# Tag Info

## Hot answers tagged returns

8

Just to be painfully clear, it only seems to make sense to consider the logarithm of returns, i.e. $X=\log (1+\frac r{100})$ for a simple return of $r\%$ in an arbitrary period because this is what sums when returns are temporally aggregated. A basic property of cumulants is that cumulants of all orders are additive under convolution, for which a proof can ...

6

In addition to John's answer and just to make things clear: The arithmetic mean is given by $$\mu_a = \frac{1}{n} \sum_{i=1}^n x_i$$ The geometric mean is given by $$\mu_g = \sqrt[n]{\prod_{i=1}^n (1+x_i)} -1$$ And we have that $$\mu_g \leq \mu_a$$ So not only would the geometric sharp ratio would be taking into account the "actual" return of the ...

5

Hmm, this table looks wrong. Here's what it should look like. After the most recent corporate action, the Close and Adjusted Close should be the same; only prices from before the most recent action should have a different Adjusted Close. Here's another example. I think Yahoo just has the wrong information. If you wanted to derive your own adjustments for ...

5

I'm not sure it makes sense to think of one as more correct than another. However, they do have significant differences. It may help to distinguish between ex-post evaluation of a strategy and ex-ante prediction of what the strategy's performance will be. For simplicity, let's assume the log returns of the strategy are approximately i.i.d. univariate ...

5

The study you cited seems to be exaggerating slightly. 1) "An interesting fact of returns is that all of the stock returns since 1993 are from overnight returns" -> This is simply factually incorrect. Why don't you pick the S&P 500 names, you calculate the log returns taking into account price changes from the open to the close, then you do the same ...

4

You will struggle to put a number on the potential returns of high-frequency trading (HFT) and I think it wouldn't make any sense anyway if you don't take into consideration its risk and its leverage. Achieving 100% return with low volatility seems highly improbable; so ask the trader in question his Sharpe ratio to start with and compare it with yours. ...

4

So those are cumulative pnl figures and you are interested in the percent changes in pnl from one data point to the next? Don't use log returns, simply generate the percent changes through r(t)/r(t-1)-1. 4.3922/5.2735-1 = -16.71% (in your example time series I made the assumption that the time series is in ascending order. Given your description of the ...

4

In my opinion you have two choices: You calculate annual returns from the daily returns that you have - I guess it is clear how. Subsequently you calculate your statistics on these $11$ data points. When I look at your comment above, this could be what you want to achieve. Then you have the ex-post statistics on your data. The drawback is that $11$ data ...

4

Some of the used heavy-tail distributions are: Log-Cauchy and Log-Gamma Lévy Burr and Weibull Mixed normal Here two papers that cover some of them and others: http://ect-pigorsch.mee.uni-bonn.de/data/research/papers/Financial_Economics,_Fat-tailed_Distributions.pdf http://www.rff.org/RFF/Documents/RFF-DP-11-19-REV.pdf

3

It depends on what you do with your returns. If your returns directly affect your capital base, regardless of positive or negative returns, and if you employ all the generated returns in new trades on which you subsequently calculate returns then you should use compounded returns. Else your returns should be treated as additive and simply aggregated through ...

3

Returns are supposed to be compounded. For example, if I make 10% today and another 10% on top of that tomorrow, then I will have made 21%. Addition would only make sense if I had taken my profits out at the end of the first day. So no, you can't add returns like this. Instead, you must multiply the returns: \prod_{i=1}^{n} (x_i + 1) - 1 ...

3

I can only repeat myself because your mentioned previously asked question is essentially identical: => I would say do not include non-trading days, do not include days with zero position, do not include days where the asset did not trade for whatever other reason. Here some reasons and pointers: Sharpe measures excess returns scaled by volatility. The ...

3

For me, I would calculate daily returns for such a series by backing out the daily PnL and dividing by some volatility number. lets define your cumsum as "c_pnl": daily_pnl = c_pnl - [0; c_pnl(1:length(c_pnl-1)] max_draw = max(cummax(c_pnl) - c_pnl) pct_returns = daily_pnl / max_draw # in terms of drawdown Don't you have capital already in the ...

3

There are many variants proposed; some useful, some not so much. As an investor, the most important thing is to compare the exact same ratio, calculated in the exact same way, for each prospect. As the prospect/fund the most important thing is to be clear about the statistic you are reporting so your investors make well informed decisions. So let's start ...

3

Even if some buy side funds are not allowed to short sell it does not mean they must buy. They could long sell, they can do nothing and stand on the sidelines and they can hedge, selling index futures or buy put protection on broad indexes or on the underlying of core holdings. Why this is an important point becomes apparent when you start to think about ...

3

Whether its possible? Absolutely. However, you should probably keep in mind a couple points: * Many people claim a lot while proving very little to none. This is fine if the issue is a small-talk conversation. Believe it or not, no harm done. However, this is about money, and from my experience I cannot stress enough how important it is to do a very ...

3

What you are looking for is an unsupervised learning algorithm algorithm: i.e an algorithm that will by itself determine the 3 most rational groups from your dataset. This method will allow you to choose the boundaries of the groups based on the dataset you provide and not by choosing some given fixed values. The algorithm I suggest you to use is the ...

3

You could test for whether the input series is I(0) vs the alternative of I(1). Specifically, regress the input series on its own lag, and test whether the coefficient on the lag is significantly different from zero. Price series should have a coefficient close to 1, while return series should have a coefficient close to 0.

2

It seems that your real question is: is the PFP (Price Formation Process) diffusive from intraday to weekly sampling rate? It is a very good question since on intraday, some academics found some multifractal features into intraday returns, meaning that the PFP is not a Geometric Brownian Motion at small scales (even considering stochastic volatility). You ...

2

I think that can never be 100% sure, and the most you could do is raise a warning, and your approach makes perfect sense to me. I want to point out one thing though. While prices cannot be negative, they are sometimes recorded with a negative sign, where negative sign conveys some other information. For example in CRSP: Price Usually, the CRSP ...

2

Concerning adjusted price series: Free yourself from terminology and definitions, as you can clearly see, Yahoo Finance got it wrong on the stock split you linked to (and as chrisaycock correctly pointed out). You need to focus on the problem not the term people use to describe the problem: You need to adjust time series for the stock split, period. So, ...

1

Generally I would annualize risk and returns even when an asset's returns/general time series (ts) does not span over the full year So, both, FB and G present risk and return over the past year. For risk and return that is calculated over longer periods I would not include an asset in the portfolio of which you have no ts available to measure risk and ...

1

Despite the rather unconventional terminology used I would say you are pretty much spot on with what you are doing and what you try to achieve. I would, however use log returns in order to get an identical percentage no matter whether you measure the distance from 100 -> 90 or 90 -> 100, for example. You can also standardize the value you capture by ...

1

Let real wealth at time $t$ be defined as $W_{t}^{R}\equiv\frac{W_{t}^{N}}{P_{t}}$ where $W_{t}^{N}$ is nominal wealth and $P_{t}$ is the price level indexed to one at the initial period. You want to withdraw a $x_{t}$ percent of real wealth. This would give $$x_{t}W_{t}^{R}=x_{t}\frac{W_{t}^{N}}{P_{t}}$$.You could then consider a withdrawal rate in nominal ...

1

For any real world applications, the difference between the arithmetic and geometric Sharpe ratios is likely to 'fall under the noise floor', i.e. be smaller, typically much smaller, than a standard error. This is even under the generous assumptions of stationarity and absence of omitted variables.

1

Even in a perfect world, a 3X leveraged ETF cannot achieve a compound return three times that of the underlying. In the case of periodic discrete rebalancing, we call this effect the "arithmetic of loss and recovery," but even in the limit of continuous rebalancing, this effect does not disappear. Ito's formula tells us that \mathrm d ...

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