# Tag Info

9

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 ...

7

You are simply doing $log(S_t) - log(S_t) = 0$ for all $t$. Instead, try > n <- length(prices); > lrest <- log(prices[-1]/prices[-n]) Should do the trick.

7

I believe the concept you are looking for without really knowing it is the information coefficient (IC). IC is the correlation between your forecast and actual subsequent returns. If your IC is 1 (perfect correlation, also known in this context as perfect foresight), then your maximum return is the compounded sum of the greatest daily return of any stock ...

6

In long-short equities, it's common to use daily returns in $\frac{\mu}{\sigma}$ and then multiply by $\sqrt{252}$ to annualize.

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 ...

6

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

Such tests should always be done using adjusted prices. In fact, ideally, you should reconstruct your own price series using the total returns series. To see this, suppose you have a 10:1 split rather than a relatively small cash dividend. Then it is clear that the cointegration relationship can only hold with respect to the adjusted series.

5

To expand on what Joshua has already stated, here is a truncated parameter list of similar functions, along with the package to which they belong. quantmod::Delt(x1,type = c("arithmetic", "log")) quantmod::periodReturn(x, type='arithmetic') # log would be "log" TTR::ROC(x, type=c("continuous", "discrete")) PerformanceAnalytics::CalculateReturns(prices, ...

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 ...

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

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

4

If I understand you correctly, your question is whether this is true: $$\sqrt[10]{\prod_{i=1}^{10}{Y_i}} < \sqrt[10]{A}$$ where $Y$ is the yearly cumulative returns (your method), and $A$ is the absolute cumulative return (your classmate's method). The question then becomes whether you find this relationship: ...

4

You're forgetting that -2.52 is still in natural logarithm terms. So the correct answer is 2.71828183 raised to the -2.52 power which equals 0.08. Your ending portfolio value is 8% of what it was a year ago.

4

For fixed income hedge funds, monthly returns are almost always used to calculate the Sharpe ratio, because some securities held are relatively illiquid and the dealers who do the pricing for the hedge funds are only willing to do month-end pricing. Daily returns are not available to be calculated for most such funds.

4

Thanks gappy for your precise response. However the answer to this auto-correlation is much more important than an academic discussion of which portfolio performance ratio is best. Auto-correlation distorts max draw-down calculations raising the question of whether the (positive) auto-correlation will continue in the future producing large draw-downs, or ...

4

I don't feel I can give you an authoritative answer on what the "standard" approach is, maybe someone with more hands-on experience will be able to help. But my quick thoughts. As to the period, I've seen both daily and monthly returns being used. Weekly probably not that often. But in the end you annualize them either way to make them comparable. The ...

4

Unless I'm missing something, your question simply boils down to arithmetic as you have the portfolio allocation and sector returns explicitly identified: Portfolio Return = (Sector 1 Allocation) * (Sector 1 Return) + (Sector 2 Allocation) * (Sector 2 Return) + ... + (Sector n Allocation) * (Sector n Return) Where the allocations among n sectors add up to ...

4

These returns are almost always modeled by finding some fundamental two-sided variable and modeling that. For options, we would model their prices as derivatives -- we would take the log-returns of underlying prices as the fundamental variable, possibly with other models for what would happen to volatilities and the like, and compute the consequences for ...

4

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 ...

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

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

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 ...

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

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 ...

4

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, ...

4

Not acutally a paper, but there is even a book on Multifractal Models. It is, to my knowledge, the standard reference on this topic by Calvet and Fisher: Multifractal Volatility: Theory, Forecasting, and Pricing (Academic Press Advanced Finance)

4

The initial investment is the capital in the account used to support the portfolio, not the cost of the assets in the portfolio. For example, when you sell a stock or bond short, your account doesn't actually accrue any cash. Instead you start receiving a regular cash flow. There isn't necessarily a difference between these quantities in a long-only ...

3

An easy way to perform what you need is do it this way: if your data are daily then : > prices <- data$cl > log_returns <- diff(log(prices), lag=1) would provide you with daily log returns, if you change the$lag=1$to$lag=5\$ then you will get weekly moving log returns.

3

I think the easiest method for calculating log returns is ROC from the TTR package: > data(ttrc) > roc <- ROC(ttrc[,"Close"]) http://cran.r-project.org/web/packages/TTR/

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