# Tagged Questions

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### Basic question on Portfolio Theory

I was revising my stuff about portfolio theory and I noticed that every single time, expected return and corresponding variance or covariance are given! (not calculating ourselves). So I'm just ...
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### 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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### Calculating portfolio weights of derivatives

A rather simple question. You have a portfolio of USD100 in cash. You now take USD10 and buy a derivative that gives you exposure of USD200 to something. What is the weighting of cash in the ...
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### Full Kelly portfolios having same weights as tangency portfolios

I'm currently comparing empirically the differences between Markowitz and Kelly portfolios. I calculated the Kelly weights for monthly return observations over 10 years for a sample of 50 stocks from ...
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### How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
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### 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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### Ledoit-Wolf portfolio weights calculation

I am trying to implement the Ledoit-Wolf minimum variance portfolio strategy on a real-world stock dataset. ...
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### Rebalancing portfolio weights

I have a matrix of returns and weights for every time period. ...
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### optimization with absolute constraints

Suppose I have an optimization where I need to impose ADV-like constraint (for a case where Shorting is allowed): $\max \mu'w - \lambda w'\Sigma w$ $|w| \le V$ $Aw = 0$ and I want to use a ...
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### 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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### Completeness and Hedging Question

A question in some private notes I'm struggling to work through (exam. prep.). (iii) is where I hit a wall with my understanding & I'm lost thereafter. Any help/clarification gratefully received. ...
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### Portfolio Return Contribution by Sectors

I have a table containing the following fields: Date, PortfolioReturn, CashReturn, Sector1Return,...,Sector10Returns 'PortfolioReturn' is the sum of CashReturn + return contributed from 10 market ...
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### 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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### 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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### Are these steps correct to calculate Value-at-Risk with a Monte Carlo simulation?

I have a problem calculating VaR with the Monte Carlo Simulation. I followed the next steps and would like know if it is a right way to calculate VaR or if I need something more? The steps ...
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### Budget Constraint in Duffie's book

On Page 5 of Duffie's Dynamic Asset Pricing Theory, the budget-feasible set is defined as: $$X(q,e) = {e+D^T\theta \in R_+^s:\theta \in R^N, q\theta \leq 0}$$ Compared to Kerry Back's presentation of ...
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### Leverage on ETF the same effect as on portfolio?

While we know that leveraged ETFs do decline in value to zero given infinity, can we also say the same with our portfolio value if we use leverage in our trading activity and seeing our portfolio ...
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### 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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### When would dedicated portfolios do better than 'immunized' portfolios?

We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said: It should be ...
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### How to deal with missing returns when creating value (equal) weighted returns

recently I am doing cross sectional regressions, and getting confused about missing returns. Suppose we have 100 stocks, then we want to construct a value weighted return (or equal weighted return). ...
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### Calculate CVaR for a portfolio

I would like to calculate the Conditional Value at Risk for a portfolio. To be honest, I'm trying for a few days to find an example to calculate for an entire portfolio, not just for one security and ...
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### Portfolio optimzation : efficient frontier with respect to risk aversion parameter with R

I am currently trying to write a little script in R to determine the optimal weights given a fixed risk aversion parameter. The problem I have is that by increasing the risk aversion parameter I think ...
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### How do I show that there is no tangency portfolio?

Question: Suppose that the risk-free return is equal to the expected return of the global minimum variance portfolio. Show that there is no tangency portfolio. A hint for the question states: Show ...
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### Right metric to manage a portfolio based on correlation?

I want to algorithmically add a new investment to an existing portfolio. The decision should be based on a low correlation to the existing assets. E. g. the following situation The portfolio ...
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### 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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### 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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### Portfolio optimised for diversification and regular yield. How to hedge?

Here is a portfolio optimisation for equity dividend and yield designed to diversify holdings and produce regular monthly returns using only ETFs complete with R code. http://prescientmuse.blogspot....
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### Comparing Portfolio Volatility with Index Volatility seems a wrong method?

thanks for looking into this question. I am comparing an investment strategy against the S&P 500 for a financial article I'm writing. I compute volatility of the Portfolio in this way, as the ...
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### I have volatility of a portfolio in year 1 and in year 2. How do I calculate the volatility over the total 2-year period?

thanks for looking into this question. See the picture below (better is right-mousebutton - open in new tab). I also have the price and return data of the Stocks if that's needed to calculate the ...
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### I have portfolio volatility for year 1 and for year 2. What is portfolio volatility for year 1 and 2 combined?

Thanks for looking into this question. Portfolio volatility in year 1 = 15%. Portfolio volatility in year 2 = 20%. What is the portfolio volatility over the timespan year 1 and 2 combined? Is it ...
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### I have portfolio volatility for individual years, can I use them to compute portfolio volatiltiy for subperiods?

Thanks for opening this question. I have constructed some rules for a portfolio with annual rebalancing and am backtesting it for the period 1990-2014. I want to compare the risk-adjusted return to ...
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### Geometric Return & Performance Results for Quarterly Rebalancing

I have a Portfolio that is rebalanced every 3-months. The portfolio is made up of assets that have daily log-returns. I am a bit confused when charting the results using ...
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### Portfolio Optimization to include ALL Securities?

I'm currently optimizing portfolio weights for an investment team with N stocks. We buy stocks with a conviction it will generate a return and it is up to me to determine weighting. However, with ...
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### Sharpe Ratio for loans

I am trying to calculate the sharpe ratio for a set of loans. These loans have already matured and I know if they were good or not: grades are the different grades of the loans. interest rate is the ...
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### 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 ...
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### In a FX options book, is the sum of P&L equal to the portfolio value?

For a portfolio containing FX options, would the sum of P&L for each option be the portfolio value?
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### 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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### How do Return.portfolio and Return.rebalancing work in Performance Analytics in R?

I have a question about the function Return.portfolio/Return.rebalancing from the Performance Analytics package in R. I take ...