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1answer
155 views

Monte Carlo VaR assuming logistic distribution

I have a Monte Carlo model which measures the Value at Risk (VaR) for given portfolio. I use the geometric brownian motion to model the prices. But let's say I assumed the returns of prices follow the ...
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1answer
178 views

Rebucketing Risk using PCA/other methods

was working on a project and could use some help. New to the community and looking fwd to being an active part of it. My question is, let's say we have a vector of securities V, and it trades with ...
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3answers
433 views

What's the disadvantage of using linear programming for portfolio optimization?

I am a MFE student and we have project on the Markowitz portfolio optimization problem. i am wondering how much impact there will be, if I use a simpler linear optimizater instead of a quadratic one....
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1answer
152 views

FX Portfolio Volatility Targeting

If I have 3 different currency trades (ex short EURSEK, short NZDUSD, long USDJPY), how do I size each trade if I wish to allocate risk equally in order to target a 12% portfolio volatility (allowing ...
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1answer
53 views

Portfolio Selection formulation

I was just wondering why in http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1601412 on page 22, the constraint (48) is a strict equality for the minimum variance formulation. Whereas in a different ...
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1answer
61 views

Desperate for help with simple derivative

Can someone help explain how differentiating the following with respect to $x$: $$ \frac{1}{2} \alpha \mathbf{x}^T \Sigma \mathbf{x} + (\mathbf{\mu} - R\mathbf{1})\mathbf{x} $$ Yields the following: ...
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2answers
64 views

Distribution of the value of a portfolio

Suppose there are k different stocks in a stock market. All of their prices are independent from each other. One year from now the price of the i-th stock will be $X_i^2$, where $X_i \sim \mathcal{N}(...
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1answer
71 views

What do “Exposure Bounds” mean in Portfolio Optimization?

I've just started reading up on Portfolio Optimization models and have come across the use of exposure bounds to mitigate the sensitivity of the optimized model solution, owing to parameter estimation ...
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1answer
296 views

Arbitrage Strategy Proof in Bjork

In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition Proposition 2.9 Suppose that a claim X is reachable with replicating portfolio h. Then any price at t=0 of ...
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1answer
748 views

derivation of formula for portfolio skewness and kurtosis

Where can I find derivation of formula for portfolio skewness and kurtosis? I can find formulas everywhere, but not their derivations? For example, the portfolio variance formula is well known and I ...
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0answers
19 views

Show the expected return of the portfolio and how to derive return variance of the long-short portfolio?

Show the expected return of the portfolio and how to derive the return variance of the long-short portfolio? (see picture)
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0answers
24 views

PortfolioAnalytics: Training window based on entire history before rebalancing in 'optimize.portfolio.rebalancing'?

I am fairly new to PortfolioAnalytics and R in general. I am trying to do some backtesting of a minimum variance portfolio. I have weekly, monthly, quarterly and yearly return data of 3 selected ...
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0answers
22 views

Value weighted Portfolio: Include Market cap of pref shares?

I got Datastream MV data for my sample and i want to exclude Preference Shares. Since Datastreams definition of MV is shares*price there are two Marketvalues, one for common stock, one for preference ...
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0answers
30 views

Factor model alternative? [closed]

Suppose there is a Fama-French model estimated for a stock of Shoemaker Ltd.: $α = 0.01$ $β_M = 0.9$ $r_M = 0.12$ $β_S = 0.3$ $S = 0.05$ $β_H = 0.2$ $H = 0.06$ $r_F = 0.03$ How would you ...
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0answers
32 views

Given multiple strategies with their ER, volatility, how would I calculate the combined Sharpe?

Without knowing the actual daily returns, I have a table something like this: ...
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0answers
46 views

Discounted self-financing portfolio still a self-financing portfolio?

Assume a self-financing portfolio $V_{t}=\theta_{t}^{0}S_{t}^{0}+\theta_{t}S_{t}$ with $S_{t}^{0}$ the value of the non-risky asset at time $t$ and $\theta_{t}^{0}$ the amount of shares of the non-...
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1answer
53 views

Why no median-CVaR optimization for portfolios?

Question Since CVaR is a concept that can be applied to all probability distribution, even if they do not follow normal distribution, I thought CVaR should be more concerned with median, not the ...
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0answers
44 views

Constructing Portfolio Beta

Suppose I have a portfolio with securities with different history. Say some securities have 15-20 years of history and some are like Uber or Lyft, which has limited history. There are assets with 1/2/...
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1answer
114 views

Leverage constraints

I am trying to complete my project on Mean-Variance Leverage Optimization, and I have found lots of helpful advice on this forum. I wanted to ask you if you have some idea on how to implement a ...
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0answers
36 views

Why can't I take the Value at Risk “VaR” as a a risk objective in PerformanceAnalytics? (it does work for "ES)

I am currently playing around with PortfolioAnalytics package in R and some data and I am aiming to create different portfolios with different VaR. However, I am struggling first of all, add.objective(...
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0answers
76 views

Applying portfolio variance weight based on logarithmic returns?

The expected logarithmic return of a portfolio is calculated as : $$𝐸_p = \log\left(\sum_i w_i e^{R_i}\right)$$ Therefore, I was wondering that how can I apply weight to use with the variance based ...
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1answer
75 views

Classifying groups of stocks beyond Market Cap/Industry/Sector

I'm monitoring margin values for a portfolio and I want to classify the stocks in my universe using different metrics/information. Just for the sake of making analysis/inferences on the data I have. ...
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0answers
409 views

Some definitions in the BARRA Predicted Beta model

I'm studying the BARRA Predicted Beta model, and the common factor covariance between portfolio $p$ and the return on the market $m$ is defined as the product of the transposed vector of the factor ...
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0answers
96 views

Holding Period Return abnormally high

I've been doing my Dissertation and I was told to create a value - weighted portfolio on the 1979's 200 largest cap corporations (based on Market Value). I was also told that the correct way to build ...
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0answers
61 views

When does funding cost of a portfolio enter into the portfolio's present value?

This question comes from some confusion when reading Hull's book and from the general concept of no-arbitrage/self-financing portfolios in stochastic finance books. I am not fully seeing the ...
1
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1answer
134 views

Fama Macbeth regression and portfolio sort result contradiction

I ran Fama Macbeth (regression) on two variables called return and lag MAX ( monthly average return and lag of maximum return over a month). the results are like the following : ...
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0answers
46 views

Resource to learn about Long / Short Commodities portfolio

As title says, I'm looking to learn more about Commodities trading and how to report and monitor a Long short Portfolio. Can anyone point me to a good book / website where I can improve my knowledge? ...
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0answers
225 views

Is the Market Portfolio on the Markowitz Efficient Frontier?

I have seen "market portfolio" defined online (Wikipedia/Investopedia) as the bundle of all available investments where the assets are each weighted in proportion to their existence in the market. I ...
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1answer
219 views

Return Contribution for Annual Returns

I have a portfolio $p$ made up of a bunch of assets $i$ where the weights change slowly over time. The returns over each period $j$ composed of the weighted returns of the asset $r^j_p$ $$ r^j_p =...
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0answers
127 views

Backtest Portfolio Analysis

I actually finished an algorithm that i can use to extract all the trades for each stock (each file for each stock). Essentially, i run this code on Excel where there are the input about one stock, ...
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0answers
102 views

Why Do Universal Portfolios Work?

I've been reading up on universal portfolios, but I haven't been able to find an intuitive explanation as to why they have the theoretical guarantees that they do, especially that they track the best ...
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1answer
45 views

What price data should I used when making minimum mean variance portfolio, optimal risky portfolio and efficient frontier using Markowitz? [closed]

I need to make optimal risky portfolio, minimum variance portfolio and efficient frontier using Markowitz . But i don't know whether to used close price data or adjusted data. If i'm using adjusted ...
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0answers
108 views

Assigning Constraints to weights

Suppose I have weights ...
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0answers
363 views

Forecasting volatility with rugarch and Covariance Matrix

I am trying to do a financial time series forecast in order to build a portfolio. I already have some code running rugarch library and I am not sure if I am forecasting correctly, after that I would ...
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0answers
69 views

Stress Test for gamma FX portfolios?

How can I create scenarios to stress gamma FX portfolios? If I shock the underlying for example +/-10%, then I gain in both scenarios. I get to capture some losses if I shock the implied volatility. ...
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0answers
1k views

Calculating weekly portfolio returns for portfolios sorted by volatility

I am having some issues with finding the right code in STATA for sorting the data into portfolios by historical volatility (standard deviation) of returns and then calculating portfolio returns and ...
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0answers
3k views

Problem with determining weights in tangency portfolio (2 risky assets)

I use the following well known formula in order to determine the weight of asset i in the tangency portfolio (in the case of two risky assets): $w_{i,T}=\frac{\sigma[r_2]^2E[R_1]-\sigma[r_1,r_2]E[R_2]...
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0answers
186 views

PnL Explained Using Scenario(Full Reval Model)

I was wondering if any quant guru can help . How to calculate the PnL explained using full reval aka scenario based = > t - (t-1) approach for linear instrument. I am finding difficulty to understand ...
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0answers
231 views

How to form Decile Portfolios based on Liquidity measure with missing data in R

I have a dataframe with over 4000 companies data (as column) and have calculted their daily Quoted spread measure ( measures liquidity for each stock) for 15 years. And then from the daily have ...
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0answers
94 views

Determining the investment strategy

I have the following problem: Consider the 5 year investment strategy and given the yearly portfolio returns $S_{t+1}/S_t$ and dividends $D_{t+1}$ paid at $t+1$ which are modeled as: $\frac{S_{t+1}}{...
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0answers
69 views

How to build a bond model portfolio (Invested in Emerging markets) [closed]

I have to build a model portfolio from the data of a portfolio composed of bonds from Emerging Markets accounted in $ (So exclusively corporate bonds from emerging markets). Do you have any ...
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0answers
118 views

Can anyone suggest book about fixed-income portfolio management? [closed]

Can anyone suggest books about fixed-income portfolio management? Thx
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0answers
65 views

How to understand stock return comovement

In his book "Asset Pricing" chapter 20, Cochrane said For example, suppose that average returns were higher for stocks whose ticker symbols start later in the alphabet. (Maybe investors search ...
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0answers
572 views

bandwith portfolio rebalancing in python

I want to calculate a bandwith rebalancing machanism for a portfolio of two assets. As soon as the performance of one ov the assets gets bigger or smaller than the other one + a defined tolerance ...
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0answers
58 views

Investing in all assets with positive expected return and allowing for positive correlation

How does the answer to this question Risk minimization by investing in all assets with positive expected return change if assets can be positively correlated (but not perfectly) and short sales are ...
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0answers
446 views

Tangent portfolio weights without short sales?

Consider a mean-variance investor in a world with a risk-free asset. Let $R_f>0$ be the return of the risk-free asset, $\mathbb{E}(R_i)>R_f$ the expected return of the risky asset $i$ and $SD(...
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1answer
73 views

In theory historical performance of a portfolio

I am looking at the quantitative model our team is using for analyzing the performance of a portfolio of stocks. However I don't understand what the model is trying to achieve. The model is supposed ...
1
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1answer
168 views

Combine together different strategies in one portfolio [closed]

Hi I have generate equity of my strategies which invest in commodities and currencies at daily interval. What the best method to combine together all strategies in one portfolio? I want to make the ...
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0answers
79 views

how to find CVaR/AVaR for triangular fuzzy no

While going through different methods of risk measure i came across AVaR/CVaR, while i was calculating AVaR/CVaR in credibilistic environment using VaR, i got stuck in the calculations eg. For ...
1
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1answer
277 views

Resampled efficient frontier length of simulation

I was provided with a VBA program from my lecturer that applies the resampled efficient frontier. We have an investment horizon $T$ (6 years) and he uses a multivariate normal distribution with ...