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17
votes
2answers
681 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 ...
11
votes
5answers
2k 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
5answers
5k 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?
10
votes
2answers
383 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
564 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
9k 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
1answer
353 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
2answers
262 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
3answers
948 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
359 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
546 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
4answers
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
2answers
4k 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
6k 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
114 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
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 ...
5
votes
1answer
667 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 ...
4
votes
2answers
179 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
425 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
447 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
143 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
2answers
294 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
0answers
156 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
3k 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
444 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
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 ...
3
votes
1answer
58 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
148 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
304 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
2answers
458 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, ...
2
votes
2answers
498 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
257 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
179 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
53 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
269 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
90 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 ...
2
votes
1answer
133 views

Predicting stock returns - in a panel data specification or by using portfolio formation strategies?

I'm working on an empirical analysis where I try to predict stock returns using weekly data. Ideally, I would like to use a panel data model like the following: $$ ...
2
votes
2answers
244 views

How to classify stocks by their volatility?

I would like to hear other possible ways of classifying Stocks by the Volatility of their returns. Assuming that I want to characterize each stock as Low, Medium or High Volatility Stock and assuming ...
2
votes
1answer
51 views

Weighting several returns over different time frames

I have a set of annualized returns over 4 time periods: 10yr, 5yr, 3yr and 1yr. Is there a way to weight each return to have a "more representative" return?
2
votes
2answers
212 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
161 views

Event studies using revenue data vs. measuring abnormal returns

This may be a silly question, but does there exist a methodology for examining the impact of "events" on companies that are not publicly traded? I suppose it would look at abnormal revenues rather ...
2
votes
2answers
196 views

Portfolio risk-return when assets have limited and inconsistent historical data / time series?

Lets say we have "today's" snapshot of asset allocation and need to determine the 6mo, 1 yr and 5 yr risk and returns of this portfolio. If the time series for every asset is very long, longer than ...
2
votes
1answer
110 views

Limits analysis

I have a few time series of models to analyse in terms of how far/close they are to their underlying limit. The limit is a simple value on the y-axis (always positive), and the series can act ...
2
votes
1answer
9k 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 ...
2
votes
1answer
73 views

Accounting for Withdrawals

I am trying to wrap my head around the proper way to do this. I would like to simulate the portfolio value adjusted for inflation with a fixed withdrawal rate. To simulate withdrawal rate, I will ...
2
votes
3answers
577 views

How to annualize dividends paid at varying intervals?

I am attempting to write a function that will calculate the annualized rate of return for individual dividends made by illiquid investments. These dividends are paid at varying intervals and the ...
2
votes
3answers
109 views

Calculate bond returns from yields

I have to construct and evaluate portfolio of bonds and stocks, namely I need to get return on portfolio, standard deviation and sharpe ratios. I have weekly data that contains stock prices, and I ...
2
votes
0answers
116 views

Correlation between idiosyncratic residuals and forward returns

The classic mean-reversion strategy is to calculate an "expected return" (alpha) by computing the raw return for each security and then remove the part which you think is market driven. Statistically ...