# Tag Info

5

It appears that you are re-running the regression with each new data point. Instead, you should use an update/online formula (see an excellent answer by the famous Dr. Huber at stats.se). You can find an implementation in the R package biglm. If it doesn't have all the features you need (no windowing out of old data) you can at least adapt it and use it ...

3

There are several measures discussed in the literature, the classical approach is Markowitz mean-variance portfolio optimization. The formula for portfolio return variance is $$\sigma_p^2 = \sum_i w_i^2 \sigma_{i}^2 + \sum_i \sum_{j \neq i} w_i w_j \sigma_i \sigma_j \rho_{ij}$$ where $\rho_{ij}$ are the correlations betweent the assets. Others suggeste ...

2

You are not doing anything wrong. You just need to multiply the absolute return by the currency conversion factor. Example: You trade 200,000,000 yen notional and generate a return of 16% on that notional, then simply multiply 32,000,000 jpy gain by your conversion factor 0.0126 to yield a return of 403,200 USD. The return of 16% was generated on the ...

2

One approach is to use an exponential utility function: $U(x) = -e^{-\lambda x}$. Here, $\lambda$ records what is known as the absolute risk aversion. Exponential utility functions are nice because they have a wealth independence property (of course, this may be seen as a drawback). As we will see below, the initial capital $X$ plays no part in the ...

2

You should have a look at chapter 8 (p. 261ff.) of Hedge Fund Market Wizards by Jack D. Schwager Excerpt from there (but it is much more detailed in the book): Perhaps the most potent risk control Platt employs in BlueCrest’s discretionary strategy is maintaining an extremely tight rein on what a trader can lose before capital is withdrawn. A mere 3 ...

2

There is a formula for calculating ES from a normal distribution. There is also a formula for ES of arbitrary distributions using a Cornish-Fisher expansions (easy for univariate processes but frustrating for multivariate). However, the most common approach is a scenario representation of the distribution. This could include using the historical distribution ...

2

Let's start by replacing $\sigma$ by its estimator formula $\sigma^2=\frac{1}{n}\sum^n_{i=1}(x_i-\mu)^2$. Now, by replacing $\mu$ by its estimator $\mu=\frac{1}{n}\sum^n_{i=1}x_i$ in the formula for the variance we obtain: $\sigma^2=\frac{1}{2n^2}\sum^n_{j=1}\sum^n_{i=1}(x_i-x_j)^2$. For the individual asset, the variance will write ...

2

I think some some terminology got mixed up here. Let $r_t$, $t=1,\ldots,T$ be a series of iid excess returns with the estimated mean excess return $\bar{r}= \sum_{t=1}^Tr_t$. Then the Stutzer Index $S$ is defined as $S=\frac{|\bar{r}|}{\bar{r}}\sqrt{2I_p}$ with $I_p$ being the "Stutzer Information Statistic", $I_p=\max_\theta -\log(\frac{1}{T}\sum_{t=1}^T ... 1 A very simple approach could be the following: draw a random number for each day for each stock. If you refer to "average/mean" by return and to "standard deviation/variance" by volatility, you could use these for the distribution parameters of the random numbers per stock. If you dislike that values can go below zero, apply Euler's exponential function on ... 1 In mean-variance analysis, you combine different assets to minimize variance and maximize expected return. The hyperbola is not a function of the number of assets, but of their mean and variance. If the efficient frontier where a tangent to the y-axis (which can't be) or nearly a tangent, that would mean you would have almost zero portfolio-variance, which ... 1 I perform this kind of analysis using the risk contribution concept. I understand from this post that your already know about the contributions, but let's just restate the idea here for the sake of completeness. We have a portfolio of$n$assets with allocation$w \in \mathbb{R}^n$and volatility$\sigma_P(w)$. The marginal risk contribution of asset$i$... 1 I did some calculations in mathematica in the 3 asset case. Assume we have exposures$w_i,i=1,2,3$and volatilities$\sigma_i,i=1,2,3$and correlations$\rho_{1,2},\rho_{1,3},\rho_{2,3}$. Let's assume$\sigma_1=\sigma_2=\sigma_3=\sigma$for some arbitrary positive$\sigma$. For the weights we assume$w_2=w_3 = 0.5$and we have a short in asset 1 of$w_1 = ...

1

You should definitely check out the Virtual Stock Exchange Games* by Marketwatch it provides simple interface, and many options for the rules of the game. Its instantly online, free, and uses real-time prices, but it only allows trading NASDAQ stocks, as far as I know. These games are meant to be played by students, and thought, so I hope it fits your ...

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I'm currently also using daily returns which I want to annualize. This is my approach: For every month, I calculate the simple return using the formula: (end-of-month closing price / beginning-of-month closing price) - 1. I use the Excel formula somproduct(geomean(A1:A12+1)-1) to find the monthly compounded return. Finally, I annualize the result of step 2 ...

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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

First of all, AM is always greater than or equal to GM $$x_1 + x_2 + ... + x_n \geq \sqrt[n]{x_1x_2...x_n}~\forall x_i \geq 0$$ You can prove it by induction from $\frac{x_1 + x_2}{2} \geq \sqrt{x_1x_2}$ or put $f(x) = \ln(x), p_i = \frac{1}{n}$ to Jensen's inequality to get it. The equality holds when $x_1 = x_2 = ... = x_n$. For author 1 and 2, We ...

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