7 votes

The possible preferences of investors for higher than first 2 moments of return distribution?

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' ...
6 votes

Modeling Long-Term Mean Reversion in Asset Returns

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'...
6 votes
Accepted

How to annualize the correlation matrix?

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 ...
  • 2,400
5 votes

Modeling Long-Term Mean Reversion in Asset Returns

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) ...
  • 448
5 votes
Accepted

Normality or Log-Normality of Regular Returns

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 (...
  • 14.1k
5 votes
Accepted

Which financial time series have a PDF and/or CDF?

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, ...
  • 1,377
5 votes

Asset Allocation with near zero rates

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, ...
  • 10.9k
4 votes

Discrete returns versus log returns of assets

To fill in the details of what "John" just explained above: Say that you have stock portfolio for several years: $t_0, t_1, \ldots, t_m$. Say that you have $n$ stocks, so that stock $i$ has ...
4 votes

Any portfolio theories not based on asset returns?

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 ...
  • 9,657
4 votes
Accepted

Does standardizing/normalizing asset returns change their skewness and kurtosis?

From the wikipedia on skewness and kurtosis, both are defined as expectations of standardised moments of the respective distributions. Hence, no.
  • 5,938
4 votes

Normality or Log-Normality of Regular Returns

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 $\...
4 votes
Accepted

Asset Allocation with near zero rates

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-...
  • 3,480
4 votes

Why does the likelihood of corner solutions in portfolios increase as the number of assets grows?

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 ...
  • 2,894
4 votes
Accepted

Expense ratio over time

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 ...
4 votes

Fat tailed can be estimated through a t-distributions?

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 ...
  • 4,962
3 votes

Central limit theorem and normality assumption of asset return distribution

No. I just published a paper on this. If return is defined as $$r_t=\frac{p_{t+1}q_{t+1}}{p_tq_t},$$ and since returns are not data while prices and volumes are, then it follows that the ...
  • 4,123
3 votes

Intuition behind Fama-French factors

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 ...
  • 554
3 votes

Intuition behind Fama-French factors

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 ...
  • 6,923
3 votes

How to compute daily compounded backtest returns closer to real-world results?

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 ...
  • 10.9k
3 votes
Accepted

Why can we assume that asset return rates are normally (or lognormally) distributed?

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. ...
  • 4,123
3 votes
Accepted

Jensen’s Inequality for returns on short positions

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/...
  • 4,961
3 votes

Any portfolio theories not based on asset returns?

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 ...
  • 3,480
3 votes

Do EWMA weights remove autocorrelation in asset returns?

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 ...
2 votes

How to get get weekly returns from daily data

You can compute daily gross returns and then simply multiply them: $R_w=\prod_i \left(1+R_i \right)-1$, where $R_i=P_{close,i}/P_{close,i-1}-1$
  • 85
2 votes

Modelling fund positioning using fund returns and linear regression

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 ...
  • 441
2 votes
Accepted

Intuition behind Fama-French factors

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 ...
  • 2,168
2 votes

Private Equity: Direct Alpha vs Excess IRR

They are "essentially" the same thing. IPP (or excess IRR) is the excess return over the annualized benchmark such that the adjusted PME is 1: $$\text{PME} = 1 = \frac{\sum_{i=1}^n d_i \left(1 + ...
  • 10.9k
2 votes

Modeling Long-Term Mean Reversion in Asset Returns

I just wrote two papers on a related topic. Let us not use the log method right now as it was originally intended as an approximation from the time we used punch cards. You can, but we will come ...
  • 4,123
2 votes

Modeling Long-Term Mean Reversion in Asset Returns

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 (...
  • 121
2 votes

Why can we assume that asset return rates are normally (or lognormally) distributed?

It is justified in that you obtain some better information than you have without it. For example, you can make the assumption and acknowledge some inaccuracy in your model. The inaccuracy of pricing ...
  • 8,099

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