# Tagged Questions

A theoretical framework for analyzing investment portfolios based on their expected return and risk.

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### Models crumbling down due to negative (nominal) interest rates

Given that the negative interest rates on a lot of sovereign bonds with maturity under 10 years are trading in the negative (nominal) interest rate territory (recently also the short term EURIBOR has ...
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### 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 ...
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### 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 ...
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### Tangency portfolio and CML - Why does it have the highest sharpe ratio?

In the book that I am studying, the tangent portfolio was defined as the regular efficient portfolio in the case with $n$ risky assets and 1 riskfree asset with the extra requirement that the ...
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### How to determine portion of portfolio's risks from components?

Say I have a portfolio of 3 stocks $A,B,C$ with $\mu_A = 5%$, $\mu_B = 10%$, $\mu_C = 15%$ and volatility $\sigma_A = 10%$, $\sigma_B = 15%$, and $\sigma_C = 25%$. Let us also say that correlations ...
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### 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. ...
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### 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 ...
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### Portfolio Theory: Must VarCovar Matrix be based on return var/covar?

I am trying to estimate the minimum variance portfolio where the assets are currency derivatives. In the specific case it does not make sense to base correlations or variance on asset returns. I am ...
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### 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 ...
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### 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. ...
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### How to set the mean matrix in fPortfolio package in R

I'm doing a mean-variance analysis of 5 ETF's and insted of using the sample mean i used a time series model to forecast it. I want to do a backtest of a tangency portfolio getting the weights with ...
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### Interpreting different factor models w.r.t. correlation matrix and min variance portfolio weights

Background In Eric Zivot's analysis of factor models he uses three models The sample (.sample) Single index model (.si) Barra factor industry model (.ind) PCA model (.pca) You can download his ...
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### Embedding the naive portfolio into economic decision theory

I am trying to gain some insights about the vast literature of portfolio optimization and I hope to get some help when it comes to embed the most standard allocation strategies into a coherent ...
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### Dealing with a constraint which is the square root of a quadratic form

I'm trying to maximize my portfolio, but don't know how to deal with the constraint which is on the form max $2u^Tx-x^T \Sigma x$ Subject to $e^Tx = 1$ $u^Tx - m (x^T \Sigma x)^{1/2} >= c$ ...
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### Mixing Portfolio Strategies

Given a set of $N$ assets, the amount of strategies proposed in literature to diversify the investors wealth in order to find the 'optimal' portfolio is overwhelming. However, for example DeMiguel et ...
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### Portfolio construction in reality?

There are various models for portfolio selection in literature, like, Harry Markowitz (HM) model ( Mean-Variance Model) [well known model] Konno and Yamazaki (1991) model: minimizes the sum of ...
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### Portfolio with lots of subportfolios

An account manager has $N$ distinct, equally-sized pots of money, which will be used to make $N$ distinct subportfolios, each of which is drawn from a slightly different (but potentially overlapping) ...
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### Reference Request: Portfolio Optimization Conditional on downside threshold

Under a standard portfolio optimization framework we have some idea of a predictive return distribution $r_{t+1}$ and a Utility function $U(r)$, in the best case in a 'nice' form (differentiable etc.)....
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### Portfolio optimization

first I just hope that this question is in the right place. I have started working on portfolio optimization and the formulation of the problem and their solution : For example in the Markowitz ...
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### Calculate mean variance portfolio

I am trying to calculate the mean variance portfolio using the plug-in approach. First I generate some artificial data: x <- replicate(10,rnorm(1000)) Then I ...
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### Interpretation of portfolio standard deviation

I have computed an efficient frontier using quadratic optimization algorithm for some stock data and then plotted it. However, I have troubles understanding how to interpret standard deviation of ...
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### Change in portfolio when IPO announced

I'm wondering whether there would be a change to my answer of the change in portfolio when there is a new stock introduced. My investment strategy is to maximise expected return such that my standard ...
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### Does anyone know where I can find a free efficient frontier tool, or an informative and legitamate/academic graph of the efficient frontier?

I'd like to build a portfolio based upon modern portfolio theory and I'd like to find a tool I can use to calculate the proper mix of asset classes. Can anyone help with this? I think a good chart/...
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### How to implement Konno's Mean-Absolute Deviation Portfolio Optimization Model using LP methods in Excel

Konno proposed a LP method for portfolio optimization using the Mean Absolute Deviation (MAD)
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### Intuitive explanation of stochastic portfolio theory

Fernholz and Karatzas have published various papers about so called stochastic portfolio theory. Basically they say that the return to be expected from a portfolio on the long run is rather the ...
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### portfolio optimization averaging weights, what are benefits?

I'm playing around with different portfolio optimization techniques. Amongst others I was also looking at the resampling method, especially the one described in Meucci. I have two general questions ...
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### Mean variance efficient portfolios and target returns

If I use mean variance optimisation to create an efficient portfolio with a target expected return of 20% in a year's time and find that the actual return at the end of the year was 24%, what explains ...
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### Portfolio construction for signals of varying time scales?

Wondering if anyone is aware of any research on combining/portfolio construction of signals on different time scales. For example, if I have a trading signal (alpha) that generates trades every hour ...
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### How to estimate variance-covariance matrix of assets with different length of historical data? [duplicate]

Consider you have 4 assets A, B, C and D, where Asset <...
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### Portfolio value containing stocks and a bond

Consider: 1000 dollars invested in stock portfolio and a zero coupon bond. Investment period: 30 years Yearly retur for the stock portfolio: Rk = eµ+σZk , k is after year k Zk are normally ...
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### High Beta 'Filter' for Minimum Variance Portfolios (MVP's) - Lower Risk/Improve Return?

I am busy conducting research in South Africa on the JSE. I am investigating several risk based portfolios with an emphasis on MVP/min vol. My process is as follows: Although the JSE has around 400 ...
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### How to calculate a hypothetical minimum-variance point?

If we have $N$ assets which are uncorrelated, but have the same mean return of $\mu$ but the variances are different where $\sigma_i^2$ is the variance of each asset $i = 1, 2,...,N$ how can you write ...
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### Why does the minimum variance portfolio provide good returns?

I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get ...
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### Which algorithms do robo-advisors use?

Some pundits claim that there is a revolution in portfolio management under way: The rise of the robots, a.k.a. robo-advisors. The most well known are Betterment.com, FutureAdvisor, Schwab Intelligent ...
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### Market portfolio [closed]

If I create portfolio consisting of three stocks and build efficient frontier for this portfolio and if there is a risk free rate for treasury bills and then I draw tangent line from risk free rate on ...
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### Mean Variance Portfolio theory and real-world problem?

There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example 1) investors have the same information at the same time: calculating expected returns ...
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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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### Can adding an uncorrelated high vol strategy to a low vol portfolio result in a portfolio with even lower volatility?

Let's say I have fund A with 20% annualized volatility and portfolio B with 15% annualized volatility. If A and B have 0 correlation, can the combination of these funds have volatility < 15% ? Are ...
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### Finding mean vector and covariance matrix for annual returns given quarterly returns

I am currently trying to calculate a vector for the mean annual returns of 4 different asset classes along with their 4x4 covariance matrix in excel. However, I am having problems since the data I ...
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### Difference between Sharpe Ratio and Information Ratio

I am finding it difficult to understand the difference between the sharpe ratio and the information ratio and the relationship between the two, and cannot find a decent reference that breaks it down ...
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### Interpretation of the CAPM model under Stochastic Portfolio Theory framework

The CAPM under the Modern Portfolio Theory approach is given as: $$R_i = \beta_i R_\pi$$ Where $R_\pi$ the portfolios expected excess returns Under the stochastic portfolio theory approach:  r_i ...