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1answer
170 views

VaR Backtesting. High frequency of exceedances

I'm preparing for thesis defense and I've got simple question connected with Value at Risk backtesting. Portfolio VaR was calculated using historical simulation approach (250 days and 500days) and ...
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1answer
103 views

Variance of returns on a portfolio

This must be very basic, but I don't seem to be able to express the variance of returns on a portfolio in terms of variances-covariance sum of returns of its constituents, which seems to be what is ...
2
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1answer
204 views

Portfolio optimization in R with factor tilting while constraining volatility

what optimizer I can use in R to solve the following portfolio optimization problem: $min(f^Tx)$ st: 1. $ -a \le \sum_{i=1} ^{n} x(i) \le b$ 2. $ -c \le x(i) \le d$ 3. $ e \le \sum _{i=1} ^n |x(i)...
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2answers
5k views

Volatility of a multiple-asset portfolio [closed]

I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant. Now I want to determine the ...
2
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2answers
1k views

Variance Matrix with 'nan' values

I am trying to optimize a simple portfolio using several random weights and choosing the best. When the number of assets is large I get a covariance matrix with 'nan' values because some asset pairs ...
1
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2answers
263 views

How do I estimate the volatiliy of my portfolio with an estimator that requires High, Low, Open, etc

I have obtained the daily returns of my portfolio $R^{port}_t$ using a certain strategy. Now I want to estimate the realized volatility $\sigma^{port}_t$ using the past 60 days. An obvious way to do ...
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0answers
594 views

Equal Risk Contribution in Portfolio Analytics r pkg

I am trying to estimate the weights of an equal risk portfolio using the PortfolioAnalytics package in r. To start with, I have tried to redo the example provided in the portfolio vignette. The code ...
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1answer
136 views

How does a Short position impact the PnL?

I have several activity records which include several transaction types: buy, sell, short, <...
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1answer
216 views

A portfolio with two risky assets - Simple exercise

I was trying to solve the following exercise: "Stocks A have $\mu_A=8\%$, $\sigma_A=2,5\%$ and stocks B have $\mu_B=6\%$, $\sigma_B=1,2\%$. Let us suppose that expexted returns are independent. What ...
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0answers
47 views

Portfolio returns from activity records

I am looking for a clean and efficient way to obtain the portfolio returns from a list of activity records. Specifically, the activity file consist of BUY, SELL, COVER, SHORT, etc. records with ...
2
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2answers
421 views

Black-Scholes model and arbitrage free price

Consider the Black-Scholes model and the derivative asset: $$ X = \begin{cases} K, \qquad \qquad \qquad \quad S_T\leq A, \\ K+A-S_T, \qquad A\leq S_T < K+A, \\ 0, \qquad \qquad \qquad \quad S_T&...
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2answers
3k views

how to calculate daily risk free rate using 13 week treasury bill

I want to calculate excess return for AAPL plus the S&P 500. I have computed monthly and daily logarithmic returns for every stock and for the market, I now need to calculate the risk free ...
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0answers
108 views

Assigning Constraints to weights

Suppose I have weights ...
1
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1answer
82 views

Self-financing portfolio under $Q$-dynamics

I know what given stocks $S_1, ..., S_N$ with SDE's, a portfolio must have a particular value dynamics shape (which depends on the dynamics of $S_1,...,S_N$), if that portfolio is to be self-financing....
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1answer
105 views

Should price impact be the same for positive/negative implied volatility shocks?

I am using a vendor system to stress a portfolio which contains (among others) derivatives with implied volatility exposure. The issue is that when using a 1000 bps implied volatility stress upwards ...
3
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1answer
1k views

How to compute the variance of a Long-Short Equity Portfolio?

I am calculating the historical portfolio variance of various long-short equity portfolios. For simplicity, assume the portfolio is long stock A with weight 1.0 and short stock B with weight -0.5. ...
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0answers
363 views

Forecasting volatility with rugarch and Covariance Matrix

I am trying to do a financial time series forecast in order to build a portfolio. I already have some code running rugarch library and I am not sure if I am forecasting correctly, after that I would ...
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1answer
857 views

optimal portfolio with different lending and borrowing rates

I have 4 risky securities (have returns and var-cov matrix for monthly data), and I can lend at 1% per annum, but borrow at 5% per annum. If i wish to obtain the s.d. of 5%, what is the optimal ...
3
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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 ...
1
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1answer
540 views

For any efficient portfolio, does there exist another efficient portfolio which has zero correlation with it?

For any portfolio on mean-variance efficient frontier, does there exist a portfolio on the frontier which has zero correlation with it? I tried to play around with the covariance, by setting ...
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1answer
433 views

Probability default calculation

I want to calculate default of probability of internal ratings for a particular bank. I have only the following data: Liquidity Ratio short-term assets / short-term liabilities = 2.6 Profitability ...
-2
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1answer
71 views

What does $\phi^{(n)}(t)$ mean for a portfolio?

I am currently in the process of deciphering the notes written by an instructor. I missed the class. He writes: Continuous time trading: $S(T) = W(T)$, "Bachelier Model". $\phi(t)$ denotes ...
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1answer
126 views

Converting Contribution To Risk from Variance to Stdev

So we have the basic structure: $\sigma^2_{Pxy} = w_x^2 \sigma_x^2 + w_y^2 \sigma_y^2 + 2 w_x w_y \sigma_{xy}$ $\sigma^2_{Px} = w_x^2 \sigma_x^2 + w_x w_y \sigma_{xy}$ $\sigma^2_{Py} = w_y^2 \...
2
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0answers
81 views

Portfolio of single stock short put options: which correlation structure preferrable?

Let's say you want to have a equally-weighted (in terms of the option price) portfolio of short put options on various stocks with the same maturity. Running Monte-Carlo simulations, it seems that ...
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0answers
69 views

Stress Test for gamma FX portfolios?

How can I create scenarios to stress gamma FX portfolios? If I shock the underlying for example +/-10%, then I gain in both scenarios. I get to capture some losses if I shock the implied volatility. ...
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1answer
67 views

Do exchanges issue position ID after order execution?

The portfolio has two types of positions: asset and cash positions. Cash positions are easy. One currency has only one position, so you can add and subtract easily. Asset positions seem to be more ...
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1answer
77 views

Is it possible to calculate the call-put parity for an option's portfolio?

Let's say I have designed an option's portfolio. The portfolio includes long as well as short positions in European-style put and call contracts based on the same underlying asset with different ...
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1answer
55 views

DJIA Portoflio Optimization

I've been practicing R for about several months, and have begun transitioning from text book examples to what actually interests me. I'm currently participating in the CFA program, but my programming ...
0
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1answer
145 views

Essential new ideas in portfolio theory

I'm supposed to write an essay on "essential new ideas in my current field of research". Hence, I'm looking for essential (= it has the potential to change the way we look at the discipline) and new (...
2
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2answers
203 views

What is a Short Option Hedging Portfolio?

In his book 'Stochastic Calculus for Finance II' Shreve uses the term: 'Short Option Hedging Portfolio' on page.156 (4.5.3). Can someone please explain this term with some kind of an example? It is ...
2
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2answers
816 views

Portfolio risk analysis in Options & Mixed portfolios

I am currently working on a risk analysis model that is primarily focused on options portfolios, but will likely be later expanded to cover mixed (options, stocks, bond, futures, etc...) portfolios. ...
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1answer
47 views

Signs for the assets in a portfolio and definition of portfolio value

Suppose that we have a market with a stock, modelled by $\{S_t\}_{t>0}$ and a riskless money market account $\{B_t\}_{t>0}$. Consider a strategy $\{ H_t^B,H_t^S\}_{t>0}$ be a portfolio over ...
3
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1answer
249 views

Should a backtester have ability to run multiple strategies simultaneously?

At the moment the backtester has a portfolio; a portfolio is associated with one strategy. The backtester is used to test different strategies one at a time, giving their return, Sharpe, drawdown. But ...
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0answers
251 views

Mean-Variance Optimization Techniques with Multiple Asset Classes

Why does it make sense to use single-period Markowitz mean-variance optimization techniques when we're trying to figure out asset allocation across multiple asset classes (bonds, stocks, REITs, etc)? ...
2
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2answers
730 views

Incremental VaR formula

According to a few resources online the formula of iVaR is : VaR (after adding the new element) - VaR (before) My question is how can this be correct given the lack of subadditivity of VaR? Meaning, ...
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0answers
1k views

Calculating weekly portfolio returns for portfolios sorted by volatility

I am having some issues with finding the right code in STATA for sorting the data into portfolios by historical volatility (standard deviation) of returns and then calculating portfolio returns and ...
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1answer
221 views

How to get the average monthly percent excess returns for portfolios formed?

I'm replicating the Fama-French five factor model. I have formed factor portfolios. I'm not sure how to calculate the average monthly percent excess returns for portfolios. In other words, I want to ...
2
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1answer
125 views

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 ...
1
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1answer
323 views

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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0answers
3k views

Problem with determining weights in tangency portfolio (2 risky assets)

I use the following well known formula in order to determine the weight of asset i in the tangency portfolio (in the case of two risky assets): $w_{i,T}=\frac{\sigma[r_2]^2E[R_1]-\sigma[r_1,r_2]E[R_2]...
2
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0answers
242 views

Minimum Variance Portfolio problem [closed]

Minimum Variance Portfolio Suppose there are N stocks in the investmentable universe and we have a fully invested portfolio investing 100% of the capital. The Covariance matrix is denoted as ∑. We ...
0
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2answers
831 views

Derivation of the tangency / maximum Sharpe ratio portfolio in Markowitz Portfolio Theory? (2 risky assets)

I’m looking for a nice & detailed explanation for how to derive the formula for the weight of asset 1 in the tangency / maximum Sharpe ratio portfolio in Markowitz portfolio theory in a world with ...
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3answers
226 views

Where to find good notations to teach investment portfolio maths?

I don't know whether this question is in order here. I do a bit of teaching and I am preparing my own notes but I thought that his should not be necessary. In which book/pdf on the web can we find a ...
3
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3answers
377 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 ...
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0answers
185 views

PnL Explained Using Scenario(Full Reval Model)

I was wondering if any quant guru can help . How to calculate the PnL explained using full reval aka scenario based = > t - (t-1) approach for linear instrument. I am finding difficulty to understand ...
3
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2answers
129 views

Do you know fast to compute, yet plausible risk attribution measures?

I am looking for a fast to compute, yet plausible risk attribution measure based on the risk measure used to compute overall risk. To be more specific, assume that my risk measure is the VaR of a ...
6
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2answers
860 views

What is the intuition of a spread portfolio and how exactly is it constructed?

In a lot of papers spread portfolios are constructed, like in Harvey and Siddique (1999), Table IV, or in Fama and French (2005 from SSRN), page 15. First, why is it important to construct such ...
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1answer
266 views

L1 norm regularization of Markowitz portfolio in matlab

Markowitz portfolio with L1 norm regularization added L1 norm regularization based on the original model. The constraint equation is as follows: The following code is the original Markowitz Mean-...
3
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1answer
197 views

Why are there two expressions for the Black-Scholes hedging portfolio

I am new to derivatives pricing and am trying to understand why there are two different expressions for the Black-Scholes hedging portfolio. The first approach, used in books like Hull, stipulates ...
1
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1answer
65 views

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/...