Questions tagged [portfolio-theory]

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15
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0answers
424 views

How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem?

How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem? In Duffie's book "Dynamic Asset Pricing," he outlines the "Martingale method" of solving ...
6
votes
1answer
250 views

Optimal consumption in Merton-like portfolio choice model with constant wage

My Questions Consider the following problem. It is almost identical to the classic Merton portfolio choice problem. Here I'm solving it using the so-called Martingale method. I have provided my ...
5
votes
1answer
47 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 ...
5
votes
1answer
95 views

Finding a maximal growth portfolio

I have the following problem that asks me to solve for the "maximal growth portfolio." Suppose that the equilibrium stochastic discount factor evolves as $$ \log S_{t+1} - \log S_t = \kappa_s(X_t,...
4
votes
1answer
312 views

Why stochastic dominance is “stochastic”?

I think the CDF is pretty much fixed, so the FOSD (first order stochastic dominance) is pretty much non-stochastic. Why does it have a "stochastic" in its name?
4
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1answer
246 views

Calculating mean variance portfolio with risk aversion parameter

I want to calculate the classic mean variance portfolio (Markowitz) with a risk aversion parameter $\gamma$. I have the following problem where I want to maximize: $max(x_t) \ \ x_t^T\mu_t - \frac{...
4
votes
3answers
197 views

A question about Lagrange multiplier(when $\lambda=0$)

I need help in a maximization problem(finding the optimal investment portfolio). where $R_s$ and $\Phi$ are $n$ by $1$, with other variables being scalars. $C^s$ is consumption (or wealth) of an ...
3
votes
3answers
273 views

Does my research prove market inefficiency?

The long story short, I have developed an index based on a certain distribution. Then I aligned NYSE stocks according to this index i.e. the stocks with the best fit are first and the worst are last. ...
3
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2answers
441 views

Modern Portfolio Theory Vs Marginal Utility Theory

I'm currently trying to wrap my head around modern portfolio theory and would love a simple explanation on how it differs from a marginal utility model (if at all). As I am understanding it, MPT ...
3
votes
1answer
67 views

Two Funds Separation & CAPM

I've read that, concerning the CAPM, in equilibrium all portfolio weights are strictly positive. Why is that? You can also go short in the risk free asset right? And then you're on the right of the ...
3
votes
1answer
54 views

Can we have incomplete markets with a continuum of securities?

Imagine there is a continuum of firms in the economy. Each draws its productivity from the same stochastic process. The stochastic process has unbounded support. The only securities in the economy are ...
3
votes
1answer
735 views

Portfolio choice problem of a CARA investor with n risky assets

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
3
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0answers
60 views

Mean Variance Optimization in a Utility Maximization Framework

I'm struggling to gain a broad understanding of Mean-Variance utility theory as it relates to finding the efficient frontier of a group of assets which each have some return and variance. The typical ...
2
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1answer
146 views

Utility theory and portfolio optimization: utility of what exactly?

In finance, a common problem is selection of an optimal portfolio given some constraints (e.g. budget constraint and perhaps nonnegative allocation constraint). One can define the optimization problem ...
2
votes
1answer
177 views

Two asset Markowitz Portfolio Optimization and Capital-Market Line construction for a Given Risk Free Rate

I practice with some excercises about the Markowitz theory. If we have a portfolio with two stocks A and B, with given return $r_A$ and $r_B$, the expected return can be computed as: $r_P= w_A \cdot ...
2
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0answers
161 views

Fundamental Theorem of Asset Pricing (Linear Algebra)

I saw this question in a textbook that I was recently reading and don't really know how to aprpoach this problem. Let $H$ be a finite dimensional vector space with inner product ($\cdotp$, $\cdotp$)....
2
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0answers
239 views

Calculating the optimal portfolio for an investor with quadratic utility

The problem is from Asset Pricing and Portfolio Theory by Back and can be found here. The relevant info from section 2.5 can be found here. Given that we have the Expected value and the variance of ...
1
vote
1answer
146 views

Derivative of CARA utility

Can someone help explain the passage here? I'm rusty with my linear algebra so the derivate of these transpose matrices isn't making any sense to me. A detailed explanation would be very much ...
1
vote
1answer
59 views

Short call in binomial option pricing model

I am pretty new at this, so my apologies in advance if the question is too out of place. I have been reading about portfolio replication models, and stumbled upon this example that I don't quite ...
1
vote
1answer
21 views

Estimated betas and optimal portfolio

I ran a regression on 20 assets to estimate their beta with different methods. I would like to see the differences of these estimation differences in terms of mean-variance optimal portfolio. How can ...
1
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1answer
71 views

How to calculate standard deviation of a portfolio?

So i have this information: Suppose that 60% of your portfolio is invested in Johnson & Johnson (JNJ) and the remainder is invested in Ford. You expect that over the coming year JNJ will give a ...
1
vote
1answer
49 views

How do economists model VNM-rationality violation?

This question concerns the need to generalise utility maximisation, the fact that it's a special case of a general problem familiar to physicists, and the question of whether economists have affected ...
1
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0answers
11 views

Simple mortgage portfolio amortization

I have a large residential mortgage portfolio that has fixed and arm mortgages. I want to roughly calculate the amortization of the arm portfolio by year without delving into loan by loan calculations....
1
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0answers
16 views

Empirical estimates of beta for Mean-variance model

I need to evaluate a lottery according to mean-variance formulation for utility. That is to say, given a lottery X, its utility is given by U(X) = E(X) - bVar(X) where E(X) and Var(X) are the mean ...
1
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0answers
114 views

Markowitz Minimum Variance Line - maximise return with a given variance?

There are many example online of how to use Lagrange multipliers to solve Markowitz's minimum variance problem (namely find the weightings for the portfolio which minimises variance for a given ...
0
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1answer
41 views

log returns in finance

Why are log returns used in finance? For example to calculate a stocks performance. There are a lot of articles on that topic yet I don't find them very helpful. Could somebody please explain step by ...
0
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1answer
94 views

Flat Term Structure and Immunized Portfolio Strategy

The current term structure is flat at 2%. You have a liability of $500,000 per year for the next five years. You decide to form an immunized portfolio. a) Describe your exact strategy if you ...
0
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0answers
2k views

Finding the covariance of a stock portfolio

So my question goes like this, I have the returns of 3 different stocks AAPL, NKE and BBRY I make 4 portfolios out of them as follows: and the question asks me to compute the correlation coefficient ...