Questions tagged [portfolio-management]

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, selection of securities, execution, revision, and evaluation.

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1answer
2k views

Calculating alpha and its meaning

According to wikipedia, CAPM model is described by: $E(R_{i})=R_{f}+\beta _{{i}}(E(R_{m})-R_{f})$ And according to website such as http://investexcel.net/jensens-alpha-excel/, $\alpha = E(R_{i}) - ...
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1answer
289 views

What is a notation '1' in risk neutral probabilities paper?

I'm reading the paper by Zhao et al (2008) and have a problem with used definitions in the text on the page 1535. First, we generate a sample, $R$, of a given size from the distribution (21). Let $\...
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1answer
1k views

What is the difference between the Single Index Model and Multi-Index Models in computing the variance-covariance matrix of stock returns?

Would be very grateful for some help in comparing the single index model with other multi-index models in computing the variance-covariance matrix.
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243 views

if you short sell? And Right issue has taken place, so Does Right issue has negative positions in Portfolio or not?

I am searching for exact accounting example of Stock right position in Portfolio when someone is short sell. Searched a lot over Google, contacted local Brokers as well..Didn't get any response. ...
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What is the total correlation between assets in a portfolio?

Suppose I have portfolio with 10 assets, each one of them with a weight of 10% from the total portfolio (equally weighted). It's well known how to measure from historical prices->returns a variance-...
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1answer
540 views

Minimize overall portfolio turnover under constraints

Assume I have M portfolios, each of them can be represented as a T by N matrix, where N represents number of stocks traded and T represents number of days. For each portfolio matrix, each row is under ...
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86 views

Compute gaussian VaR with a “1-month horizon”

I am trying to compute VaR for a long-only equity portfolio, under the assumption that all stock returns are normally distributed, using a "1-month horizon" methodology. How do I do it? Do I compute ...
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43 views

Future Quotes on the S&P 500 Index

I am looking at the following quotes of the futures prices of the S&P 500: http://finance.yahoo.com/q/fc?bypass=true&s=ESM16.CME&ltr=1 The way I read this, the market thinks that ...
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1answer
119 views

Covariance matrix for VaR: what to do with missing data?

I need to compute a covariance matrix using three years of stock returns from a portfolio which has a couple of stocks with only one or two years of history (being relatively new stocks). Should I ...
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1answer
127 views

What does “1-month horizon” mean in VaR calculations

For a simple equity portfolio, I need to compute historical 1-year simulation VaR with a "1-month horizon". I imagine this means I need to compute the 1-month return of the portfolio at each point in ...
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1k views

How to compute VaR of a simple equity portfolio?

How do I compute VaR of a simple equity portfolio? I know current weights and can easily access the history of the stocks' daily returns.
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1answer
119 views

would multiplying a co-variance matrix by the inverse of a variance matrix generate a beta matrix?

I was multiplying the popular calculation w' * Σ * w and got the idea of generating a beta matrix. multiplying Co-variance by inverse variance. Would this work? generating the beta of each asset to ...
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481 views

Delta hedge value formula

When we delta hedge with implied volatility, and dynamically adjust every day, I believe the PnL theoretically is $$PnL = 0.5 \Gamma S^2 (\sigma_r^2 - \sigma_i^2)dt$$ where $\sigma_r$ is realized ...
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1answer
98 views

Show that two formulations of Markowitz problem are equivalent

I would like to solve (as mathematically and formally as possible) that the following Markowitz problems are equivalent. The big point is: I want to show that it is equivalent to constrain the return ...
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1answer
202 views

Solving a Markowitz problem with restrictions (lower and upper bound) to the weights vector

I would like to find a step by step solutionfor the following Markowitx problem. It is a standard markowitz problem. The unique detail (wich is why I am posting this question here) is that there is a ...
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2answers
337 views

Portfolio optimisation with conditional weight restrictions among asset

I want to optimise a portfolio of assets from different countries (A,B,C...) where the set of all country-asset combinations is (A1, A2, A3, A4.... B1, B2, B3... C1...). I want to include a ...
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1answer
91 views

What instruments help me receive a premium?

Apart from selling options , what other instruments can I trade(sell) to collect a premium ? The main problem that I face is as follows : I am buying a Call option which I would like to fund by ...
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2answers
549 views

What's the exact definition of alpha?

I am quite new to finance and I often hear people say 'I have 2 bps of alpha' or 'I have an alpha of two bps' I don't quite understand what does this mean For me alpha is about predicting power. At ...
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411 views

What is the profit and loss of a hedged call option portfolio?

Could somebody explain the following to me: Essentially, an approximative (ignoring higher-order terms) formula for the change in a call-price is computed. If we delta-hedge, then delta is set to 0, ...
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637 views

Greeks for a portfolio? PnL for gamma trading

I am a little bit confusded with respect to the PnL of a delta-neutral portfolio. We have $$d\Pi = \Theta dt + \frac{1}{2} \Gamma \Delta S^2$$ So, if our portfolio consists of 1 call options, and ...
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1answer
126 views

Capitalization constraint in portfolio optimization

My problem boils down the the classical $$ a \cdot w - \lambda w \Sigma w \rightarrow Max $$ under the constraints $$ A \cdot w \le b, $$ where the above constraints also contain information about my ...
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1answer
289 views

Simple Sharpe Ratio Question Related to Trading Strategy

Given a price vector $(p_1,p_2,...,p_n)$ for some stock, then the corresponding return at $k$th day is described by $$ R_k = \frac{p_{k+1} - p_k}{p_k} $$ On the other hand, let $W_k$ be wealth at day ...
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Proof for the Duplication Invariance property for the Most-Diversified portfolio

In Properties of the most diversified portfolio by Choueifaty, he shows that the Most-Diversified portfolio (MDP) has three quantitative properties. The Paper: http://www.tobam.fr/wp-content/uploads/...
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P2P lending and correlation with other major asset classes

I am looking for a credible study (i.e. a good/reputable source) into the correlation of returns on assets in Market Place Lending / Online Direct Lending / Alternative Finance with other major asset ...
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46 views

How to hedge a MV portfolio against crises

I have constructed an adjusted Mean-Variance portfolio optimization method that optimizes the exposure in a set of X assets. The portfolio works perfectly fine during normal periods (even when there ...
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53 views

How to find the ideal options trade given certain return distribution?

Suppose I have a probability distribution for the return of a given stock from now until some expiration date. Is there any algorithm/process/software that will take that probability distribution and ...
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1answer
141 views

Adjusting a daily log return for a cash inflow/outflow [closed]

If I had a portfolio with one stock with an initial value of 100 and the next day the stock gained 5 and I added 50 too, would I adjust the log return this way: ln [(155-50)/100]?
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Is the exponential Shannon entropy sub-additive?

In a recent paper of Salazar et al. (2014), The Diversification Delta: A Different Perspective, forthcoming in the Journal of Portfolio Management , the authors propose to use the exponential Shannon ...
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2answers
1k views

Dmat argument in solve.QP R function: Cov or 2*Cov?

Background My final objective is to find a portfolio located on the efficient frontier from a choice of 100 stocks from a stock index (eg. S&P500). This efficient portfolio will be such that ...
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1answer
427 views

PortfolioAnalytics R package - Error with the function “create.EfficientFrontier”

Issue The function create.EfficientFrontier from the PortfolioAnalytics package is outputting an error message that reads: <...
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0answers
168 views

What are examples of boosting, bagging, stacking or subspace method in quantitative finance?

The above ensemble methods appear useful in several machine learning competitions, like Netflix prize or KDD. They work by diversifying between several model variants. Are they also useful in ...
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4answers
170 views

What ultimately determines trading costs?

In equity markets, there are obvious transaction fees such as brokerage, commission fees etc. But if I wanted to do a more in-depth analysis of the determinants of transaction costs, what would be ...
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1answer
950 views

Orthogonal sources of risk and return

I am sorry for my incompetence. I am new in Quantitive Finance, so I read an article about the relationship between Alpha and Portfolio Risk and I can not understand what is the meaning behind the ...
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1answer
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Portfolio optimization subject to transaction costs

Mean-Variance portfolio optimization attracted lots of attention in this forum so far. I am interested in the effect of incorporating transaction costs into the decision framework and I would like to ...
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1k views

How to build a market-neutral portfolio using CVXPY?

I am trying to implement a simple minimum variance portfolio optimisation with a few simple constraints: long-only portfolio fully invested (sums to one) market-neutrality, i.e sum(betas) = 0. I am ...
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1answer
207 views

How large are transaction costs in practice?

I am wondering, what kind of transaction costs practitioners (institutional investors) are faced to. Portfolio optimization literature often evaluates portfolio performance after adjusting for a value ...
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1answer
549 views

Low beta and high correlation

Assuming that time period used to calculate the beta and correlation between an index and an asset is the same, is it possible to observe low beta while having high correlation? If yes, how would ...
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2answers
907 views

A comprehensive list of risk measures for different asset classes

Is there any list of risk measures commonly used in Equity, FI, FX, Commodities portfolio management? For instance: Equities - standard deviation, beta; Bonds - duration, convexity, DV01; FX/...
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229 views

Diversification investment metric for a FI portfolio

What is a good investment metric to reward diversification within a portfolio. Suppose we have a fixed income universe and prefer stable currency, mid yield and mid tenors. Our stressed spread var ...
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2answers
407 views

Maximum Certainty Equivalent Portfolio with Transaction Costs

Out of curiosity I tried to compute the portfolio weights of a maximum certainty equivalent allocation, however, by incorporating (quadratic) transaction costs. However, my result is not as intuitive ...
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1answer
63 views

What does equilibrium return on 90-day Treasury Bills mean?

I have been reading NZ Superfund's 2015 Ref Portfolio Review (here) and came across this notion: Our estimate of the equilibrium return on 90-day Treasury Bills is 5%. And this is under the column ...
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1answer
58 views

Do we have arbitrage if the probability measures are less than zero

Background Information: This question follows from here It is tempting to write $$V_0(X) = \beta\left[\left(\frac{\beta^{-1}S_0 - S_1(d)}{S_1(u) - S_1(d)}\right)X(u) + \left(\frac{S_1(u) - \beta^{-1}...
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1answer
102 views

Value of a perfect hedge

Background Information: The price of a portfolio at time $t$ ($t = 0 ,1$) is $$V_t(\pi) = \phi S_t + \psi B_t$$ The portfolio $\pi$ is a perfect hedge for the claim $X$ if $V_1(\pi) = X$ a.s. as ...
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2answers
98 views

Significance of return under stable distribution

if I want to use t-test to test significance of my returns, it assumes the random variable is distributed normally. But in my work I work under stable distributed ...
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Comparing two portfolio construction strategies

Suppose that I have two long-only portfolio construction strategies and that I backtest both of them on the same data. If I wanted to find out whether one of these methods would have outperformed the ...
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1answer
2k views

Creating a Beta-Neutral Portfolio

Given a portfolio of assets (say 10) and trading signal (1=Hold): ...
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165 views

Expected shortfall of stable distribution by Stoyanov

I've been working on calculating parametric ES assuming the returns follow Paretian stable law. Given the four parameters - $\alpha, \beta,\sigma,\mu$- Stoyanov introduces closed form solution of the ...
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2answers
177 views

Calculating Expected Return from Historical Data Alone

Say that my returns are normally distributed. I have the historical returns data for 3 index funds and nothing else. I want to compute expected return and standard deviation solely from this data. ...
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1answer
69 views

ETFs mimicking world economy?

We can find ETF that usually mimick some stock index, for e.g. SP500 has SPDR, Dow Jones Industrial Average has DIA, etc. Does an ETF that tracks all these indexes exist?
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Formula for Optimal Portfolio of 2 Assets when No Shorting Allowed?

I am looking for a formula to calculate the weights of two risky assets that produce the optimal portfolio (i.e highest Sharpe ratio). So far I have found the following formula from a website of ...