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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6
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1answer
147 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 ...
3
votes
1answer
59 views

Implementation of an option tail-hedging strategy

This question directly refers to the paper "Capital Asset Pricing Mistakes: The Consistent Opportunities in Tail Hedged Equities", http://www.universa.net/Universa_SpitznagelResearch_201501.pdf. Very ...
1
vote
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 ...
3
votes
1answer
100 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. ...
2
votes
0answers
40 views

How to understand quadratic finance or practice of Value-at -Risk(VaR)

We define the following notions for a jointly normally distributed random vector $P=(P_1,...,P_n)$ with f the density function. $$\mu=\int_{-\infty}^{\infty}(x_i-\mu_i)f_i(x_i)dx_i$$ $$\sigma^2_{ij}=...
1
vote
0answers
22 views

Architecture and Infrastructure for Robo-Advisor [closed]

Does anybody have any knowledge of Architecture and/or Infrastructure needed for building your own Robo Advisor. I am looking for directions to get in-depth knowledge for building your own Robo ...
3
votes
1answer
84 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 ...
1
vote
1answer
44 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 ...
1
vote
2answers
337 views

“Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
0
votes
1answer
64 views

Portfolio with a certain pay-off curve

I would like to find a relevant optimization option's portfolio models which can describe a certain pay-off curve (objective function) under same assumptions. For example, assumptions on how to limit ...
0
votes
1answer
32 views

Beta = 1 and 0. Type of portfolios

I read in E. Quian's "Quantitative Equitity Portoflio Management" the following: A traditional long-only portfolio [with unit beta] would have most of its risk in the market risk. However, a zero ...
0
votes
2answers
30 views

What is a definition of “Benchmark”?

The word "benchmark" is often used in Finance, but in a rather fuzzy manner, there for a rough idea of what it is, and how it is 'defined'. Can someone provide a rigorous and precise definition of ...
0
votes
0answers
50 views

Physical interpretation of variance in returns in a portfolio design

I have a downloaded the log-returns at successive times of 98 stocks from S&P index over 753 days. I calculated the total daily return according to the formula 1 below, where ...
1
vote
0answers
31 views

Black Litterman: Is it possible to have multiple views (from different sources) on the same asset?

From the basics of Black Litterman I understand that each view on a stock is implemented via the pick matrix P with the expected value of the views in Q. I have read several papers where each stock ...
2
votes
1answer
30 views

Are financial returns considered more volatile in recessionary times as opposed to expansionary times?

I need help in understanding some results that I have obtained. I am doing some out-of-sample performance analysis for different targets of volatility in mean-variance optimization where I solely ...
0
votes
1answer
6 views

What is the u vector in the expression for the weights of the min variance portfolio

I was working on my finical math homework where I need to find the minimum variance portfolio. I need to use the following matrix expression. Nowhere in the class notes does the instructor say ...
0
votes
0answers
19 views

How to Neutralize Portfolio across economic sectors and industries using modified Alpha?

I am reading about Alpha and Portfolio Construction topic while reading i came across below point. Active management should be easy with the right alphas. Sometimes it isn't. Most active managers ...
1
vote
2answers
60 views

How to Calculate Minimun total Risk?

Is it possible to calculate Minimum Total Risk mathematically for below problem. ...
0
votes
0answers
22 views

Fund Separation Theorem for Performance Seeking Portfolio

Can someone explain this statement? "The beauty of the fund separation theorem is that the performance seeking portfolio mandate is the same for all investors"
3
votes
0answers
52 views

subadditivity of VaR

It is known that the VaR (Value at risk) doesn't fulfill subadditivity, i.e. $VaR(X)+VaR(Y) \le VaR(X+Y)$ But for elliptical distributions subadditivity is true. Questions: (1) Which ...
1
vote
1answer
206 views

how can we know the residual return will be uncorrelated with the market return

I was reading that if we know a portfolios beta we can break the excess return on that portfolio into a market component and a residual component. ...
1
vote
0answers
31 views

calculating long short portfolios currency exposure

I have calculated the currency exposures of a long short portfolio simply by summing the weights of each stock. However I was told that I need to incorporate the dollar borrowing (short dollars), I ...
1
vote
3answers
40 views

How to compute the foreign exchange volatility within a portfolio

Suppose I have a portfolio of 5 assets. Assets 1 and 2 have foreign exchange exposures and therefore foreign exchange volatility. How can I calculate the marginal contribution to the total portfolio ...
1
vote
1answer
41 views

given someone's past investing history, is there a way to calculate his risk aversion?

given someone's past investing history, is there a way to calculate his risk aversion? Say, we know this client's investment history for example his past return, is there a way to calculate his risk ...
1
vote
0answers
21 views

How to Rank assets in Portfolio? [closed]

I am working on active equity Portfolio. I have total 30 securities in my Portfolio. Can someone please guide me how can I rank those assets in my portfolio. ...
1
vote
1answer
47 views

Portfolio optimization - maximize variance with exposure to risk factors equal to zero

Optimize a portfolio such that the exposure to risk factors is zero and the variance is maximized (instead of traditional minimization problem). so the optimization problem look like: $$maximize\;w^...
0
votes
1answer
25 views

Which rate of return to use in portfolio weight estimation?

I am learning the basics of portfolio management. I am confused about different ways to calculate rate of returns mentioned in the text investment and portfolio analysis. There are three methods to ...
1
vote
1answer
40 views

Having Difficulty With Sharpe Ratio and Optimal Portfolio

I have begun by using such equations as: By finding the $Rp$ and $\sigma p$ with the weighted values, and then I followed the equation using a value of $.02$ for the fixed asset, $rf$, but this ...
4
votes
4answers
810 views

What to use as portfolio diversification measure?

Suppose that we have a portfolio of $n$ assets. A perfectly diversified portfolio is one in which each asset has equal weights, i.e. each asset has weight $\frac{1}{n}$. Of course this is usually not ...
0
votes
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
votes
3answers
107 views

What assets other than bonds are risk free?

I saw a question the other day that said Assume you have only two assets to build a portfolio. Name and explain three scenarios under which a completely risk-free portfolio can be formed? I ...
9
votes
0answers
188 views

Real world application of stochastic portfolio theory

There is a branche of stochastic portfolio theory (see also this question). Fernholz and Karatzas have published research in this field (e.g. "Diversity and relative arbitrage in equity markets") and ...
0
votes
0answers
12 views

One period optimizations with tcosts, few predictions and getting positions unstuck

Consider a one period portfolio optimization with objective that maximizes $\omega E(r) - \lambda_r\omega^t\Sigma\omega - TC$ Where TC is however we calculate tcosts/impact. Importantly, most ...
3
votes
3answers
97 views

Construct option and stock portfolio

If a riskless security costs 100 today and will cost 120 at time T, a stock costs 50 today and will either be 70 or 30 at time T, and call options on the stock have strike price 50 expiring at time T, ...
0
votes
0answers
19 views

Asset weights in asset allocation

I am trying to solve an asset allocation problem by approximating the expected utility of a portfolio. I am using the following formula: $E_t [U(1 + w_t' r_{t+1} + w_{ft} r_{f, t + 1})] = m_{1,t+1} - ...
0
votes
0answers
30 views

Calculating returns when number of securities in a timeseries varies over time?

I have a timeseries of security returns in which the number of securities in the timeseries varies over time. More specifically, I have a universe of events where securities(their returns) are added ...
2
votes
1answer
88 views

Correlation -1 and standard deviation [closed]

My book says that for a portfolio of two stocks: $\sigma_p = \sqrt{w_A^2 \sigma_A^2 + (1-w_A)^2 \sigma_B^2 + 2 w_A (1 - w_A) \rho_{AB} \sigma_A \sigma_B}$ Elsewhere it says that if the correlation ...
1
vote
1answer
54 views

Parametric bootstrap in generating returns and hypothesis testing

I am trying to test a hypothesis of a statistic calculated from portfolio returns. To do so I estimate a model on the original returns series and want to obtain 100 bootstrapped series using ...
0
votes
0answers
29 views

Approximating the conditional expectation in simulations

I am simulating stock returns, which are governed by the following equations $r_t = \mu + \delta r_{t-1} + \sigma_t z_t$ $\sigma^2_t = \omega + \alpha \varepsilon_{t-1}^2 + \beta \sigma^2_{t-1}$ $\...
0
votes
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 = ...
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 \, \...
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
vote
0answers
29 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
2answers
91 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} ...
1
vote
1answer
63 views

How do I find the standard deviation of a portfolio? [closed]

Compute the expected return $\mu_V$ and standard deviation $\sigma_V$ of a portfolio consisting of three securities with weights $\omega_1=40\%$, $\omega_2=-20\%$, $\omega_3=80\%$, given that the ...
0
votes
1answer
34 views

how to find the weights in a portfolio? [closed]

Compute the weights in a portfolio consisting of two kinds of stocks if the expected return on the portfolio is to be $E(K_v)=10\%$, given the following information on the returns on stock 1 and 2: $$ ...
2
votes
1answer
124 views

How to scale $\alpha$, trading costs in a standard portfolio optimization problem

In the usual "portfolio optimization problem under linear constraints". Let me define the terms here. $$ \text{Find } w^*=\underset{w}{\text{argmax}} \ \ r^Tw - \lambda w^{T} \Sigma w - tradingCost(|...
3
votes
0answers
92 views

Non-parametric estimator - CVAR / Expected shortfall

Is the estimation of the CVAR using known non-parametric methods (histogram , kernels) is different than the estimation of any other R.V.? If the answer is yes, then I am interested to know whether ...
11
votes
3answers
3k views

How do I calculate the skewness of a portfolio of assets?

I need to calculate the skewness of a portfolio consisting of 6 assets. I know that for that I would need the co-skewness matrix between the assets. Does anybody know the formula for co-skewness or ...
3
votes
1answer
158 views

Portfolio with lots of subportfolios

An account manager has $N$ distinct, equally-sized pots of money, which will be used to make $N$ distinct subportfolios, each of which is drawn from a slightly different (but potentially overlapping) ...