The asset rate of returns is the profit on a particular investment; it includes any change in the asset value, interest, commission or dividends and so, all other cash-flows which an investors receive or pays due to the investment.

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17
votes
2answers
720 views

How do you correct Max Draw-Down for auto-correlation?

When returns are auto-correlated, calculating a Sharpe ratio := $\frac {mean(x)}{\sqrt{var(x)}}$, (where $x$ are the returns) is complicated, but basically solved (see, e.g. Lo (2005)). Without the ...
12
votes
8answers
7k views

Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?

What are the advantages/disadvantages of using the arithmetic Sharpe Ratio vs the geometric Sharpe Ratio? Is one more correct? Or is one better in certain circumstances?
11
votes
5answers
3k views

Should Sharpe ratio be computed using log returns or relative returns?

I am trying to reconcile some research with some published values of 'Sharpe ratio', and would like to know the 'standard' method for computing the same: Based on daily returns? Monthly? Weekly? ...
10
votes
2answers
411 views

How to estimate the following model?

Suppose I have the following model: $$r_t=\sigma_t * \epsilon_t$$ where $r_t$ is the return at time t, $\sigma_t$ is the volatility, the model used to model this volatility is an exponentially ...
9
votes
1answer
2k views

Skewness and Kurtosis under aggregation

Returns possess non-zero skewness and excess kurtosis. If these assets are temporally aggregated both will disappear due to the law of large numbers. To be exact, if we assume IID returns skewness ...
8
votes
2answers
599 views

What is a reasonable upper bound on the performance of a daily trading strategy?

I am backtesting an equity trading strategy which trades only once per day. Is there a general rule of thumb for the reasonable upper bound on the rate of return of such a strategy? For example, a ...
6
votes
3answers
13k views

Calculating log returns using R

I am trying to calculate the log returns of a dataset in R using the usual log differencing method. However, the calculated data is simply a vector of zeroes. I can't see what I'm doing wrong. Here ...
6
votes
2answers
298 views

How do I statistically differentiate a series of prices from a series of returns?

I developed an optimization algorithm that uses returns (among other parameters) as input and basically output an allocation. As I'm pretty happy with the results, I am in the process of putting the ...
6
votes
1answer
375 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 ...
6
votes
3answers
1k views

How to calculate compound returns of leveraged ETFs?

Forewarning: this is a complete newbie question :-) I am starting to learn about ETFs by trying to do the numbers. When learning about the compounding effect in leveraged ETFs, I wanted to simulate ...
6
votes
2answers
838 views

How do Return.portfolio and Return.rebalancing work in Performance Analytics in R?

I have a question about the function Return.portfolio/Return.rebalancing from the Performance Analytics package in R. I take ...
6
votes
3answers
599 views

Testing the validity of a factor model for stock returns

Consider the following m regression equation system: $$r^i = X^i \beta^i + \epsilon^i \;\;\; \text{for} \;i=1,2,3,..,n$$ where $r^i$ is a $(T\times 1)$ vector of the T observations of the dependent ...
6
votes
1answer
841 views

Price volatility instead of return volatility for spread option parameter

I overheard someone at work today talking about a commodity spread option pricing model and he was asking our quant if he should use price volatility instead of return volatility as the volatility ...
6
votes
3answers
1k views

Using rolling returns in a multivariate linear regression?

I am trying to use fundamental factors such as PE, BV, & CFO in a multivariate linear regression with the response variable being the rolling 1 month returns. But this approach seems flawed as the ...
5
votes
3answers
376 views

Why do we usually model returns and not prices?

I think this is a quite similar question for most of you, however it is not completely understandable for me at the moment: Why do we usually use returns and not prices to model financial data in ...
5
votes
2answers
5k views

Daily returns using adjusted close

I want to chart the daily returns of a stock, and I'm using Yahoo finance data to download historic data. I was told to use Adjusted Close, but there seems to be an issue with this. For ANTO.L, you ...
5
votes
3answers
7k views

Correct way to find the mean of annual geometric returns of monthly returns?

Say I'm given I set of monthly returns over 10 years on a monthly basis. What is the correct way to find the geometric returns of this data? I ask because a classmate and I are on different sides of ...
5
votes
2answers
2k views

Quantmod: what's the difference between ROC(Cl(SPY)) and ClCl(SPY)

I feel like I'm missing something fundamental here, but I can't shake the feeling that these two series should be equivalent. /edit: there is also dailyReturn(Cl(SPY)). I've seen all 3 of these ...
5
votes
2answers
221 views

How to annualise the volatility of non-iid returns?

I have a series of monthly log-returns; let's assume the log-returns are normally distributed, but exhibit significant serial correlation. In the case of normal, i.i.d. returns, I can annualize the ...
5
votes
3answers
177 views

Can Gaussianity of returns depend on the time frame?

I would be interested in knowing if the fact that returns are Gaussian is disproved on all time frames, or if, for example, the 5 minute intra-day time frame could exhibits Gaussian returns assuming ...
5
votes
1answer
4k views

Annualzing the log of daily returns riddle

Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or ...
4
votes
2answers
225 views

Multifractal Model, Generating Sample Paths with Correlations between Assets

I have studied option pricing using Geometric Brownian Motion to generate sample paths. Because of the normal distribution, it is easy to create a covariance matrix and get correlated asset returns. ...
4
votes
1answer
460 views

Should cointegration be tested using close or adjusted close prices?

When doing cointegration tests should I use the adjusted close price or just close price for the time series? The dividend of each stock is on different dates and can cause jumps in the data.
4
votes
2answers
686 views

Looking for C# library that provides/contains performance analytics

I am looking for a C# .Net library that provides trade performance analytics similar to R-PerformanceAnalytics. Basic return statistics, draw-downs, risk-adjusted returns, risk (variations), ...
4
votes
1answer
3k views

How to annualize skewness and kurtosis based on daily returns

I'm trying to annualize the four moments based on a string of daily returns (continuously compounded) for 11 years. The formulas for the annualization of the mean and the standard deviation I did ...
4
votes
1answer
151 views

What are some common models for one-sided returns?

One typically models the log returns of a portfolio of equities by some unimodal, symmetric (or nearly symmetric) distribution with parameters like the mean and standard deviation estimated by ...
4
votes
3answers
316 views

Comparing Returns on a Sector Basis

I'd like to compare the returns of a portfolio segregated by groups to the returns of those groups in total. So say for example I have a portfolio with 40% Industrials and 60% Technology, then over ...
4
votes
2answers
665 views

Volatility of a rolling window strategy

What methods can be applied to determine the volatility of strategy using a rolling window? Using normal standard deviation would bias the results as the returns will be highly correlated. Although, ...
4
votes
0answers
161 views

Is it more accurate to analyze returns on a calendar day basis than a trading day basis?

I'm rather new to the actual practice of this kind of analysis, but it just seems wrong to me to throw Mondays' returns in with the rest without accounting for the passage of time on the weekend when ...
3
votes
2answers
4k views

What kind of return can an average algorithmic trading firm achieve today?

What kind of rate of return can an average, equities-focused algorithmic trading firm expect to achieve today? I come from a background of control and optimization, working in the industry in China, ...
3
votes
2answers
474 views

When gains are made: Overnight or during trading hours? What is the connection to volatility?

Falkenblog reports an interesting finding: All of the stock returns since 1993 are from overnight returns and cross-sectionally, volatility receives a positive overnight risk premium, a negative ...
3
votes
2answers
81 views

Does heteroskedasticity of returns depend on the time frame?

Similarly to my last question, for which I obtained very interesting and useful answers, I would like to know if there has been any study regarding heteroskedasticity and time-frames of the returns. ...
3
votes
1answer
52 views

French Data from daily to monthly returns

Ken French on his website publishes daily, monthly and yearly returns for the Fama-French 3 Factors model which are excess market (Rm-Rf), small-minus-big (SMB) and high-minus-low (HML) returns. I ...
3
votes
1answer
63 views

How consequential are violations of the efficient diversification assumption of asset pricing models?

When using asset pricing models such as the CAPM or the Fama-French four factor model to determine the risk-adjusted return of a portfolio, does this strictly require efficient diversification of the ...
3
votes
1answer
12k 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 ...
3
votes
1answer
166 views

Estimating Beta from unevenly spaced price history

I have a certain non-stock asset that has 1 transaction every 1 to 8 months. I also have a price index of that class of asset compiled by another party on monthly basis. If I regress $price = \alpha' ...
3
votes
2answers
459 views

Calculating and interpreting cumulative returns is R

I have buy and sell signals,and accordingly, I artificially generate a signal series,for which,I assign 1 to every buy and -1 to every sell: ...
3
votes
3answers
532 views

Portfolio software that shows 'total return' for each investment

I'm a high school technology teacher and sponsor for the Charity Student Investment Project. Currently our students track our investment portfolio via a google spreadsheet ...
2
votes
3answers
992 views

How to model the daily return using intraday data?

Say, I have hourly returns $r_1,r_2,...,r_T$, where $r_t$ = $ln(p_t)$ - $ln(p_0)$ for $t = 1...T$. So what is the value of $E[r_t]$? Would $r_T$ be the $\prod{(r_t)}$? Basically $r_t$s are the ...
2
votes
1answer
138 views

On an application of Ito's lemma

Assume that instantaneous returns are generated by the continuous time martingale: $$dp_t = \sigma_t dW_t$$ where $W_t$ denotes a standard Weiner process and One day returns are denoted by $r_{t+1} ...
2
votes
2answers
1k views

Definition of Return of A Long/short Portfolio

This can either be a silly question or a question with no sure rigorous answer but defined with some convention. Any way, here it is. What is the (industrial recognized) definition of the return of a ...
2
votes
2answers
295 views

Calculate Daily Returns for Sharpe Ratio

For the purposes of Sharpe ratio, I calculate a trading strategy's daily returns using realized P/L only: $$ \frac{K(t + 1) - K(t)}{K(t)}, $$ where $K(t)$ is the cash balance after market close on day ...
2
votes
1answer
196 views

How to group mutual funds by volatility?

I want to group Mutual Funds by their volatility. Ideally, I would like to end up with the mutual funds beings attached to different groups: High volatility Medium volatility Low Volatility My ...
2
votes
1answer
46 views

How to deal with missing returns when creating value (equal) weighted returns

recently I am doing cross sectional regressions, and getting confused about missing returns. Suppose we have 100 stocks, then we want to construct a value weighted return (or equal weighted return). ...
2
votes
1answer
50 views

What is the relationship between arithmetic versus geometric averages and simple versus logarithmic prices?

I know that the geometric mean is used in order to make percentage returns across time comparable. Similarly, I know that log prices make percentage returns comparable for example when prices are ...
2
votes
1answer
54 views

Attributing change in yield as a result of structural change

Suppose your portfolio has $w_0$ amount of bonds with yield $r_0$. Now you buy additional $w_1$ amount of bonds with yield $r_1$, then buy additional $w_2$ amount of bonds with yield $r_2$. ...
2
votes
1answer
362 views

annual excess returns from CAPM on monthly total returns

I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the ...
2
votes
2answers
249 views

Block Bootstrapping Relative Returns

I want to run a block bootstrap on the relative returns, but I'm not sure if subtracting the mean is important. A bootstrap sequence is a synthetic sequence generated using the original sequence. If ...
2
votes
1answer
22 views

Calculating the rate of return over a year then the data for a year before does not exist

I am trying to find the growth rate of a stock over a given year. Let's say I wanted to find the growth rate from today, June 11, 2015 to June 11, 2014. This is easy enough when you have perfect ...
2
votes
1answer
72 views

Can you use a t-test on bootstrapped Value at Risk (VaR) figures?

I need to compare VaR before and after the recession. I have a series of market returns for a period before, and a series of market returns for the period immediately after. Both have been ...