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

learn more… | top users | synonyms

0
votes
1answer
29 views

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 ...
1
vote
1answer
190 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. ...
11
votes
1answer
516 views

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 ...
1
vote
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 ...
0
votes
2answers
38 views

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 ...
1
vote
1answer
39 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 ...
1
vote
0answers
16 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. ...
0
votes
0answers
9 views

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 ...
3
votes
0answers
39 views

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 ...
1
vote
0answers
24 views

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 ...
3
votes
2answers
37 views

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 $ ...
4
votes
1answer
96 views

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 ...
10
votes
3answers
179 views

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 ...
3
votes
1answer
152 views

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) ...
0
votes
0answers
17 views

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 ...
1
vote
1answer
67 views

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 ...
4
votes
1answer
93 views

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 ...
0
votes
3answers
65 views

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 ...
1
vote
0answers
27 views

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 ...
2
votes
2answers
80 views

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 ...
5
votes
2answers
215 views

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 ...
6
votes
0answers
76 views

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 ...
0
votes
1answer
58 views

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 ...
0
votes
0answers
20 views

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 ...
0
votes
0answers
24 views

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 ...
0
votes
0answers
18 views

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 ...
2
votes
1answer
56 views

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 ...
32
votes
12answers
16k views

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 ...
6
votes
2answers
750 views

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 ...
1
vote
0answers
21 views

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 ...
2
votes
2answers
87 views

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 ...
2
votes
2answers
268 views

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 ...
2
votes
1answer
30 views

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 ...
3
votes
0answers
51 views

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 ...
4
votes
1answer
206 views

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 ...
0
votes
0answers
116 views

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 ...
1
vote
0answers
68 views

Definition of sharpe ratio maximising and variance minimising portfolios

In this paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2226985, in the derivation of the mean variance efficient portfolio using lagrangians in the appendix, on page 29, the two portfolios ...
0
votes
1answer
119 views

Asset Liability Management Test Topic Interpretation

I will write a test based on Excel and one of the topics is "The Asset Liability related analysis: including the input assumptions generation, constraints, portfolio optimization analysis and results ...
3
votes
1answer
126 views

Combining modern portfolio theory and Kelly betting?

I'm using modern portfolio theory to compute the frontier of efficient portfolios. I'd like to pick the best one in the spirit of Kelly betting, ie. maximising expected growth. I'm looking for a ...
5
votes
2answers
225 views

Beta Constrained Markowitz Minimum Variance Portfolio - Closed Form Solution

This question is related to recent rule changes in the Quantopian Open. I am trying to figure out a closed form solution to a beta constrained minimum variance portfolio problem but it doesn't seem ...
1
vote
1answer
49 views

Understanding portfolio weights and purchasing stock in modern portfolio theory

Recently I've been learning about the markowitz algorithm. It's pretty interesting, but I'm curious how we apply this in practice. Lets say I have some optimal portfolio: $R_p = x_aR_a + x_bR_b$ ...
0
votes
1answer
66 views

calculating portfolio volatility [closed]

Given: vector of portfolio weights $W = [w_1 w_1 ]$ correlation matrix $C = \left( \begin{array}{ccc} a & b \\ d & e \end{array} \right) $ standard deviation of the asset returns $S = [s_1 ...
1
vote
1answer
93 views

What Exactly is Expected Return

Consider the following plot, courtesy of this page: Regarding the $y$-axis, how does this "expected return" relate to the "instantaneous expected return" in a geometric Brownian motion (GBM)? E.g., ...
1
vote
1answer
79 views

On a source for a mean-variance portfolio optimization result

In the context of a mean_variance framework consider an optimizing investor who chooses at time $T$ portfolio weights $w$ so as to maximize the quadratic objective function: $$U(w) = E[R_p] - ...
1
vote
3answers
332 views

Finding Expression for Optimal Markowitz Weights

So there are two assets with return rates $r_1$ and $r_2$ which have identical variances and a correlation coefficient $p$. The risk free rate is $r_f$. I need to find an expression for the optimal ...
2
votes
2answers
109 views

When to adjust portfolio weights?

In portfolio allocation literature there is lot of effort made in obtaining 'better' portfolio weights, for example via improving parameter estimates, introducing Bayesian approaches, incorporating ...
3
votes
0answers
61 views

Reference Request: Horse Race for Portfolio Allocation

Probably the most popular horse race study for portfolio strategies is Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?, with DeMiguel, L. Garlappi and R. ...
3
votes
0answers
63 views

Residual Covariance Matrix, and MVO for Residual Variance and Alpha

My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$. We know the equation for residual variance ...