# Questions tagged [portfolio]

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### Finding a PDE for an option $V(t,r(t),S(t))$

I have 2 approaches in my mind for finding a pde of an option that depends both on the short rate as well as the stock price- $V(t,r(t),S(t)$. Are these equivalent? Find a hedging portfolio by ...
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### Is there a clear mathematical statement of what problem Hierarchical Risk Parity is solving?

Prado's paper is really just an algorithm for solving some inverse problem. Has anyone seen a clear statement of that inverse problem? Or do you know how to write it simply? The first step is just a ...
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### annualised returns and volatility for 3 month data

I have a portofolio with 30 indexes and I want to calculate the annulised returns and volatility because I want to compare it with another portofolio with different number of indexes (but same time ...
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### Global portfolio alpha

How does one compute the alpha of a global portfolio. Let's say we are using the Fama French 3 factor model and we have a portfolio of 50% US stocks and 50% German stocks. Should the regression be ...
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### Efficient portfolio standard deviation

Is annualized/ or average monthly standard deviation applied on the x-axis of efficient portfolio graph? Assuming expected annualized portfolio return is applied on the y-axis. thanks for your help!
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### How to build a portfolio following the Smart beta process by dividend? [closed]

I'm having trouble finding the method to track smart beta dividend management. I have an Excel file which contains the prices and the dividends of certain companies, and I want to build a portfolio ...
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### Assessing transaction costs of different portfolio strategies

I am trying to evaluate different dynamic allocation strategies based on the same stocks' universe according to their transaction costs. I was thinking to simply compute it as some sort of turnover ...
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### What’s the best Backtest Software/method? [closed]

I have a CSV which looks like this. Ticker | Buy Date | Sell date AAPL | 2018-01-03 | 2019-03-30 TSLA | 2019-03-01| 2019-04-05 What’s the best way to backtest this CSV performance given that ...
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### How does negative performance of a portfolio constituent affect its weight?

This is an easy question, I hope. Suppose we have a swap A with a long position, which, originally, has a weight of 30%. Over time, it has a positive performance of 3%, meaning we have a multiplier ...
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### Univariate Portfolio Analysis

We want to form 10 portfolios based on the level of VAR (99%) for equity data over a 30 year period. Portfolio 1 is the portfolio of stocks with the lowest value-at-risk and Portfolio 10 is the ...
36 views

### Option pricing PDE Black Scholes one-factor Hull-White (or Vasicek) model

I am trying to find the option pricing PDE of the Black Scholes one-factor Hull-White (or Vasicek) model using a self-financing portfolio strategy. The system is as following \begin{equation*} \begin{...
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### Equity risk factors with daily rebalancing

I am building some well known equity factors on the S&P for research purposes. It means those are going to be used for general evaluation purposes but do not need to be replicable. Would it be a ...
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### Variance of the risk systematic component in Fama and French Three Factor Model

in my assignment i have to compute the variance of the risk systematic component in the Fama and French Three Factor Model. Does anyone know the formula or how to compute it? Thank you
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### Beta of sum or sum of betas

When interested in the beta of a portfolio, I see people make a weighted sum of the portfolio components' betas. Intuitively, I would have calculated the beta of the portfolio based on its aggregate ...
63 views

### CVaR portfolio optimization with risk aversion parameter

I'm trying to implement the Rockafellar's function described in this paper http://past.rinfinance.com/agenda/2009/yollin_slides.pdf with a risk aversion parameter for my thesis. The function to ...
42 views

### Why does Merton's fraction give unintuitive quantities using real world data?

The solution to Merton's portfolio problem suggests that an investor invest $\frac{\mu - r}{\sigma^2 \gamma}$ percent of their wealth in the stock market, where $\mu$ is the rate of return of the ...
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### Time and asset weighted rate of return of a portfolio

If I have a portfolio with 3 initial assets on day 1 (say, stock 1 with beginning market value of \$100, stock 2 \$150 and stock 3 \$175) and after 10 days the stock 2 is sold for \$200, how can I ...
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### R - Portfolio construction based on own calculations, with rebalancing of components

I have used random forest in R to get probabilities for stocks being in a certain class. With those probabilities i would like to construct portfolios containing the 5 stocks with the highest ...
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### Understanding what is 'special' about the security market line

I am trying to get my head around the CAPM model and all the intricacies of portfolio management. I have written some code to help me visualise what happens to the risk-return characteristics of my ...
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### Is it possible to construct a hedge that matches value Delta Gamma and Vega?

Given a strike price, current price, risk free rate, dividend yield and volatility, I have been asked to calculate: - a hedge which matches the value Delta and Gamma - a hedge which matches the value ...
38 views

### Variance/VaR calculation for a Portfolio

I'm considering a portfolio of multiple stocks (>2), and calculating their Standard Deviation/Variance and VaR for the portfolio. My question is about the below two ways to calculating them Consider ...
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### How to Calculate Discrete Currency Returns for Short Positions

I need to calculate currency returns for 1) short selling the currency and 2) going long in the currency. When going long, the currency is sold at Forward price $F_t$ and bought at spot price $S_{t+1}$...
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### What does “invest in portfolio volatility” mean?

In this paper, Barnea, Amir, Henrik Cronqvist, and Stephan Siegel. "Nature or nurture: What determines investor behavior?." Journal of Financial Economics 98.3 (2010): 583-604. it is mentioned ...
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### How to compute a portfolio value?

I am learning fundamentals of option market and ran into an example I do not understand : Let's assume I have a portfolio of 3 shares priced \$22, and a European call option to buy a share for \$21 ...
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### portfolio volatility over time

When estimating portfolio vol. with: $\sigma = \sqrt{w^T \cdot cov \cdot w}$ How does the sample length of returns affect $\sigma$? Is it possible to exponentially weight something to give more ...
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### Value at Risk for portfolio with different maturities

I am new to StackExchange and relatively new to quantitative finance. I work at a commodity trading company and we have an extensive portfolio of futures and options on commodities (traded on the CME, ...
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### What is the appropriate breakpoints for portfolio sorting (using CRSP stocks) based on size?

I want to sort stocks based on size. I use CRSP database from 1962 to 2018. My question is that in order to create quintiles, what is the appropriate breakpoints? and how can I calculate them? I saw ...
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### Constructing an arbitrage opportunity for a company involving Forwards

Let's say an investor enters a long forward contract on 100 units of underlying assets $S$ and maturity $T$ = 4 years. The asset $S$ pays no dividends and the spot price of one asset is $S_0$ = £5. ...
120 views

### Calculating Delta of option portfolio using average of inputs

Trying to think through two options portfolio scenarios, which are highly similar. I'm wondering if you can take a portfolio of options, all written against the same underlying product, and use ...
112 views

### Duration of portfolio equals to zero

I am solving the following problem: Consider a 2000 dollars bond with maturity of 5 years and a half-year coupon of 25 dollars at a nominal interest rate of 8% p.a and a consolidation bond (...
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### Correlation of a portfolio of trading strategies to a benchmark [closed]

I have two trading strategies, both having a correlation of 0.5 to an indicator 'i'. If I take a portfolio of these two strategies, what will be the correlation of this portfolio with the indicator 'i'...
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### Surface plots of the mean-variance efficient frontier

3d surface plots contain an X, Y and Z axis. For the mean-variance efficient frontier: X axis is portfolio volatility ($\sigma_p$) Y axis is portfolio expected return ($\mu_p$) any ideas for what ...
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### Tracking a portfolio's annualized return

Sorry for this dumb amateur question, but looking for some help. I’ve created an Excel line chart that tracks a portfolio’s annualized rate of return. For example, a year ago the portfolio had an ...
261 views

### Value-weighted return: which date should the market-capitalization be based on?

I got a short question regarding calculating the value-weighted return of portfolios. Example: The portfolio is constructed based on the value of a certain criteria on date 31.1 (Jan 31st). The ...
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### Why is Portfolio Theory not using the distribution of portfolio returns

Portfolio Theory uses things like Expected Value, Risk, Confidence. I wonder why it's not ...
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### Adjusting volatility while constructing portfolio

I am trying to construct a portfolio based on a macro momentum strategy for backtesting purposes as outlined in https://www.aqr.com/-/media/AQR/Documents/Insights/White-Papers/A-Half-Century-of-Macro-...
111 views

### Value-weighted Portfolio Confusion

just a very short question regarding value-weighted portfolios. As the results are not as expected I try to cancel out any possible wrong assumptions. I created five portfolios à 100 companies out of ...
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### Show the expected return of the portfolio and how to derive return variance of the long-short portfolio?

Show the expected return of the portfolio and how to derive the return variance of the long-short portfolio? (see picture)
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### Is there a quicker algorithm for calculating 'drifted' portfolio weights? (R, Pandas/NumPy, MATLAB)

'Sup, QuantSX. BLOT (Bottom Line On Top): Is there a nice clean algorithm for rapidly calculating portfolio weight drift? In R, Python or MATLAB - I'm not fussed which. Details I'm in the final ...
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### Some interpretation on some plots / statistics

I have been playing with a model just for learning purposes (I don't expect to make any money from the model) but I wanted to get some opinions on what you think are "good" values and some opinions on ...
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### Sharpe Ratio and Sortino Question: Standard practice

For Sharpe ratio calculation, I have seen several variations for the denominator; either the standard deviation of portfolio returns or standard deviation of excess returns. Is there an accepted ...
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### How long a time horizon should be for verifying the effectiveness of an investment strategy?

Question To verify the effectiveness of a certain asset allocation strategy, how long a time horizon should be? Is there any academic paper regarding this topic? Question in more detial I know ...
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### PortfolioAnalytics: Training window based on entire history before rebalancing in 'optimize.portfolio.rebalancing'?

I am fairly new to PortfolioAnalytics and R in general. I am trying to do some backtesting of a minimum variance portfolio. I have weekly, monthly, quarterly and yearly return data of 3 selected ...
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### How to calculate Turnover Ratio of a scaled Portfolio

I want to calculate the Turnover of my scaled Momentumportfolio (Barroso und Santa-Clara 2015) They described Turnover Ratio with the following formula: While i understand the general concept (...