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, ...

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3
votes
2answers
151 views

Sharpe Ratio : why the normalization factor?

I try to understand why a $\sqrt{252}$ normalization factor is useful for Sharpe Ratio: Let's compute the Sharpe Ratio for this imaginary portfolio, for various sampling periods: ...
3
votes
0answers
115 views

Is Low-Volatility expensive these days? How can we analyze this?

Low volatility investing became somewhat fashionable in recent years. In general there are two approaches to this Ranking stocks of a certain universe by either stand-alone volatility or by beta and ...
0
votes
0answers
20 views

Portfolio construction for signals of varying time scales?

Wondering if anyone is aware of any research on combining/portfolio construction of signals on different time scales. For example, if I have a trading signal (alpha) that generates trades every hour ...
0
votes
0answers
24 views

Portfolio value containing stocks and a bond

Consider: 1000 dollars invested in stock portfolio and a zero coupon bond. Investment period: 30 years Yearly retur for the stock portfolio: Rk = eµ+σZk , k is after year k Zk are normally ...
0
votes
5answers
115 views

What can I use to measure of diversification?

I have to come up with a measure of diversification for trade (this can tie in closely to diversification as regards portfolios). Are there any well known measures of portfolio diversification?
0
votes
0answers
23 views

High Beta 'Filter' for Minimum Variance Portfolios (MVP's) - Lower Risk/Improve Return?

I am busy conducting research in South Africa on the JSE. I am investigating several risk based portfolios with an emphasis on MVP/min vol. My process is as follows: Although the JSE has around 400 ...
1
vote
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
votes
0answers
43 views

Hwo to create a benchmark for a portfolio?

How does one create a benchmark for a portfolio? I realize if I were using strategic asset allocation, I could just look at the already existing benchmarks associated with the various asset classes ...
2
votes
0answers
49 views

OHLC Covarianc Estimation

Is there an R package which can estimate a covariance matrix using OHLC (Open/High/Low/Close) share prices for upwards of 40 shares using the Yang & Zhang method using daily data? I google ...
2
votes
1answer
65 views

How to calculate a hypothetical minimum-variance point?

If we have $N$ assets which are uncorrelated, but have the same mean return of $\mu$ but the variances are different where $\sigma_i^2$ is the variance of each asset $i = 1, 2,...,N$ how can you write ...
2
votes
1answer
66 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 ...
4
votes
3answers
91 views

Abritrage when Put Option Greater then Strike Price?

I am having a tough time conceptualizing this question here: Let $P$= Price of European Option, $S$ = Present Price of Option and $K$ = Strike Price. If $P > K$, why does abritrage exist? Assuming $...
1
vote
0answers
34 views

Can anyone suggest book about fixed-income portfolio management? [closed]

Can anyone suggest books about fixed-income portfolio management? Thx
2
votes
2answers
101 views

Mean Variance Portfolio theory and real-world problem?

There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example 1) investors have the same information at the same time: calculating expected returns ...
2
votes
0answers
46 views

Given (past) stock values for N assets, how to find the maximum - theoretical - profit?

In the past few days I have been thinking about a question which seems trivial, yet I can't think of any efficient way to find the optimal solution... Here is the problem: imagine you have a ...
7
votes
2answers
1k views

Which algorithms do robo-advisors use?

Some pundits claim that there is a revolution in portfolio management under way: The rise of the robots, a.k.a. robo-advisors. The most well known are Betterment.com, FutureAdvisor, Schwab Intelligent ...
4
votes
2answers
93 views

Computing $\gamma$ and $\mu$ at the efficient frontier

Consider the condition which the weights of any portfolio belonging to the efficient frontier satisfy: \begin{equation} \gamma\boldsymbol{wC} = \boldsymbol{m} - \mu\boldsymbol{u}\end{equation} ...
4
votes
1answer
118 views

Tests for Mean Reversion in a Portfolio Rebalancing

On a single time series one can run a Dickey-Fuller test to determine if the asset is mean reverting or at least has been mean reverting during your sample. Is there a way to test for mean-reversion ...
3
votes
0answers
78 views

Portfolio insurance strategy with path dependence

I have the following problem. Let us assume that $S_t$, the stock price follows, geometric Brownian moation with parameters $(\mu,\sigma^2)$. We are given an amount of money $M$ and at each point in ...
4
votes
1answer
61 views

Sum of two GARCH(1,1) Models

I have two GARCH(1,1) processes ($q=1,2$) $$ \sigma_{q,t} = \gamma_q + \alpha_q \, \sigma^2_{q,t-1} + \beta_q \, \epsilon^2_{q,t-1} $$ that have a constant correlation $\sigma_{12,t} = \rho \, \...
3
votes
1answer
113 views

A question on immunization and Macaulay duration

I am studying for the Society of Actuaries - Exam FM and encountered the following problem: Let $x$ be the face amount of the 5-year bond and let $y$ be the face amount of the 10-year bond. Since ...
0
votes
1answer
440 views

How to calculate annualised tracking error?

I have 36 months of relative returns and I need to calculate the annualised tracking error. So, using 36 months of returns is it simply like below: ...
0
votes
1answer
58 views

Isolating single assets standard deviation in a portfolio accounting for correlation

I am running a simple Monte Carlo analysis in Excel using mean return, standard deviation and the =NORMINV(RAND(),mean,std dev) method. I have a correlation matrix that I use to compute the portfolio ...
5
votes
1answer
110 views

How to calculate Skulls Financial Turbulence for one asset?

I have just read this paper http://www.cfapubs.org/loi/doi/abs/10.2469/faj.v66.n5.3 In the paper they define financial turbulence formula as: Could anyone help me calculate/understand this formula,...
1
vote
1answer
79 views

Investor choice problem

Guys I'm stuck with a problem... Consider the portfolio choice problem of a risk-averse individual with a strictly increasing utility function. There is a single risky asset, and a risk free asset. ...
4
votes
3answers
181 views

market neutral weights and cash values

I am looking at a market neutral portfolio and have a question which I think is probably pretty simple. So I can see the individual stock weights. ...
3
votes
1answer
100 views

Return.portfolio error from PerformanceAnalytics package

When using the PerformanceAnalytics package of R, I am getting an error from the Return.portfolio function whenever I ask it to rebalance_on any frequency. If the rebalance parameter is removed, the ...
3
votes
1answer
104 views

How to evaluate minimum-variance strategies against perfect information mvp

The minimum variance portfolio should minimize the standard deviation (variance) of the portfolio at time $t+1$. The covariance matrix $\Sigma_{t+1}$ needs to be estimated in order to form the mvp. ...
6
votes
1answer
441 views

Calculate turnover for portfolio

I am trying to calculate the turnover for a portfolio strategy. First I generate some random data and assign it dates: ...
2
votes
0answers
89 views

Ledoit-Wolf portfolio weights calculation

I am trying to implement the Ledoit-Wolf minimum variance portfolio strategy on a real-world stock dataset. ...
6
votes
1answer
152 views

How to perform risk budgeting for non-linear portfolios?

I am using this question to compute optimal weights following a risk budgeting approach. The problem is I am using non-linear portfolios (options,equity,fixed income,fx). What I am looking for is ...
1
vote
1answer
55 views

Understanding portfolio weights and purchasing stock in modern portfolio theory

Recently I've been learning about the markowitz algorithm. It's pretty interesting, but I'm curious how we apply this in practice. Lets say I have some optimal portfolio: $R_p = x_aR_a + x_bR_b$ ...