# Questions tagged [portfolio-theory]

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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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,...