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10 views

Why do we assume quadratic utility in portfolio theory?

In my text (Investments by BKM), the investor's mean-variance utility (given as $U = E[R] - \frac12A\sigma^2$) is stated to be the objective function we wish to maximize. Upon further digging, it ...
0
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1answer
46 views

Is there a way to meaningfully generate daily returns from monthly?

I have a set of 7 investments in a portfolio and I need to optimize the weightings based on some exposures to various markets/styles/economic factors. I was hoping to do some sort of simple exposure ...
1
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0answers
43 views

Optimize a trading strategy created in excel with R

I have created quite a complex back test in excel spanning 15 years with 17 parameters. I would like to optimize the parameters which would give me maximum return given a maximum draw-down percentage. ...
0
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2answers
36 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
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1answer
42 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: ...
0
votes
1answer
33 views

Closed-form solution to optimal single assset position sizing with predicted returns

Say that I observe a predictor $w_t \sim N(0,\sigma_1)$ for the returns in a single asset over the next time interval: $$ r_t = \alpha w_{t-1} + z_t $$ where $z_t \sim N(0,\sigma_2)$ is unobserved ...
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0answers
12 views

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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0answers
36 views

First step of Black-Litterman portfolio

I tried to implement Black-Litterman model. I have a covariance matrix, market capitalization for each asset. I assume a risk aversion factor to be 10. First I use the following code to get ...
8
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0answers
144 views

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 ...
5
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1answer
128 views

Portfolio Optimization using Parametric Portfolio Policy Method in MATLAB

I want to contruct an optimized stock portfolio with the restriction of a zero-investment strategy. The portfolio weight in each stock needs to be modeled as a function of state variables (factors ...
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 $ ...
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0answers
23 views

derive variance of a portfolio

I'm stuck on a derivation of the variance of a portfolio of securities $K_1,K_2$ formula The end result is $Var(K_v) = w_1^2Var(K_1)+w_2^2var(K_2)+2w_1w_2cov(k_1,k_2)$ Proof so far: Let $K_v = ...
4
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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 ...
1
vote
1answer
37 views

Effect of different maturity options in delta-gamma-hedging

I read about hedging with options and think i got it. However there is a case am not sure how to handle. Is there any exception in the delta-gamma-hedging-(calculaton-)technique? - say: solve an set ...
3
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0answers
19 views

How to optimize an arbitrage portfolio when taking into account different speeds of mean reversion?

In portfolio optimization, it is insufficient to just note the size of price deviation - that only tells the amount of profit if held to maturity. One also needs to take into account reversion speed - ...
0
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0answers
25 views

Properties of optimization under shortfall constraints in R

Properties of optimization under shortfall constraints in R. Hi, I'm having trouble optimizing a portfolio for a school project, which has been bothering me for a week. What I want to do is to ...
0
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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
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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 ...
5
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2answers
114 views

Is it possible to deal with non-normal distribution in Black-Litterman model?

Suppose that I know that the normality assumption about my data is unrealistic (as it is very frequently): is it possible to apply any distribution that I judge the right one to the Black-Litterman ...
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0answers
59 views

Implementation of Kelly in multivariate case using modeled distributions

I am exploring how to determine an "optimal" portfolio in the context of real life data and systems. Specifically, I want to calculate a Kelly Optimal Portfolio (see this paper, especially section 8.4 ...
1
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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 ...
0
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0answers
50 views

How can i build a portfolio of n assets that maximizes sortino ratio?

I want to construct a portfolio of n assets that maximizes the Sortino ratio. I want to use SOCP for the optimization but cannot formulate the Sortino ratio as a SOCP problem. How can I do this?
2
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1answer
237 views

Portfolio Analytics Optimization

I have a large dataset, 10,000 investments I am trying to create an optimized portfolio for. The portfolio has 3 restrictions. Long Only, Only 50 assets can be selected and every invested asset has ...
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0answers
54 views

Portfolio Optimization with equal weight for assets selected

I have a data frame of bets, with 1 being a win and 0 being a loss. These bets are correlated so I cannot just pick the highest winning percentage. Goal is to get 2 optimizations, 1 for max sharpe ...
0
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0answers
21 views

Bond's bid-ask spread with no arbitrage assumption

Suppose I have a bond with unknown bid-ask spread, and a portfolio, containing it and also other bonds, all with known bid-ask spreads. How can the unknown spread be inferred? I assume there should ...
6
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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 ...
2
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1answer
64 views

Understanding CAPM, CML, and efficient portfolios

I'm trying to understand the CAPM model and how we can use it to understand efficient portfolios. Specfically, I'm trying to use the CML line (mapping expected returns and standard deviations of ...
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0answers
25 views

Constrained portfolio optimization - orthogonalize factor exposure

I am optimizing a stock portfolio with a few factors. If I constraint exposure to one of the factors to be a constant and set the exposure to other factors as zero. It is ok to use a diagonal factor ...
0
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0answers
14 views

Min-VAR portfolio construction in a universe of dividend stocks - choosing the observation period

The portfolio construction method of min-variance and similar concepts were discussed quite heavily in the recent past (see for example Thierry Roncalli's page). Over long horzon's we see ...
0
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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
0answers
45 views

OHLC Covarianc Estimation

Is there an R package which can estimate a covariance matrix using OHLC (Open/High/Low/Close) share prices for upwards of 40 shares using the Yang & Zhang method using daily data? I google ...
2
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2answers
80 views

How to perform portfolio optimization with user-defined expected return and variances using R?

I found some functions for Markowitz mean variance portfolio optimization in R such as portfolio.optim in tseries package. ...
1
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0answers
30 views

Commercial Vendors for Risk Management and Portfolio Optimization and Performance Attribution

So this question is directly about companies such as Axioma, Barra, Northfield, and etc. that provide risk management, portfolio optimization, and performance attribution related services. I want to ...
2
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2answers
86 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
267 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 ...
3
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3answers
171 views

Could we estimate a portfolio's volatility using a GARCH on the portfolio returns?

Estimating the volatility of a portfolio is typically done by first estimating the covariance matrix. This, however, can be difficult to do accurately and predictivly. This paper gives a nice summary ...
3
votes
1answer
48 views

optimization to maximize number of positive days

suppose I have $N$ models, with returns $r_{n,t}$ over $1,...,T$ periods ($T>>N$). I want to find weights $w_n$ for model $n \in 1,...,N$ such the final model $p$, whose returns will be $r_{p, ...
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2answers
165 views

Utility Theory and portfolio optimization - Proof of a lemma

I have a question on the following problem from chapter 9 of D. Luenberger, Investment Science, International Edition: (Portfolio Optimization) Suppose an investor has utility function $U$. ...
1
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0answers
26 views

Portfolio Hedging under Uncertain Correlations

I have a portfolio ($w_0=1$) and two hedging assets ($w_1,w_2$) and a co-variance matrix for the three $\Sigma$. However the co-variance $\Sigma$ is only an estimate. For fairly well behaved assets ...
1
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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 ...
1
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2answers
85 views

Portfolio Strategies Project

My first assignment for my Quantitative Finance Masters is to design a portfolio that theoretically makes money under any market movement. I am also asked to state all necessary assumptions. What ...
1
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0answers
37 views

Shrinkage Estimator giving unrealistic portfolio variances

I have a historical covariance matrix which is invertible for daily and monthly returns. I used the Ledoit,Wolf shrinkage estimator for the covariance matrix and now I get really small portfolio ...
4
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3answers
164 views

market neutral weights and cash values

I am looking at a market neutral portfolio and have a question which I think is probably pretty simple. So I can see the individual stock weights. ...
2
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0answers
55 views

soft vs hard contraints in portfolio optimizations

Consider two sample portfolio optimizations: Optimization 1: $\begin{matrix} \\ \min \frac{1}{2} w'\Sigma w \\ w'\mu = r \\ Aw = 0 \\ w_l \le w \le w_u \end{matrix}$ Optimization 2: $\begin{matrix} ...
1
vote
1answer
55 views

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 ...
0
votes
2answers
70 views

Correlation Between 2 Portfolios

I have a set of assets, n. I'm trying to find the correlation between 2 portfolios, say x and y, where x is nested in, or, a sub-set of y. That is, x is a portfolio based on a sub-set of n, while y is ...
2
votes
1answer
123 views

How to scale $\alpha$, trading costs in a standard portfolio optimization problem

In the usual "portfolio optimization problem under linear constraints". Let me define the terms here. $$ \text{Find } w^*=\underset{w}{\text{argmax}} \ \ r^Tw - \lambda w^{T} \Sigma w - ...
3
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0answers
177 views

Calculating Net Annualized Return on LendingClub historical data

I am interested in the formula LendingClub provides as their measure of "Net Annualized Return": $\big(1 + \frac{\sum_{i=1}^N{((I_i + L_i - S_i - C_i + R_i) / P_i) ...
4
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1answer
123 views

Matlab Portfolio Optimization with bid ask spread

I'm trying to find the optimal portfolio of options and stock which minimizes the standard deviation of the portfolio returns but also taking into consideration the bid and ask prices of the assets. ...
8
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1answer
131 views

Are there references about liquidation, transaction, market impact costs in portfolio optimization

I am looking for some references treating of what I would call liquidation cost market impact cost transaction cost(*) in the usual "portfolio optimization problem under linear constraints". Let ...