calendar days. If you are calculating CAGR for internal reporting of trading strategy returns on a product with 5 market sessions per week, it would seem fair to use 252 calendar ...

2

If you do step 1 and step 2 every day, then you indeed assume that you rebalance the strategy every day. If you want to assume differently, for example monthly, you need to first compound the returns for each asset separately during the whole month and then do a weighted sum of the compounded returns using the weights of each asset at the beginning of the ...

2

Evans and Schmitz (2015) might give an answer to your question if the Fama-French factors are indeed working or not. Value, size and momentum have a long history as stock price predictors, and similar indicators have been applied to stock indices in order to predict the performance of one national index against another. Published back tests of trading ...

1

You will need a 'pseudo' random number generator - most stats programming languages have them (Matlab, R, Python...). But GBM is defined with Normal increments $N(0,\sigma^{2}(T-t))$ so I dont think using Student's t distribution is a good idea, never seen it in any literature/applications. It is however used for instance in GARCH modelling.... Random ...

1

It is just partial answer to your question. The Fama and French three factor model can be written as: $$R_{it}=\beta_{im}R_{Mt}+ \beta_{iSMB}SMB_t+\beta_{iHML}HML_t + e_{it}$$ In this model the market index is supposed to capture systematic risk originating from macroeconomic factors. Whereas, SMB and HML are firm specific variables and are chosen ...

1

Your intuition is not exactly right. To start with often the facts that small minus big or high minus low explain the cross-section of returns is called a puzzle. It is called a puzzle precisely because there is no unifying explanation for them. It is fairly agreed among academics that the Size effect is most likely a January effect, or probably it even ...

1

Use your total wealth allocated to the trades as denominator. Total wealth allocated would include all collateral. In this way you (or your broker) make sure that the denominator is always positive. Presumably this would also reflect what you really want to track. The only problem that remains is what amount of your wealth needs to be allocated. But this is ...

1

When we hear that the Dow is up for the day, it is not relative to the open, but rather to yesterday's close. Accordingly, I believe the yearly returns for 2013 are calculated, using the yearly adjusted closing prices, as $(C_{2013} - C_{2012}) / C_{2012}$. I looked up adjusted closing prices on finance.yahoo.com: substituting $C_{2012} = 20.96$ and \$C_{...

1

You can use both standards, but when you apply or compare this rate the standards must be equal, and it should be noted which convention you used. Note that 300/365 yeardays would in percentage be equal to 205/250 tradingdays, so its really just a convention that would make no difference in actual time.

1

According to the literature in market microstructure, the price pressure is defined as "the change in price when large quantities of a security are traded". Here you can find an example of how price pressure influences the bond market and in which the authors provide a complete definition of the phaenomenon and the relative problem of the information ...

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 ...

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