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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24 views

Expected return of general multi-index model [closed]

How would I go about solving this mathematically?
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16 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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81 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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18 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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61 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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30 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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75 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
81 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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55 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
34 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
151 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
90 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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14 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
32 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
80 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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47 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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49 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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37 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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35 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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2answers
340 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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63 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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115 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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48 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
80 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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139 views

Unwinding a Portfolio

I have a portfolio ${\mathbf P}$ made up of positions $n_i$ in each of $N$ securities, which I'm assuming are jointly normally distributed with means $x_i$, and covariance matrix ${\mathbf M}$. ...
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31 views

Higher risk = high reward?

Some theory (in my understanding) suggests that price is the expectation of future cash flows discounted by expected return: $$p_t=\frac{\mathbb{E}^m_t[c_{t+1}+p_{t+1}]}{1+\mathbb{E}_t^m[r_t]}$$ where ...
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1answer
73 views

Criteria for excluding an Asset Class from a Strategic Asset Allocation

While historically the return, volatility and correlation characteristics justified the inclusion of Sovereign Bonds (US Treasuries, European Central Bank Debt, etc) in Strategic Asset Allocation ...
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28 views

Correlation of two strategy's returns, is it a good standard to select strategies?

Let say I have two strategies, A and B. Historically, when the portfolio value of strategy A moves up, then that of portfolio B moves up. Same in the down case. Then, we can say both strategies are ...
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170 views

How to compare mean-variance-skewness-kurtosis portfolios obtained by expected utility maximization?

Suppose I have some portfolios which are the result of maximizing the expected utility of different approximations of a utility function, how do you test these portfolio's out-of-sample and how do you ...
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2answers
122 views

calculating sharpe and sortino ratio given monthly returns [closed]

suppose I have (fictitious) monthly returns: ...
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2answers
101 views

PCA on the stocks

I have N stocks, and a covariance matrix that indicates the covariance of these N random variables. Now, if I run PCA on the covariance matrix, what can you tell about the principle component?
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1answer
91 views

How do you simulate returns for a portfolio when you have Lumpsum + Monthly investments (SIP) in place?

I'm trying to simulate portfolio returns using Norm.inv function in excel. Inputs to the formula: Prob= Rand, Std dev= Historical, Mean= 5 year historical average. Its easy to do this when you're ...
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43 views

How To Create Daily Leverage?

After doing some analysis on daily leveraged funds one of the biggest risk factors I find is regulatory risk. My goal is to have a risk parity portfolio with daily leveraged funds but if some of these ...
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74 views

How to set a portfolio turnover ratio threshold according to volatility?

With the various crises affecting the financial markets, here a pandemic, this ratio skyrockets almost every time, which limits its interpretability. We know that the ratio increased during the ...
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1answer
150 views

Does mean variance optimization work in real life? If so, why are defined benefit pension funds so underfunded?

I understand the theoretical underpinnings of mean variance optimization and modern portfolio theory. But does the application of modern portfolio theory work in real life? If so, why are all the ...
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74 views

Momentum strategy with Entropy Pooling

i'm currently trying to implement a ranking based on momentum indicators into my Entropy Pooling approach. Basically, the idea behind Entropy Pooling is to incorporate views into a reference model (...
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1answer
119 views

Derivation of mean-variance portfolio weights as closed-form analytical solution from Lagrangean equations

I am trying to find a closed form solution for the constrained MVO problem below. $\max_w w'\mu - \frac{\lambda}{2}w'\Sigma w $ s.t. $w'$1 = 1 The Lagrange for the objective is $L(w, \gamma) = w'\mu ...
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34 views

Immunization of Portfolio of Bonds

I have a question regarding immunization portfolios that are continuously compounded. Suppose we have the following three bonds: Bond 1: one year zero coupon with principal of $100 Bond 2: two year ...
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79 views

Replicating portfolio

I have a doubt about the replicating portfolio methodology. Example - Consider an European Call with $K=21$ and underlying with current price $S_0=20$. We assume that, at the maturity, the underlying ...
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47 views

Proof of existence of one only martingale measure

I know that: Hypothesis 1 (Girsanov Theorem) Let $\theta=\begin{Bmatrix} \theta_t \end{Bmatrix}_{t\in [0,T]}$ be a square-integrable and $\Im_t$-adapted process such that $\mathbb{E}[e^{\frac{1}{2}\...
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1answer
85 views

Correlation sensitivity in multivariate $t$-copula for portfolio VaR of electricity futures using Kendall's tau-$b$ correlation matrix

My t-copula model captures the daily dollar returns of a portfolio of approximately 400 assets. I am curious if there's a generally accepted way to quantify the sensitivity of portfolio movements with ...
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1answer
74 views

Strategic Asset Allocation and Multi-Asset Class Option Based Tail Risk Hedging

If a Strategic Asset Allocation is defined as an asset allocation to weather all investment environments and one which should be employed in the absence of any market views, it would appear that the ...
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2answers
120 views

Portfolio selection with no risk-free asset

Can someone explain why some papers on portfolio construction assume that there is no risk-free asset? For example, this paper: Machine Learning and Portfolio Optimization. What could be the reason(s) ...
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3answers
469 views

Asset Allocation with near zero rates

With central banks pegging interest rates to near zero rates, an argument could be made that the future distribution of interest rates and bond returns are not normally distributed. How has modern ...
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1answer
152 views

Fama-French vs. Arbitrage Pricing Theory of Ross

Is there a specific reason for why Fama-French papers on CAPM extensions do not refer to APT of Ross? In textbooks, APT is always an extension of CAPM and the foundation of extending the set of risk ...
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4answers
408 views

How to determine what's driving the VaR?

I am given the following data: Historical (260 days) P&L vector of a portfolio. Specific P&L's for each investment in the portfolio, for the 10 days with the lowest P&L. The question ...
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187 views

Portfolio Optimization via Entropy Pooling in R (Meucci)

does anybody have experience with the Entropy Pooling Approach by Meucci in R? I am currently trying to do a portfolio optimization with Stocks & Bonds, where a 101 example would be very helpful. ...
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42 views

internal rate of return ((M/X)IRR ?) of a fund

I have the following data for a fund. The contributions come from the LPs (i.e., the investors invest more in the fund, or withdraw money from the fund), MV stands for market value. The timing is not ...

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