# Tagged Questions

The professional management of an investment portfolio of various securities (shares, bonds and other securities) in order to meet specified investment goals. The process includes the specification of investment objectives and constraints, choice of asset mix, formulation of portfolio strategy, ...

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### How exactly are correlated defaults used/analyzed?

I've read a lot about correlate defaults but I can't seem to understand how they're used practically in a portfolio theory setting. Suppose I have two (?) companies, X and Y, and historic default ...
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### Evaluating trading strategies by the skewness of returns

How to deal with skewness of returns when evaluating different trading strategies? More specifically, I'm back testing different strategies to be implemented as an automated black box strategy. While ...
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### How to evaluate minimum-variance strategies against perfect information mvp

The minimum variance portfolio should minimize the standard deviation (variance) of the portfolio at time $t+1$. The covariance matrix $\Sigma_{t+1}$ needs to be estimated in order to form the mvp. ...
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### Return.portfolio error from PerformanceAnalytics package

When using the PerformanceAnalytics package of R, I am getting an error from the Return.portfolio function whenever I ask it to rebalance_on any frequency. If the rebalance parameter is removed, the ...
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### What does each bar in the empirical average eigenvalues spectrum of the correlation matrix of log-returns of stocks represent?

An example diagram, taken from this paper, looks like follows: What is its physical interpretation? The highest eigenvalue, the paper says, represents market mode. So, what does the difference in ...
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### “Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
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### help with p&L vectors historical simulation

My question is about the calculation of the Value at Risk based on historical simulation. I have a table which contains the P&L-vectors of each day of one year. But I don't know what is contained ...
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### Portfolio with a certain pay-off curve

I would like to find a relevant optimization option's portfolio models which can describe a certain pay-off curve (objective function) under same assumptions. For example, assumptions on how to limit ...
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### How to perform risk budgeting for non-linear portfolios?

I am using this question to compute optimal weights following a risk budgeting approach. The problem is I am using non-linear portfolios (options,equity,fixed income,fx). What I am looking for is ...
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### Implementation of an option tail-hedging strategy

This question directly refers to the paper "Capital Asset Pricing Mistakes: The Consistent Opportunities in Tail Hedged Equities", http://www.universa.net/Universa_SpitznagelResearch_201501.pdf. Very ...
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### What does an optimized portfolio really tell us?

I am very new to this field, and have very recently started doing some self study on this topic. After reading some papers and reproducing some of the results in them, I am not very clear about what ...
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We define the following notions for a jointly normally distributed random vector $P=(P_1,...,P_n)$ with f the density function. $$\mu=\int_{-\infty}^{\infty}(x_i-\mu_i)f_i(x_i)dx_i$$ $$\sigma^2_{ij}=... 0answers 24 views ### Architecture and Infrastructure for Robo-Advisor [closed] Does anybody have any knowledge of Architecture and/or Infrastructure needed for building your own Robo Advisor. I am looking for directions to get in-depth knowledge for building your own Robo ... 1answer 32 views ### Beta = 1 and 0. Type of portfolios I read in E. Quian's "Quantitative Equitity Portoflio Management" the following: A traditional long-only portfolio [with unit beta] would have most of its risk in the market risk. However, a zero ... 2answers 35 views ### What is a definition of “Benchmark”? The word "benchmark" is often used in Finance, but in a rather fuzzy manner, there for a rough idea of what it is, and how it is 'defined'. Can someone provide a rigorous and precise definition of ... 0answers 52 views ### Physical interpretation of variance in returns in a portfolio design I have a downloaded the log-returns at successive times of 98 stocks from S&P index over 753 days. I calculated the total daily return according to the formula 1 below, where ... 0answers 33 views ### Black Litterman: Is it possible to have multiple views (from different sources) on the same asset? From the basics of Black Litterman I understand that each view on a stock is implemented via the pick matrix P with the expected value of the views in Q. I have read several papers where each stock ... 1answer 32 views ### Are financial returns considered more volatile in recessionary times as opposed to expansionary times? I need help in understanding some results that I have obtained. I am doing some out-of-sample performance analysis for different targets of volatility in mean-variance optimization where I solely ... 1answer 6 views ### What is the u vector in the expression for the weights of the min variance portfolio I was working on my finical math homework where I need to find the minimum variance portfolio. I need to use the following matrix expression. Nowhere in the class notes does the instructor say ... 0answers 23 views ### How to Neutralize Portfolio across economic sectors and industries using modified Alpha? I am reading about Alpha and Portfolio Construction topic while reading i came across below point. Active management should be easy with the right alphas. Sometimes it isn't. Most active managers ... 2answers 65 views ### How to Calculate Minimun total Risk? Is it possible to calculate Minimum Total Risk mathematically for below problem. ... 0answers 26 views ### Fund Separation Theorem for Performance Seeking Portfolio Can someone explain this statement? "The beauty of the fund separation theorem is that the performance seeking portfolio mandate is the same for all investors" 0answers 54 views ### subadditivity of VaR It is known that the VaR (Value at risk) doesn't fulfill subadditivity, i.e. VaR(X)+VaR(Y) \le VaR(X+Y) But for elliptical distributions subadditivity is true. Questions: (1) Which ... 1answer 216 views ### how can we know the residual return will be uncorrelated with the market return I was reading that if we know a portfolios beta we can break the excess return on that portfolio into a market component and a residual component. ... 0answers 33 views ### calculating long short portfolios currency exposure I have calculated the currency exposures of a long short portfolio simply by summing the weights of each stock. However I was told that I need to incorporate the dollar borrowing (short dollars), I ... 3answers 40 views ### How to compute the foreign exchange volatility within a portfolio Suppose I have a portfolio of 5 assets. Assets 1 and 2 have foreign exchange exposures and therefore foreign exchange volatility. How can I calculate the marginal contribution to the total portfolio ... 1answer 41 views ### given someone's past investing history, is there a way to calculate his risk aversion? given someone's past investing history, is there a way to calculate his risk aversion? Say, we know this client's investment history for example his past return, is there a way to calculate his risk ... 0answers 22 views ### How to Rank assets in Portfolio? [closed] I am working on active equity Portfolio. I have total 30 securities in my Portfolio. Can someone please guide me how can I rank those assets in my portfolio. ... 1answer 49 views ### Portfolio optimization - maximize variance with exposure to risk factors equal to zero Optimize a portfolio such that the exposure to risk factors is zero and the variance is maximized (instead of traditional minimization problem). so the optimization problem look like:$$maximize\;w^...
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I am learning the basics of portfolio management. I am confused about different ways to calculate rate of returns mentioned in the text investment and portfolio analysis. There are three methods to ...
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### Having Difficulty With Sharpe Ratio and Optimal Portfolio

I have begun by using such equations as: By finding the $Rp$ and $\sigma p$ with the weighted values, and then I followed the equation using a value of $.02$ for the fixed asset, $rf$, but this ...
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### What to use as portfolio diversification measure?

Suppose that we have a portfolio of $n$ assets. A perfectly diversified portfolio is one in which each asset has equal weights, i.e. each asset has weight $\frac{1}{n}$. Of course this is usually not ...
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### Calculating portfolio returns from a dynamic, optimal re-balancing strategy

I am calculating a dynamic strategy with optimal re-balancing as in here. As a result of maximizing the expected utility function I obtain the weight for the risky asset in period $t=0$. All such ...
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### What assets other than bonds are risk free?

I saw a question the other day that said Assume you have only two assets to build a portfolio. Name and explain three scenarios under which a completely risk-free portfolio can be formed? I ...
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### Real world application of stochastic portfolio theory

There is a branche of stochastic portfolio theory (see also this question). Fernholz and Karatzas have published research in this field (e.g. "Diversity and relative arbitrage in equity markets") and ...
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### One period optimizations with tcosts, few predictions and getting positions unstuck

Consider a one period portfolio optimization with objective that maximizes $\omega E(r) - \lambda_r\omega^t\Sigma\omega - TC$ Where TC is however we calculate tcosts/impact. Importantly, most ...
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### Construct option and stock portfolio

If a riskless security costs 100 today and will cost 120 at time T, a stock costs 50 today and will either be 70 or 30 at time T, and call options on the stock have strike price 50 expiring at time T, ...
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### What is the difference between group and inequality constraints in Matlab?

Sorry if this seems stupid. I was wondering what the difference between a group and inequality constraint is in Matlab. As far as I can tell they are the same: From Matlab (http://uk.mathworks.com/...
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### Under which conditions the minimum variance portfolio involves no short selling?

If $\rho_{12} < 1$ or $\sigma_1 \not= \sigma_2$ then $\sigma_v^2$ representing the variance of the portfolio with weights $(w_1, w_2) = (s, 1-s)$ as a function of $s$ attains its minimum value at: ...
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### Computing $\gamma$ and $\mu$ at the efficient frontier

Consider the condition which the weights of any portfolio belonging to the efficient frontier satisfy: $$\gamma\boldsymbol{wC} = \boldsymbol{m} - \mu\boldsymbol{u}$$ ...
Compute the expected return $\mu_V$ and standard deviation $\sigma_V$ of a portfolio consisting of three securities with weights $\omega_1=40\%$, $\omega_2=-20\%$, $\omega_3=80\%$, given that the ...