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24 votes
2 answers
21k views

Discrete returns versus log returns of assets

There have been similar posts here already but nevertheless I find the question worth posting: why do some people claim that log returns of assets are more suitable for statistics than discrete ...
Richi Wa's user avatar
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13 votes
2 answers
5k views

Computing the Sharpe Ratio

The building blocks of the Sharpe ratio—expected returns and volatilities—are unknown quantities that must be estimated statistically and are subject to estimation error. The main problem I have is ...
user4796's user avatar
  • 131
10 votes
2 answers
1k views

Empirical distribution function of overlapping time series data

If we model asset return volatility for periods of more than one (say more than one day) there is the square-root rule which holds true under some assumptions. The situation is more tricky if we look ...
Richi Wa's user avatar
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9 votes
5 answers
2k views

Modeling Long-Term Mean Reversion in Asset Returns

Fortunately, for obvious reasons, few applications require simulating asset returns over horizons in excess of 30 years. Nevertheless, simulations over long horizons are sometimes conducted as part ...
RRL's user avatar
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8 votes
1 answer
574 views

Toy models of asset returns

When making simple agent-based models of banking systems to look at global properties (say systemic risk) one of the basic decisions you have to make is how to model returns on external (to the ...
Artem Kaznatcheev's user avatar
7 votes
2 answers
20k views

What is the price pressure?

What is the definition of price pressure and what does it imply? In a number of paper I read that the price pressure can influence the portfolio returns; can you explain why and in which way it can ...
Quantopik's user avatar
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7 votes
3 answers
2k views

Why are factor models so popular for risk analysis of portfolios?

As titled, my question consists on asking for why in the most of academic papers one almost always finds that when you try to model asset returns, one needs to adjust for risk factors before analyzing ...
Quantopik's user avatar
  • 2,486
7 votes
5 answers
4k views

Intuition behind Fama-French factors

In the Fama-French 3-factor model the portfolio returns are explained by the market the SMB factor (Small [market capitalization] Minus Big) and the HML factor (High [book-to-market ratio] Minus Low)...
Richi Wa's user avatar
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4 votes
3 answers
525 views

Asset Allocation with near zero rates

With central banks pegging interest rates to near zero rates, an argument could be made that the future distribution of interest rates and bond returns are not normally distributed. How has modern ...
AlRacoon's user avatar
  • 6,612
4 votes
3 answers
502 views

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

Can anyone explain in an intuitive manner a justification for possible preferences of investors for moments of return distribution beyond the first two moments (i.e. mean and variance). For example, ...
user31827's user avatar
4 votes
4 answers
1k views

Central limit theorem and normality assumption of asset return distribution

Can central theorem justify normality assumption of assets return distribution? And if it can why the empirical evidence show this assumption, which many finance models are based on, is a far cry from ...
Soroush Kalantari's user avatar
4 votes
1 answer
568 views

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

I often run quick tests of trading strategies in my analytics suites by: multiplying a vector of signal (lagged, {-1,0,1}) with a time series of daily percentage returns doing a cumulative product of ...
Air's user avatar
  • 126
4 votes
2 answers
34k views

How to calculate equally weighted market portfolio

There's two studies that test the same thing in different markets (i.e. they apply the identical methodology). They state: 1) "$R_{mt}$ is the equally weighted average stock return in the dual-listed ...
user avatar
4 votes
1 answer
1k views

Back to Basics -- Cumulative Returns

I recently came across a chart of Fama-French's (FF) HML factor cumulative performance. I first saw this in an article by AQR's Cliff Asness: http://www.institutionalinvestor.com/Article/3315202/Asset-...
Juan Mier's user avatar
3 votes
2 answers
1k views

Normality or Log-Normality of Regular Returns

Another old question on this site (How to simulate stock prices with a Geometric Brownian Motion?) inspired me to ask the following question: if we assume that regular returns could be normally ...
Jan Stuller's user avatar
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3 votes
2 answers
3k views

How to annualize the correlation matrix?

If asset returns are daily, and the asset return covariance matrix, $\Sigma$, is annualized by $\Sigma \times 252$, do I also multiply the correlation matrix by 252 to annualize it?
develarist's user avatar
  • 3,000
3 votes
2 answers
106 views

Expense ratio over time

I'm trying to reproduce the results in the table below from this article of Investopedia, but none of my calculations match. What is the correct way to calculate the expense ratio in this case?
rmorel's user avatar
  • 33
3 votes
2 answers
280 views

Interpretation of a uniform asset return distribution

Typically asset return distributions are bell-shaped with most mass occurring in and around the center, 0% returns, and less so in the tails, with the left tail representing the probability of large ...
develarist's user avatar
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3 votes
3 answers
1k views

What data transformations to use in regression of credit spreads on equity prices?

Clearly there is a strong relationship between credit spreads and equity prices (both theoretically and empirically). But how would one go about formulating a regression which seeks to explain this ...
Yugmorf's user avatar
  • 791
3 votes
1 answer
356 views

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

A three- asset portfolio doesn't seem prone to generating corner solutions, which are very high allocations to one of the assets and $0$ to the others. Instead, when the number of assets is low, these ...
develarist's user avatar
  • 3,000
3 votes
2 answers
445 views

Why in Fama-French factor model relative market capitalization and book-to-market aren't used directly for predicting return rate?

Fama and French use the following formula for predicting stock returns \begin{align*} r=r_{riskfree} + \beta_1(r_{market}-r_{riskfree})+\beta_2(SMB)+\beta_3(HML) \end{align*} which basically means ...
kandi's user avatar
  • 45
3 votes
2 answers
636 views

Distribution of simple returns vs logreturns

I understand that stock prices are conditionally modeled using a log normal distribution by the relationship $ y_t/y_{t−1}∼logN(μ_{daily},σ^2_{daily})$ $y_t∼logN(log(y_{t-1})+μ_{daily},σ^2_{daily}))$ ...
Sanju's user avatar
  • 39
3 votes
1 answer
232 views

Modelling fund positioning using fund returns and linear regression

I want to measure the positioning of an active bond mutual fund vs. its benchmark via rolling linear regression of returns vs several factors. The intuition of using linear regression is that the ...
Alex's user avatar
  • 31
3 votes
2 answers
123 views

Significance of return under stable distribution

if I want to use t-test to test significance of my returns, it assumes the random variable is distributed normally. But in my work I work under stable distributed ...
Jan Sila's user avatar
  • 732
3 votes
0 answers
48 views

Polynomial interpolation of corrected lognormal distribution

Can anyone provide a formula for a polynomial interpolation of the corrected lognormal distribution used to model returns traditionally resulting from the wrong Brownian motion generated model? ...
Jack Maddington's user avatar
3 votes
0 answers
274 views

Marginal Distribution using GARCH model: How to do inverse probability transform?

I have $n$ return series. I fitted AR(1)-GARCH(1,1) to each return series. Then used probability integral transform, PIT(residuals), to transform the residuals to have a uniform distribution. Then I ...
user20333's user avatar
  • 121
2 votes
1 answer
369 views

Fat tailed can be estimated through a t-distributions?

I have a simple question that makes me doubt a bit. In a multiple choise exam I ecountered this question: "if the stocks returns are not normally distributed, the fat tail effect can be estimated ...
gabriele's user avatar
2 votes
3 answers
2k views

Daily to Monthly Performance Attribution - Getting Effects to equal the Excess Return

I am building a performance attribution tool on Python to help us understand the asset allocation, stock selection effects of our fund. We are using daily price data for each component within the ...
financeapprentice1's user avatar
2 votes
2 answers
1k views

Problem when calculating the daily return on a forex trade, what is the best way to do such a calculation?

I intend to calculate the daily return on my investment in forex. Assume a trader invests $\$$40 at a leverage of 100:1, so in total he is trading $\$$4000 worth of currency, and assume the position ...
finstats's user avatar
  • 403
2 votes
0 answers
63 views

Is a position-weighted sum of nominal returns for a single asset a mathematically sound calculation?

A friend of mine insists that that the following is a sound method to calculate the performance of a single holding in a portfolio, given that over time more capital has been allocated to that holding....
jmabs's user avatar
  • 131
1 vote
3 answers
548 views

Any portfolio theories not based on asset returns?

For data, the mean-variance model for portfolio optimization uses asset returns to minimize portfolio risk (covariance matrix), which is asset returns volatility, and sometimes simultaneously ...
develarist's user avatar
  • 3,000
1 vote
3 answers
944 views

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

In many theories of financial mathematics it is assumed that asset return rates are normally distributed (e.g. VaR models) or lognormally distributed (e.g. Black-Scholes model). In practice, asset ...
B_B's user avatar
  • 83
1 vote
1 answer
533 views

Do EWMA weights remove autocorrelation in asset returns?

I know that the exponentially weighted moving average (EWMA) volatility estimator drapes a decaying weight function over historical returns in order to weight the past according to the decay of their ...
develarist's user avatar
  • 3,000
1 vote
1 answer
167 views

Jensen’s Inequality for returns on short positions

this is puzzling me. Say you have an asset A, that on day t+1 returns 1%, and then on day t+2 returns 1% again. If you invest $1 in A on day t (take a long position), then on day t+2 you have earned:...
Nulife's user avatar
  • 13
1 vote
3 answers
10k views

How to calculate return rates with negative prices?

I'm dealing with electricity options and I'm considering the possibilty of negative prices. I want two estimate the historic volatility. However, an arithmetic mean doesn't feel appropriate and $\log(\...
Joao Serafim's user avatar
1 vote
1 answer
116 views

Clustering the observations in a price or returns series [closed]

Given one stock, what value would there be in clustering the individual sample observations within that stock's historical prices series, or its return series? is univariate clustering done in finance?...
develarist's user avatar
  • 3,000
1 vote
1 answer
938 views

How to compute returns from cumulative returns in Python? [closed]

If X is a $T\times N$ pandas DataFrame of multivariate asset returns, the cumulative returns can be computed in python as (1 + X).cumprod() - 1 How can I reverse this operation so that I go ...
develarist's user avatar
  • 3,000
1 vote
1 answer
151 views

How to simulate asset prices/returns that display market regimes?

Are there any techniques that can make a multivariate random number generating process for stock prices/returns, like geometric Brownian motion via Cholesky, also include the simulation of a finite ...
develarist's user avatar
  • 3,000
1 vote
1 answer
50 views

How to evaluate prediction(s) made of the asset return mean?

In finance, it is well-known that the expected value of asset returns, $\mu$, otherwise known as the average return or mean or first statistical moment, is difficult to predict. I think it was ...
develarist's user avatar
  • 3,000
1 vote
1 answer
2k views

How to get get weekly returns from daily data

Good day I would like to get weekly returns data from daily data , I want to use the Wednesday-to-Wednesday approach – the returns (rt) are computed from the Wednesday closing prices Pt , i.e., rt = ...
Ama's user avatar
  • 11
1 vote
1 answer
76 views

Measuring extra return investors demand for a stock which cannot be sold?

How to roughly measure how much premium investors would demand if a stock could not be sold and its investors had to stick with it permanently using just dividends not capital gain as return? I am not ...
Soroush Kalantari's user avatar
1 vote
1 answer
80 views

How to adjust a portfolio's rate of return for contributions and withdrawals?

Suppose we have a portfolio with many assets. Since this portfolio receives monthly contributions and withdrawals, what is the best method to evaluate its global rate of return and avoid computing ...
Vinícius Lopes Simões's user avatar
1 vote
1 answer
280 views

The ratio of upside deviation to downside deviation in portfolio weighting

I've been calling this ratio "acceleration" in my head, so I'll do the same in this post. The question is, is this relationship used anywhere and if so, how? My thought process is as follows. Risk ...
user46252's user avatar
1 vote
1 answer
154 views

Portfolio & Asset Returns across Multiple Periods

The stocks of CK Tan's, Robertson's, and Tamashimaya are held by the hedge fund SSK. They hold an equally weighted portfolio. The end-of month prices of the stock during five months this year is given ...
SMLJKNN's user avatar
  • 103
1 vote
1 answer
4k views

Definition of log return of an asset [closed]

What is the general usage of the term daily log returns $Y_t$ of an asset? (1) or (2)? $$(1) \text{ } Y_t = log (\frac{p_t}{p_{t-1}})$$ OR $$(2) \text{ } Y_t = log (\frac{p_t-p_{t-1}}{p_{t-1}})$$ for ...
user avatar
1 vote
1 answer
162 views

Simple simulation model of bond plus cash returns

Is there a robust way to model 'bond plus cash' simulated returns, say in Excel, for an asset allocation problem between stocks vs bond plus cash? For equity, ...
rrg's user avatar
  • 969
1 vote
1 answer
981 views

How to simulate asset returns using student t?

I am currently trying to simulate an asset return using the student-t distribution, but I can't find how I should do this. I began with the Geometric Brownian motion and just changed in order that ...
lechim's user avatar
  • 21
1 vote
1 answer
243 views

Calculating returns for a mutual fund with dividends

I'd like to calculate returns for a given mutual fund (in this case, PRWCX from troweprice). When I look at their published performance, it says the Calendar Year Total Returns for 2013 is 22.43% but ...
asahi's user avatar
  • 113
1 vote
0 answers
260 views

Calculating returns from transactions

I have a collection of client transactions representing the trades of a single portfolio across multiple securities. What I'd like to do is the calculate the accurate ROI of each security and of the ...
user1467422's user avatar
1 vote
0 answers
779 views

Source on multivariate correlated geometric Brownian motion returns, not prices

Can anyone provide a source that formulates how to generate multivariate geometric Brownian motion returns using the Cholesky method with target correlation matrix, instead of correlated GBM prices? ...
develarist's user avatar
  • 3,000