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6

This is indeed a subtle point. What is generally meant with this statement is that correlation is going up in bear markets, so it is not so much the "turmoil" part (i.e. volatility per se) but the "trend" (i.e. negative in this case) part. Putting it another way is that when you control for volatility not the correlation but the covariance (which is the part ...


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

Accurately stated: Diversification helps during turmoil, but helps less as what would be expected by using $w^T \Omega w$ as the portfolio variance where the off-diagonal covariances are estimated during tranquil periods. This is because correlations and covariances change during turmoil, typically increasing. This reduces the benefit of diversification ...


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

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 ...


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

Given that by delta means that if the price goes up by 0.01% i.e. one basis point, you gain 15 and vice versa if the price goes down by one basis point. You know that the daily standard deviation is 2.2%, than again you know that $ 220*15 = 3300$ is the standard deviation of your portfolio. So, since we are using a normal distribution you can look at a table ...


1

In many cases, clients want to be fully invested and don't want their assets lying around in cash. Hence the budget constraint $\sum_i w_i = 1$ is fairly common in practice. By the way, there are also cases where the constraint $\sum_i w_i = 0$ is applied: the result is a dollar neutral portfolio with long and short positions, but no net investment (short ...


1

I see your argument with the math. "1" is an arbitrary choice of positive numbers, and you could choose anything. In the end, you're going to scale the whole thing to fit your capital anyway. If you are using a numerical optimizer, it will be happier with something noticeably away from 0 and away from infinity, so I recommend choosing a specific positive ...


1

Portfolio management is about solving problems in the real world. In the real world, it is highly unlikely that EVERY asset has a negative expected return. If all the assets in your universe have negative returns, expand your universe to include a short-term fixed income security that is bound to produce a return greater than (or at a minimum equal to) ...


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

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

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

The approach of reflecting is expensive, since the $d$-simplex has $d$ maximal faces, all of which have to be checked for intersection at each step. Additionally, if the random walk moves into a corner, the number of moves which have to be discarded can become very high. Depending on the configuration of the constraints this could well be your best solution. ...


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 ...


1

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 ...


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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