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## Hot answers tagged returns

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 ...

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The PerformanceAnalytics library reflects several years worth of development by Brian Peterson and Peter Carl, as well as multiple collaborators. It is fairly widely used, tested and debugged. Basic software engineering practices suggest that you should strive to re-use it if possible. Options for that include accessing a remote R instance via RServe ...

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Are you sure the return for two years is 0.7214? It should be 0.3422 per year if you are using 31/12/2011, and 0.3416 if you are using 01/01/2012 as the end date. Assuming the last number (because it makes for two full years, therefore easier to calculate), yes, there is a formula to derive it from the return of the individual years. It's the geometric ...

2

I think this is a no-brainer. Only log-returns make sense. The average return can only be computed by averaging the sum of individual log returns. Taking the average of standard (relative) returns does not give you an average of the individual returns. Consider a simple case where the value of an investment alternates between 100 and 50 an odd number of ...

2

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$then you will get weekly moving log returns. 2 2) you only take trading days for your analysis because taking in account days on which no price changes took place would shift results in a wrong direction. For exmple, you mostly take 250 trading days p.a. 3) Your time interval up to 2007 is okay and excludes the financial crisis, which is a non-normal circumstance. Therefore, your time interval can be ... 2 This is not a perfect solution but perhaps the following approach could also serve you well as an indicator. Assuming you are only using a finite number (e.g.$n$) of bonds with fixed yields$r_i$you can write$r_f(w_1, \dots,w_n)=\frac{\sum_0^n w_ir_i}{\sum_0^n w_i}$with most of the weights being zero. Using the quotient rule you can now calculate ... 2 I would absolutely use a mark-to-market value in your daily pnl for the purposes of evaluating performance (e.g. Sharpe). So, yes, that would include the value of open positions in addition to your cash balance. If you hold something for a year, that performance was earned one day at a time, not all at once. If you only look at cash, you will have a large ... 2 It depends on what makes more economic sense: If you are calculating CAGR for FX (which is traded effectively 24/7) strategy returns for instance, it would seem fair to use 365.25 calendar days. If you are calculating CAGR for internal reporting of trading strategy returns on a product with 5 market sessions per week, it would seem fair to use 252 calendar ... 1 There are a lot of ways of doing this and what a good way of doing this will be driven by your needs as well. Criteria such as whether the method needs to be (in)sensitive to outliers and whether or not your groups need to be of the same size will influence this. One way to do this would be sorting the volatilities and group them: in groups of equal size ... 1 I don't think there is a correct answer to this question. If you're trying to study short-term correlations (e.g., to construct short-term trading signals), then 1-month or 3-month rolling correlation of daily returns is a feasible option. These short-term stock/bond correlations are quite unstable though. On the other hand, if you're studying long term ... 1 No, it's not. First, what you ought to be regressing are returns, not prices. Second, by interpolating you're underestimating the variance of the asset price in the interval between index price observations. Through your choice of interpolation method, you're essentially picking an arbitrary price in the middle. What you ought to be doing is maximum ... 1 You can use both standards, but when you apply or compare this rate the standards must be equal, and it should be noted which convention you used. Note that 300/365 yeardays would in percentage be equal to 205/250 tradingdays, so its really just a convention that would make no difference in actual time. 1 You can weight the returns and use them in calculations as shown below. From this site:- http://disc.sci.gsfc.nasa.gov/giovanni/additional/users-manual/G3_operation_time_series_stats.shtml The weighted mean is and the weighted standard deviation is So, making up some annualised returns for time spans, 1 yr, 3 yrs, 5 yrs & 10 yrs: r = {0.01, ... 1 In your question you do not provide any reference. I believe that we are in front of two possibilities: annualized linear returns and Compound Annual Growth Rate (CAGR). If compounding is not mentioned, I would assume annualized linear returns.$n$-years Annualized linear returns$n$= number of years$ n * r_A = r_* $, where$r_*$is the return over the ... 1 Long story short, thanks to Dirk Eddelbuettel's suggestion I played a bit with rredis and indeed it offers quite a number interesting solutions. However, I still decided to start to write my own performance analytics library (albeit obviously smaller and more specific to my use case) in combination with an established Math/Stats library because I need more ... 1 For a single day as long as$K(t+1)$includes the intraday cash flows it is the same, however if you do not simulate your cash balance interest rate you forget that your cash get compounded over time, which is slightly incorrect. This is why someone suggested you simulate your cash balance. This is more correct as well if you are not always 100% invested or ... 1 This is the equity line i got after i repeated your code. how is this good ? may be you have run with only one set of numbers. any ways here are a few things you can do to come closer to reality : take the close prices as lognormal distribution instead of a normal distribution. you are adding up the returns later on. this is only right if you have ... 1 It seems to me that you want to use the series of option prices to estimate the Sharpe ratio given the option prices in your sample. If so, the idea is to realise that for each option price you have at different times$t_1, t_2, ...$you could actually close the position and realise the profit or loss. So, basically if you have the option prices you just ... 1 Did the portfolio manager have the option of investing in emerging markets? If yes, use MSCI All-World. If the portfolio has holdings based in countries with "developed markets" yet has has emerging markets exposure to revenue/earnings, the convention is to use MSCI World. 1 I have never seen such an adjustment. While monthly data are irregularly sampled in time (in every way...calendar days, trading days, seconds, etc), that irregularity is likely to be a smaller effect than your choice of data frequency (monthly, weekly, daily data). That said, your question is intriguing because in other fields they do have to deal with ... 1 Normalize for trading days if possible. 1 It obviously depends on what you're trying to do but since we're speaking about returns zero centering is what's usually done because of the null hypothesis claiming that expected excess returns are zero. You zero center the distribution because you want to obtain a distribution satisfying the null hypothesis. In this distribution you then plug your sample ... 1 I would suggest writing the joint density as the product of the conditional densities then estimate parameters using an optimization package. The joint density is given by $$f(r_0, \ldots, r_T) = f(r_0) \prod_{t=1}^T f(r_t|r_0, \ldots, r_{t-1})$$ then the log likelihood function is$\$L = \log(f(r_0)) + \sum_{t=1}^T \log(f(r_t | r_0, \ldots, r_{t-1}) ...

1

I think this is a no-brainer. Only log-returns make sense. The average return can only be computed by averaging the sum of individual log returns. Taking the average of standard (relative) returns does not give you an average of the individual returns. Consider a simple case where the value of an investment alternates between 100 and 50 an odd number of ...

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