Questions tagged [portfolio-theory]

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Why is the portfolio weight of the risk-free asset capped at 1?

I am reading Investment Science by David Luenberger, and in it he creates a portfolio with a risk-free asset and a risky asset. α is the weight of the risk-free asset, and he sets α ≤ 1. Why is that? ...
wwjwjwjwj's user avatar
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Implications for the economics literature of possible mistakes in Black-Scholes-Merton option pricing?

If this preprint (which is discussed here on QSE) is correct in showing that there are mathematical mistakes in the Black-Scholes-Merton option pricing framework, are there strands of the economic ...
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Dynamic investing problem - Private Equity

I've been thinking about the following problem. Consider an agent who starts out with \$1 and on any given day $t$, is given the opportunity to invest in an asset with expected return $\mu_t$ and ...
user357269's user avatar
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Can data be created using Monte Carlo Simulation

I am aware that Monte-Carlo Simulation is used for making accurate assumptions by introducing randomness. But can it be used to synthesize or create a dataset? If yes, can someone share an example?
Marmik Pancholi's user avatar
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Asking for the reference of difference between frontier and developed stock market in portfolio construction

I am looking for references highlighting the differences between the developed market (e.g., US) and frontier market (e.g., Vietnam) in portfolio construction (e.g., Markowitz's mean-variance ...
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Why do stock returns seem to be uncorrelated with interest rate?

Since expected return of stock is risk-free rate plus risk premium, intuitively they should be correlated. Of course the size of risk premium is not constant, but it's hard to imagine why risk premium ...
ssamtkwon's user avatar
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Experimenting with Mean Variance Analysis

here with a question about mean-variance analysis and utility theory hope you can help me. First point My main objetive is to maximize the expected utility from portfolios given by $\sigma_p^2=\frac{C}...
CobbDgls's user avatar
1 vote
1 answer
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Budget line for mean variance utility

Consider the mean-variance utility used in CAPM. The budget line when allocating a risk-free and a risky asset is the line connecting the $r_f$ and the risky asset. Suppose that I have fixed amount ...
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Asking for citation that not all investor can access to borrow at a risk-free rate?

One assumption criticized of Markowitz(1952) is that all investors are able to access to borrowing money at a risk-free interest rate. Is there any reference for that in reality, all investors cannot ...
Phil Nguyen's user avatar
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Curiousity about the choice of risk-takers investors in Modern Porfolio Theory?

By reading the explanation and example of Modern Portfolio Theory (Markowitz, 1952) from this link, I saw a picture as below From this website, I also see The portion of the minimum-variance curve ...
Phil Nguyen's user avatar
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Black-Litterman Weights for Intersecting Asset Classes

I'm trying to implement Black-Litterman for an arbitrary selection of assets some of which might be subsets or intersect with others. For example, one portfolio might be US Equities (VTI) A global ...
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risk aversion and convexity of indifference curve

This is a question from the CFA exam. With respect to utility theory, the most risk-averse investor will have an indifference curve with : (a) greatest slope coefficient (b) most convexity The answer ...
aff0gato's user avatar
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1 answer
180 views

Quadratic utility: monotonicity and risk aversion

I am taking macro class this fall. One of the problems asks whether decreasing absolute risk-aversion and ever-increasing consumption are two unattractive implications of the quadractic utility ...
user30845's user avatar
3 votes
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How can you interpret one of the parameters of optimal consumption at the Merton portfolio problem?

Statement: Let the dynamics of wealth of the agent satisfy $$dX_{t} = \pi_tX_t\Big(\mu dt+\sigma dB_{t}\Big)- c_t X_t dt, \qquad \textrm{with}\quad X_0=x_0 \in \mathbb{R},$$ where $(\pi,c)$ is an ...
epine_se's user avatar
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How is equilibrium reached in CAPM such that the tangency portfolio = market portfolio?

From my research online, when learning CAPM with $n$ risky assets and a risk free asset with return $r_f$, I always see the conclusion that in equilibrium, the market portfolio = tangency portfolio ...
user523384's user avatar
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The efficient frontier in mean variance criterion

The efficient frontier is the portfolios with the minimum of variance ($V$) at a given mean ($E$) or a maximum of mean at a given variance,Why do the optimal portfolios in the effcient frontier, is ...
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Negative Risk Free Rate Sharpe Ratio

currently I am writing my Master-Thesis about SRI-Fonds. For analysing Sharpe Ratios from different Fonds I need to use the risk free rate (e.g. Euribor 3M). Unfortunately I can‘t find anything about ...
user29948's user avatar
3 votes
1 answer
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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 ...
Richard Hardy's user avatar
3 votes
0 answers
1k 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 ...
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1 answer
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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 ...
albertdomyo's user avatar
1 vote
1 answer
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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 ...
Sara Salvante's user avatar
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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 ...
Philipp Chetibi's user avatar
1 vote
0 answers
28 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....
Ian's user avatar
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6 votes
1 answer
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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?
High GPA's user avatar
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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 ...
Hank's user avatar
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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 ...
james black's user avatar
3 votes
1 answer
105 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 ...
Green's user avatar
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1 vote
1 answer
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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 ...
caverac's user avatar
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3 votes
3 answers
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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. ...
Commissar Vasili Karlovic's user avatar
1 vote
1 answer
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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 ...
J.G.'s user avatar
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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 ...
JOHN's user avatar
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0 answers
312 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 ($\cdotp$, $\cdotp$)....
Arthur L's user avatar
1 vote
0 answers
170 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 ...
user7185's user avatar
2 votes
1 answer
242 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 ...
clubkli's user avatar
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4 votes
1 answer
511 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{...
tyr's user avatar
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3 votes
2 answers
582 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 ...
JDilla's user avatar
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3 votes
1 answer
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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 ...
Daniel Wills's user avatar
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0 answers
3k 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 ...
asosnovsky's user avatar
1 vote
1 answer
215 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 ...
user2034's user avatar
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2 votes
0 answers
382 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 ...
user2034's user avatar
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8 votes
1 answer
457 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 ...
jmbejara's user avatar
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20 votes
0 answers
885 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 ...
jmbejara's user avatar
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4 votes
1 answer
1k 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 ...
user2034's user avatar
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5 votes
1 answer
113 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,...
jmbejara's user avatar
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