# Tag Info

10

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 ...

7

Investor preferences for higher level moments are probably most easily explained by behavioral finance. Investors' tendency to overvalue out-sized positive and negative outcomes, such as gamblers' willingness to play negative expectancy casino games, is consistent with many of the intuitions underlying Prospect Theory. There are several possible behavioral ...

6

You could use the two factor model of Schwartz-Smith. It's a very standard model in commodities, where you observe this kind of long term mean reversion (where "long-term" is here around a year). It's a mean reversion model where the long-term mean reversion is itself a brownian proccess. This way you can have the desided stochasticity in the short term, ...

5

One economic model you could look at is the Habit model of Campbell and Cochrane (1999). The basic idea is that as the consumption of the representative investor approaches the (appropriately defined) habit level of consumption the representative investors risk aversion spikes: this means discount rates increase dramatically and we see a big drop in stock ...

5

You're right but a GBM doesn't assume that percentage returns are normally distributed. It's about log-returns. If the log-return $r_t=\ln\left(\frac{S_{t+dt}}{S_t}\right)$ is normally distributed (GBM assumption), then $r_t$ can indeed be any arbitrarily large (positive or negative) number with positive probability. This also implies that stock prices are ...

5

For a continuous variable the PDF is the derivative of CDF. So returns or prices don't have a pdf if the cdf is not differentiable, e.g. it "jumps" at some point. The simplest models we use, like normally distributed log-returns, imply that returns, cumulative returns and prices all have a pdf.

5

No, because correlation is a unitless quantity. As you use volatilities to do the scaling, the $\sqrt{252}$ factor should already be taken into account in them. If you take a correlation of 1 between two assets, multiplying your correlation matrix by a factor $C \neq 1$ risks either to underestimate correlations (by hiding perfect (anti)correlations) or have ...

5

I'll add some comments, recognizing that 1) they are highly opinionated, and 2) they don't actually offer any real solutions. Hopefully more thoughtful and useful answers will emerge. First of all, purely from a philosophical perspective, I have to admit that I sometimes find these discussions on strategic asset allocation (SAA) "strange." ...

4

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 ...

4

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 ...

4

In the colloquial sense of the word "justified," it is not justified. I will describe why it is justified mathematically and under what circumstances and in what case it is not justified. Let me begin with the simplest of equations $$\tilde{w}=R\bar{w}+\epsilon,\epsilon\sim\mathcal{N}(0,\sigma^2).$$ Let us assume that this equation is an element ...

4

The "hedging theory of investment" (which I first heard about from R. C. Merton) says you should invest not for returns but to hedge your liabilities. LDI (Liability Driven Investment) is one name for it. So for example a pension fund should hedge pension liabilities. A university endowment should hedge the cost of producing education, which might entail ...

4

From the wikipedia on skewness and kurtosis, both are defined as expectations of standardised moments of the respective distributions. Hence, no.

4

Many pension funds use projected asset class returns (capital market assumptions or CMAs) and backward-looking estimates of volatilities and correlations to set the strategic asset allocation. A 10-year period for the return projection is typical. The determination of actual weights is more or less an exercise in constrained mean-variance optimization. ...

4

The source of the problem is twofold: Dimensionality of variance directions is low (most directions have close to 0 variance) Portfolio Optimization is prone to an unstable covariance matrix (which almost always is the case) And now I will try to explain what that means in more detail and then sum it up in a simple, intuitive statement: If you have a ...

4

Generally, anything on Investopedia needs to be taken with a big grain of salt. (Wikipedia sometimes has correct information, but Investopedia - almost never.) Let us try to reverse-engineer Sabrina Jiang's table on Investopedia. The first column is easy to reproduce. We start with 10,000. Every year we earn 10%. So our assets are: year 1: 10,000.00 year 2: ...

4

B is the correct choice. I honestly would wish multiple choice would not even exist. It is the worst way of testing knowledge in my opinion. Without knowing the details of what was taught, I would say choosing C is definitely the wrong answer. The df in t-student can be used to estimate/model fat tails. According to Fat Tails in Financial Return ...

3

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 ...

3

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 ...

3

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 ...

3

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 ...

3

To summarise what "John" just explained above: Say that you have stock portfolio for several years: $t_0, t_1, ..., t_m$. Say that you have $n$ stocks, so that stock $i$ has a vector of prices $X_i$. The length of each price vector is $m$ because there are $m$ years. Then, for the first year $t_1$: Calculate the $n$ different arithmetic returns for ...

3

In a nutshell, this is the "variance drag" problem. The mechanics of how you short something matter, and it's relevant to the discussion of levered/inverse ETFs that behave differently from classic/vanilla positions. Consider an XYZ future at 100. A day later it's 1% up, at 101. Two days later, it's up 1% again, at 102.1. If I go long, I make 2.1 profit. ...

3

For some clarification, what assets are you allocating and what is the objective? Does it include stocks, bonds, real estate, etc.? Do you care about returns, volatility, drawdown, etc? Assuming the answers are yes and you are concerned with what is usually referred to as asset allocation, I would next ask why you want to completely ignore historical ...

3

The return $R_i$ as expressed in $$R_{i+1,i}=\frac{S_{i+1}-S_i}{S_i}=\mu \Delta t + \sigma \Delta W(t_{i+1},t_i)$$ is not possible. To see this, let's get the returns over two small time steps of $\Delta t$ each. Then $$R_{i+2,i+1}=\frac{S_{i+2}-S_{i+1}}{S_{i+1}}= \mu \Delta t + \sigma \Delta W(t_{i+2},t_{i+1})$$ but $$R_{i+2,i}=\frac{S_{i+2}-S_{i}}{S_{i}}= ... 3 EWMA (and other sort of moving averages) introduces positive autocorrelation into otherwise uncorrelated returns. The fitted values of EWMA are linear combinations of past returns, and the constituent elements of these combinations overlap. Therefore, positive autocorrelation arises. If you have autocorrelated returns to begin with, they would in all ... 2 Another important reason for using risk-adjusted returns is to disentangle "skill" from "risk-taking". Think of a equation for a fund's performance like: r_{i,t}-r_f=\alpha_i+\epsilon_{i,t} where \alpha_i gives you the average excess return of fund i. Alpha is often interpreted as measure of a managers' skill in timing the market and selecting ... 2 It is just partial answer to your question. The Fama and French three factor model can be written as:$$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 ...

2

That's a quite interesting problem, a few thoughts on how to attack it: Calculate the correlation and beta between the benchmark and the fund. If the above imply a link between these two then proceed with the betas' comparison. Regarding the three approaches you mention, the one which subtracts the betas sounds mathematically-speaking wrong since beta is a ...

2

Although I agree with jd8 answer, practical implementation issues may arise. Here I suggest a parsimonious engineering solution relying on economic intuition of Habit model of Campbell and Cochrane (1999). 1 – Assume time varying mean and standard deviation in standard GBM dynamics. 2 – Use “drawdown” as an observable variable for measuring risk aversion. ...

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