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1answer
45 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 ...
0
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1answer
19 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 ...
0
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3answers
82 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 ...
6
votes
1answer
172 views

Completeness and Hedging Question

A question in some private notes I'm struggling to work through (exam. prep.). (iii) is where I hit a wall with my understanding & I'm lost thereafter. Any help/clarification gratefully received. ...
2
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1answer
43 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 ...
0
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1answer
45 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 ...
3
votes
2answers
58 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 ...
1
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1answer
56 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 ...
2
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3answers
83 views

Calculating Portfolio Returns Across Sectors

I have a table of asset (mutual fund) returns and the percentage that each asset is in a particular stock sector: ...
7
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4answers
427 views

Calculating VaR with Monte Carlo simulation

I would like some help here :) I have a problem calculating VaR with the Monte Carlo Simulation. I have followed then next steps, is this a right way to calculate VaR or I need something more? 1....
1
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0answers
26 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]...
1
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0answers
34 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 ...
3
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1answer
112 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 ...
5
votes
2answers
164 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 ...
0
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0answers
47 views

measuring portfolio performance using monte carlo simulation

I have a financial portfolio comprising standard asset classes such as equities, bonds, and commodities. I developped a strategy (optimized) and I include it in the financial portfolio. I want to ...
0
votes
2answers
55 views

Portfolio return for assets held for different lengths of time

How does one calculate the return on a portfolio if the assets in that portfolio were held for varying periods of time? For Example: $t_0$ Buy AAPL at 100 $t_5$ Buy MSFT at 20 $t_1$$_0$ Sell MSFT at ...
0
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0answers
28 views

combining returns in portfolio analysis

In portfolio analysis, can anyone think of a reason it might be a bad idea to simply combine all the past returns into a single return based on your asset allocation and then determine portfolio and ...
22
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11answers
13k views

What is the reference python library for portfolio optimization?

Does anyone know of a python library/source that is able to calculate the traditional mean-variance portfolio? To press my luck, any resources where the library/source also contains functions such as ...
1
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0answers
28 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 ...
0
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0answers
22 views

Calculating portfolio returns from a dynamic, optimal re-balancing strategy

I am calculating a dynamic strategy with optimal re-balancing as in here. As a result of maximizing the expected utility function I obtain the weight for the risky asset in period $t=0$. All such ...
0
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1answer
59 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-...
0
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0answers
38 views

Bond portfolio optimization

Problem is that I want to match single country term structure return as closely as possible. What would be best way to construct proxy to do this, with less bonds than in original term structure? I ...
1
vote
1answer
84 views

Monte Carlo VaR assuming logistic distribution

I have a Monte Carlo model which measures the Value at Risk (VaR) for given portfolio. I use the geometric brownian motion to model the prices. But let's say I assumed the returns of prices follow the ...
0
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0answers
25 views

derive variance of a portfolio

I'm stuck on a derivation of the variance of a portfolio of securities $K_1,K_2$ formula The end result is $Var(K_v) = w_1^2Var(K_1)+w_2^2var(K_2)+2w_1w_2cov(k_1,k_2)$ Proof so far: Let $K_v = ...
10
votes
3answers
185 views

Portfolio construction in reality?

There are various models for portfolio selection in literature, like, Harry Markowitz (HM) model ( Mean-Variance Model) [well known model] Konno and Yamazaki (1991) model: minimizes the sum of ...
1
vote
1answer
30 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/...
1
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0answers
30 views

Under which conditions the minimum variance portfolio involves no short selling?

If $\rho_{12} < 1$ or $\sigma_1 \not= \sigma_2$ then $\sigma_v^2$ representing the variance of the portfolio with weights $(w_1, w_2) = (s, 1-s)$ as a function of $s$ attains its minimum value at: ...
4
votes
1answer
88 views

What is smart beta, alternative index, factor investing?

What is smart beta, alternative index, factor investing? Are they basically the same thing? Construct a benchmark index using schema other than market cap?
0
votes
1answer
161 views

Matlab code for equally weighted portfolio

I have daily returns of 10 stocks. I need to construct an equally weighted portfolio that goes long in the 3 highest returns and short in the 3 lowest returns. The portfolio needs to be re-balanced ...
2
votes
0answers
80 views

Liquidity Adjusted Asset Pricing Model

I have a data set with 4000 companies and I have calculated a liquidity measure of each of the company in the dataset as Where, Turnover is the monthly average ratio of daily volume to shares ...
1
vote
1answer
315 views

Portfolio Management in R

I’ve been looking around for a R-package that will allow me to track my stock portfolio - basically I would like to enter stocks that I own, track the trades I make, calculate my open position & ...
0
votes
0answers
15 views

building a correlation of equity portfolio to custom benchmark 60/40

Hi i have built a custom portfolio of equities with weights but would like to plot the daily, monthly and annual correlation to 60/40 benchmark. Please see code below and suggest how I can do the ...
1
vote
0answers
42 views

How to form Decile Portfolios based on Liquidity measure with missing data in R

I have a dataframe with over 4000 companies data (as column) and have calculted their daily Quoted spread measure ( measures liquidity for each stock) for 15 years. And then from the daily have ...
4
votes
2answers
91 views

When would dedicated portfolios do better than 'immunized' portfolios?

We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said: It should be ...
3
votes
1answer
118 views

VAR of portfolio containing options, equities and forwards

If we want to calculate VAR of a portfolio using variance covariance matrix (delta normal method), containing equities, forwards and options, how do we treat each asset class for making the variance ...
1
vote
1answer
76 views

Portfolio construction

Suppose I have 3 stocks. Their historical returns and some variables like RSI, ATR, EMAs for all 3 of them. The goal is to compute the weights each stock should have in a portfolio. If I do something ...
0
votes
1answer
36 views

Do I calculate weights of assets correctly?

I solved attached question but I am not sure whether I did part a and c correctly. Is there a way to calculate weights of A and B by just knowing their standard deviation and correlation's value?
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2answers
1k views

Risk Budgets with Target Portfolio Volatility

I'm working through the implementation of a risk budgeting approach as described in the recent Roncalli paper. The idea is that the portfolio manager sets a contribution of total portfolio volatility ...
0
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0answers
37 views

Solving inequality constraint

I am trying to solve the following inequality constraint: Given time-series data for N stocks, I am trying to construct a portfolio weight vector to minimize the variance of the returns. the ...
3
votes
1answer
53 views

Equivalent Definitions of Self-Financing Portfolio

Consider a multi-period model with $t=0,...,T$. Suppose there is a bond with $B_0=1$ and $B_t=(1+R)^t$ and a stock with $S_0=s_0$ and $$ S_{t+1}=S_t\,\xi_{t+1}, $$ with $\xi_t$ iid random variables....
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votes
0answers
24 views

Find all possible permutations of asset weights in a given portfolio?

I need to find all possible asset weight combinations for an 8 asset portfolio. Each weight is a multiple of 10 (0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1) Some assets can be weighted with ...
2
votes
1answer
36 views

efficient portfolio with given risk

Is there a formula to derive an efficient portfolio to maximise the return, x'mu, for a given risk, x'S x (where x are the portfolio coefficients, mu is the mean return for each asset and S is the var-...
0
votes
0answers
30 views

Constrained portfolio optimization - orthogonalize factor exposure

I am optimizing a stock portfolio with a few factors. If I constraint exposure to one of the factors to be a constant and set the exposure to other factors as zero. It is ok to use a diagonal factor ...
2
votes
0answers
115 views

Behaviour of out of sample efficient frontier

I am comparing the efficient frontier of a set of portfolios that are in and out of sample. The first period is from 1991-01-03 until 1992-10-03 and the second one from 1992-10-03 until 1994-03-03. I ...
1
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0answers
86 views

Determining the investment strategy

I have the following problem: Consider the 5 year investment strategy and given the yearly portfolio returns $S_{t+1}/S_t$ and dividends $D_{t+1}$ paid at $t+1$ which are modeled as: $\frac{S_{t+1}}{...
0
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0answers
16 views

Where can I find information about the “Target Portfolio Pattern”?

It might not be known as a "pattern" but basically it's a way of (low-frequency) order management where a 'target portfolio' is built using notional amounts which is then compared against an 'actual ...
0
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0answers
87 views

Calculating CoSkewness and CoKurtosis from univariate skewness and kurtosis and calculate portfolio skewness and kurtosis

I have calculated skewness and kurtosis for n assets and got a skewness vector skew = [S1,...,Sn] and kurt = [K1,...,Kn]. Now with having covariance matrix and these vectors I would like to calculate ...
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votes
1answer
188 views

How to compute simple and log portfolio returns?

I am looking for more details to perform simple and log returns for an entire portfolio. However, I've only been able to find the following semi-reliable source (see Page 9 and Page 19): Here are my ...
2
votes
1answer
65 views

How to optimize a portfolio using skewness?

I am trying to do portfolio optimization for 5 stocks taking into account skewness of the portfolio but I am unable to incorporate skewness to the mean variance model. Can anyone please help on how ...