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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79 views

What are some advanced portfolio rebalancing strategies?

Want to write some portfolio rebalancing code but have found only simple portfolio rebalancer strategies like calendar and threshold. I want to rebalance a portfolio with different asset groups (EQ, ...
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30 views

Calculation of Long-Short-Portfolio returns for different holding periods

I have monthly stock returns I want to invest in according to my trading signals. Now I want to figure out the optimal holding period of the long-short-positions. (The same time for both positions). I ...
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52 views

structural model - exposure estimation

The following example is from the book Active Portfolio Management by Grinold and Kahn. Suppose we have the factor returns and want to estimate the exposures/factor loadings. Say the factor returns ...
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30 views

Log Returns or Simple Returns for Portfolio Performance Analysis

Simple question but one thats stumping me slightly. I am doing a study analysing historical portfolio performance related to portfolios constructed with separate factors in mind. I realise simple ...
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47 views

Volatility targeting / sizing for option strategies

I am trying to work out how to properly size an option strategy to a given target volatility. Assuming I have \$100 capital and I would like to have a strategy's long-run daily volatility to be \$1 (e....
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1answer
249 views

Best books on portfolio construction?

I am a master of finance student and although I understand the basics and the theory of portfolio construction I am still struggling when it comes to the practical side of things, i.e. building a real-...
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34 views

Factor Models vs. Risk-Adjusted Performance Measures

I am building a study focusing on portfolio returns relative to a number of portfolios constructed using various ESG screening techniques. My intention is to measure and compare the performance of '...
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36 views

Portfolio variance over time vs. Portfolio variance from mix of two assets

Here are two facts about finance: 1. If stock returns are not independent, for example tomorrow's return equals today's return, then the variance over two days will be less than the variance of 1day*2....
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45 views

Correct way of making sharpe optimized portfolio?

I have monthly returns of about 977 securities of past 10 years. If I keep the returns as it is i.e. I do not multiply by 100 and keep the returns as 0.1, 0.2 , -0.3, 1.2 then I get different results ...
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57 views

Consensus expected excess return from Active Portfolio Management

In the book Active Portfolio Management, when discussing components of expected return (page 92 in edition 2), the authors mention that the consensus expected excess return $\beta_n\mu_B$ is the ...
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71 views

OLPS in real conditions

The Online Portfolio Selection problem has been extensively researched over the years, and various models have been implemented in open-source projects on GitHub. However the theoretical frameworks of ...
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48 views

How to model when to buy and sell a stock? [closed]

Given a set of historical data and volatility of price in each day, how is it possible to determine a price to purchase a stock at each day? For example, I want to find a price like $125 and receive a ...
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31 views

CAPM derivation - active portfolio management

In the book Active Portfolio Management by Grinold and Kahn, the author presents the derivation of CAPM. I am rather confused by the notation of $\beta$ in this derivation and hope to seek some help. ...
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53 views

Black-Litterman Weights Don't Change for Assets Without Views

I am using Idzorek 2002 (https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Idzorek_onBL.pdf) as a reference to implement the BL model in R. I have specified the model in its standard form, ...
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53 views

Calendar time portfolio construction

I am writing my master's thesis about analyst star-rankings and whether their recommendations have investment value. For these purposes I am trying to construct calendar time portfolios as it was made ...
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78 views

Portfolio returns, volatility and weights of capital

I would just like to check if I've done these questions right, I feel like I might have used the complete wrong methods to get my answers. I've been given information on 3 stocks: I've filled in the ...
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101 views

replicating self-financing portfolio for risk neutral measure

Let the price process $S_{t}, 0 \leq t \leq T$, be a diffusion, and savings account be $\beta_{t}$ such that the Equivalent Martingale Measure $Q$ exists. Let $C_{T}=g\left(X_{T}\right)$ be the claim ...
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Capital Charge or Capital add on for Concentration risk using Model-free measure standardised HHI (Herfindahl Hirschman Index)

I am looking to calculate the Capital Charge or Capital Add on for Concentration risk using standardised approach using HHI Below is the HHI index calculation What is procedure to calculate the ...
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54 views

Sharpe ratio differs from Tradingview

I tried to backtest a simple strategy on TradingView, it made 6 trades with these results: Now I want to calculate Sharpe ratio using definition provided by TradingView. So, my daily returns(...
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19 views

Interpretation of holding lower beta assets leveraged to a beta of one and short high beta de-leveraged to a beta of one

I was reading the famous paper "Betting against Beta" by Frazzini et al. They created BAB factor in which a portfolio is created by holding low beta assets, leveraged to a beta of one" ...
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20 views

Adjust the CAPM/CML model for VIX index

Adjust CML model for VIX factor I’m trying to incorporate the VIX index into my efficient frontier model. One way of doing this that I thought about was to extend the model to include investor ...
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2answers
147 views

How to evaluate Asset Allocation skill?

There have been studies that show that Asset Allocation can explain 90% of the variance of returns on a portfolio. If true and Asset Allocation is the primary driver of return risk, how can you ...
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43 views

How do I have to calculate the risk free rate of my two asset portfolio?

Good afternoon everyone! I have a question regarding the risk free rate of my two asset portfolio. For my course, we have to create a two asset portfolio with the time frame of 2015-2020 with monthly ...
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55 views

Do options have diversification benefit?

Imagine the universe where we have one investable volatile asset but with an available liquid options chain for it. The question: can a portfolio consisted of this asset, and some options have any ...
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59 views

How to calculate if a portfolio has diversification

I writing a paper and wanted to know the best way, method or theory to know if a portfolio is diversified. To give you some context, I wanted to know if whether putting Bitcoin into a portfolio with ...
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25 views

Multiple independent variables (returns) on common dependent variables (Fama-French risk factors): Efficiency and data structure in Python

As a common topic in factor investing, I wish to implement the well-known Fama-French regressions on several stocks (+2000 IDs). In a deep sense, factor regressions tell how the right hand (returns) ...
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1answer
110 views

Monthly rebalancing portfolio of daily returns

Tried to ask this already, but I am still a bit unsure on how to proceed. What I wonder is how to handle the returns and weights of the stocks in a portfolio after rebalancing monthly, so within the ...
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21 views

How to prove that the return criteria for adding an investment A to an existing portfolio can be represented using Sharpe Ratio Approach

How can I prove that the return criteria for adding an investment A to an existing portfolio can be represented as the below inequality using the Sharpe Ratio Approach for risk adjusted returns as ...
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116 views

Daily weights and returns of portfolio that rebalances monthly

I am to replicate the Betting against beta strategy by Pedersen and Frazzini. We use daily returns of the stocks and construct two portfolios based on their ranked betas. Weights is also based on the ...
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32 views

Best bibliography on the classic Merton portfolio problem

I am writing a small section on my thesis about the classic Merton portfolio problem. I was wondering what are the best books on the subject. I am looking for something from the beginner to the ...
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80 views

From annualized Sharpe Ratio to number of daily losses

I have seen a few statements that link a particular annualised Sharpe Ratio to the likely frequency of 'loss day' across a given period: e.g. "A annualised Sharpe Ratio of X, implies the ...
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1answer
92 views

RIsk-retun of 2-asset portfolio with perfect negative correlation

Risk-retun of 2-asset portfolio with perfect negative correlation $(\rho=-1)$ is a straight line with slope of $\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1}$ since $\sigma_P=|\omega_1\sigma_1 -\omega_2\...
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82 views

global minimum variance portfolio vs all-bond portfolio

I'm leaning portfilio theory and have got some questions. global minimum variance portfolio is defined as the leftmost point on the efficient frontier which suggest it is a all-bond portfolio if risk ...
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1answer
37 views

Do equity mutual funds typically have industry-level diversification constraints? [closed]

For instance, are there limits to how concentrated a portfolio in terms of industry allocation? If so, where can I find such information about the constraints each fund has?
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4answers
161 views

Cant replicate minimum variance portfolio variance by simulating many random portfolios in R

I have computed the theoretical minimum variance portfolio using the 30 stocks in the Dow. The formula used is: $$\underset{N\times 1}{\omega_{mvp}}=\frac{\lambda}{2}\cdot \Sigma^{-1}\iota=\frac{\...
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36 views

Controlling for factors that influence minimum variance optimization

I am trying to compare the performance of two minimum variance optimization (mvpo) methods applied on stocks Hierarchical risk parity (HRP) vs the analytical global minimum variance formula. I feel ...
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2answers
147 views

Portfolio rebalancing to optimal weights including transaction costs and without cash component

Consider a portfolio with 4 assets (A, B, C, D) with prices, quantities, current weights, and target weights as follows: I want to rebalance the portfolio from the current weights to the target ...
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16 views

Portfolio return attribution by styles

Say I have a time series of portfolio returns (mutual fund xyz), time series for the benchmark, and time series for MSCI style indices (value, momentum, quality, low vol). Note: style indices are long ...
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1answer
34 views

Valuation of the minimum guaranteed return that (some) pension funds provide - how would you do it?

Let's say a pension fund guarantees an annual return of at least 5% to their customers/investors, such that the investors face a payoff like the one of a call option (no downside). For this guarantee ...
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1answer
110 views

Calculation of Market portfolio from efficient frontier

I have a specific Portfolio frontier. Can someone provides me with details about how can I calculate the market portfolio from the efficient frontier? I know that I have to draw the tangent line from ...
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51 views

How to implement a buy and hold strategy?

Cheers, I am measuring the impact of a particular variable on a sample of stocks. To accomplish this, I am ranking stocks into decile portfolios based on this variable and then estimating the ...
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52 views

Index to track my portfolio of all ETFs

I have the following portfolio of all ETFs: I am attempting to apply Black Litterman and on the step of calculating market weights. I have the following questions: How can I define what index to use ...
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38 views

Bonds portfolio - total return

TRICKY QUESTION ON BOND PF RETURNS I am working on a bond portfolio, so for each line i have a monthly price change (equal weighted by the numebr of bonds in the portfolio this month) then the return ...
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41 views

Brinson attribution for arbitrary set of style factors (size, momentum, vol, etc)

I'm looking to do a Brinson performance attribution on a portfolio of stocks where instead of decomposing the returns in terms of sectors we use factors instead. Basically, I want to do what Style ...
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3answers
508 views

Deep Reinforcement Learning in Quant Finance?

I've been struggling to find engaging papers on the application of deep reinforcement learning in quantitative risk analysis, portfolio management, algorithmic trading and/or options pricing. What are ...
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94 views

Calculating portfolio weights for Black-Litterman model

I am attempting to construct a portfolio using the step by step Black-Litterman model. My idea is to have a portfolio of, say 10 ETF's (equity based) in one sector and then add some uncorrelated asset ...
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124 views

How is the total return of an alpha strategy being calculated during backtesting?

I am using a quant simulation platform and I have chosen a formulaic alpha to be used. Now the platform is backtesting and displaying the total return of the alpha strategy over 12 years. The trading ...
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20 views

Example of one-period model that satisfies law of one price but is not free of arbitrage

We know that by the law of one price: in a one-period model $(\overline{\pi},\overline{S})$ for an arbitrage-free market model it follows that for two strategies $\overline{\rho}$ and $\overline{\xi}\...
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57 views

Do you need multi-period ahead covariance forecast, in order to construct portfolios with weekly/monthly rebalancing?

Suppose I want to rebalance my portfolio each week. Do I then need weekly covariance forecasts, from some multivariate volatility model to do this? Ie. Insert the weekly covariance forecast $\Sigma_{t+...
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1answer
87 views

Build a portfolio with $\beta=1$ and minimize $\sigma^2$ using CAPM

Suppose there are two stocks A and B: expected returns are $E[R_A]=0.1$, $E[R_B]=0.15$; standard deviations are $\sigma_A=0.1$, $\sigma_A=0.2$; correlation is $corr(A,B)=0.6$; their betas to some ...

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