Questions tagged [portfolio-theory]

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I have tried to solve it but my answers are wrong so i needed help

anyone can solve this question and make me understand
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Interest rate increase and levered portfolio rebalancing

Joseph Wang (“Fed Guy”) in the following podcast gives the following argument to question whether the markets can handle the Fed hiking to 3-4%: What happens if you are a high levered fund and you ...
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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 ...
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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 ...
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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 ...
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2 votes
1 answer
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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....
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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?
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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 ...
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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 ...
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3 votes
1 answer
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ($\cdotp$, $\cdotp$)....
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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 ...
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2 votes
1 answer
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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 ...
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4 votes
1 answer
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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{...
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3 votes
2 answers
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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 ...
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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 ...
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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 ...
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1 answer
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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 ...
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2 votes
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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 ...
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8 votes
1 answer
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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 ...
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19 votes
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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 ...
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4 votes
1 answer
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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 ...
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5 votes
1 answer
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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,...
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