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7

If you have the mathematical sophistication, you should review the original papers referenced on the Equity Premium Puzzle page, particularly Mehra and Prescott (1985). Note, however, that contrary to other opinions on this page, the puzzle is NOT that there is an equity risk premium. On the contrary, the puzzle is that the premium had been so high, at ...


7

I would recommend Marc Wildi's work on signal extraction.


6

If you look in the portfolio management sections of the CFA (chartered financial analyst) curriculum, you'll find a listing of commonly used portfolio management techniques. It is by no means exhaustive, but the content in the CFA curriculum comes directly from industry professionals, so it is reasonable current and applicable. CFA Candidate Body of ...


6

In the academic literature it is extremely widely applied in the last 20 years. I would estimate maybe 200 empirical papers, or more. For example a common finding is that higher frequency (daily) wavelet correlations have been high since 2007, attributable either to increasing financial interation or the financial crisis. It is also popular to estimate the ...


6

This is the equity premium puzzle. (See that article for references.) My thoughts are that individual investors are rational to be risk-averse and demand a premium for bearing a type of market risk that cannot be diversified away. This risk is actually worse and more insidious than it appears, because "personal" circumstances tend to correlate in ...


5

There is a very famous math finance cheat sheet already (by Prof. Wystup), you can find the content here: https://mathfinance2.com/Products/CheatSheet#Content


5

Orthogonality and independence are different concepts. The concepts are the same for Wiener processes because in the context of normal random variables, independence is equivalent to orthogonality (i.e. uncorrelatedness) Independence is the standard definition for probability. Let $\mathcal{F}, \mathcal{G}$ be the sigma algebras generated by two processes,...


5

Some of the used heavy-tail distributions are: Log-Cauchy and Log-Gamma Lévy Burr and Weibull Mixed normal Here two papers that cover some of them and others: http://ect-pigorsch.mee.uni-bonn.de/data/research/papers/Financial_Economics,_Fat-tailed_Distributions.pdf http://www.rff.org/RFF/Documents/RFF-DP-11-19-REV.pdf


5

In my opinion you should question EVERYTHING. Recently I read this article Ten Things We Should Know About Time Series by Michael McAleer which is to my opinion a good summary of some common issues in time series analysis. These ten things are: Knowledge of Econometrics and Statistics is Essential Be Aware of Measurement Errors Test for Zero Frequency, ...


4

Yes. Check out Time-Series Analysis by Shumway and Stoffer. Spectral Analysis and Filtering is covered in Chapter 4.


4

Simplest explanation is Feynman-Kac theorem https://en.wikipedia.org/wiki/Feynman%E2%80%93Kac_formula Blackscholes is a parabolic PDE Solution can be written as a conditional expectation over an integration term. Conditional expectation means you need to simulate it using some distribution which leads to monte-carlo


3

I have asked myself the very same question when I first read the book. As far as I can tell, the "scalability" condition is only imposed for technical reasons. It simplifies the subsequent proof of the Fundemental Theorem of Asset Pricing in constrained markets. There are several papers that have shown that the theorem is valid for conic constraints. ...


3

A very good book covering such fundamentals with no or only a minimal amount of maths — highly recommended! Puzzles of Finance: Six Practical Problems and Their Remarkable Solutions by Mark P. Kritzman The topics that are covered here are: Siegel's Paradox Likelihood of Loss Time Diversification Why the Expected Return Is Not To Be Expected Half Stocks ...


3

Let me know whether this helps, but the author mentions a paper from Fujii and Takahashi; I have been looking for it on the internet and I have found what seems to be a version of it: Collateral Posting and Choice of Collateral Currency. I think they give a relatively transparent explanation $-$ in terms of funding costs $-$ of why the discount rate for ...


3

Another observation that the connection between return and risk is not that straightforward (and in contradiction to modern portfolio theory!) is the low-volatility anomaly. It turns out empirically that stocks that have low-volatility or low-beta show higher returns than high-volatility or high-beta stocks. See also this question and answers: Why does ...


3

Exact Discretization of the Solution to the Geometric Brownian Motion Stochastic Differential Equation Let $P_{t}$ represent the time series of market prices of the underlying, $\mu$ be its mean continuous log-return, $\sigma$ be its instantaneous volatility and $W_{t}$ be a Wiener process. Here is the stochastic differential equation for the geometric ...


3

Ignoring to account for possibly omitted variables Ignoring to account for possibly omitted variables has arguably lead to both of the severe problems below: The fall of the US mortgage market in 2008 as risk on mortgage bond portfolios were grossly underestimated as the strong dependence of their bonds on common variables like the state of the business ...


2

Fractal spectra are covered in Multifractal Volatility: Theory, Forecasting, and Pricing. Also note that your run-of-the-mill moving average of a price series is a low-pass filter (filters out the higher frequencies), and moving averages are very used in basic financial analysis.


2

This one is far from straight-forward, although bear with me. It is possible to infer from first principles an ERP reasonably close to normative consensus expectations. The attached from Howard Marks at Oaktree is a classic: "Everything you wanted to know about the equity risk premium (and much more)". The simple point is that there are four different ...


2

That means the null is not rejected and therefore test is inconclusive. With this type of testing you can only try to reject the null. Your non-rejection could have been due to lack of data, therefore you cannot conclude anything from it. If you want to somehow support your null, compute the confidence interval for your parameters and show that its ...


2

At this stage your sheet is focus on "stochastic calculus for derivative pricing". It is just a subset of math finance. You are missing: risk management (VaR, quantiles, etc) -- more statistics than stochastic calculus. See for instance the content of Attilio Meucci's book. quantitative trading (optimal trade scheduling, smart order routing, microstructure) ...


1

I think that there are two points to be made here. First, the distinction between returns and price. Secondly, the agnosticism of quantitative finance to upside versus downside risks. "Idiosyncratic" firm risks should be reflected in the price such that its returns are capital are independent of idiosyncratic risk. Therefore, returns are only a function ...


1

...but according to traditional finance it wouldn't. Why not? If valuation is about discounting expected future cash flows, then after an oil spill, investors expect hefty fines, i.e. cash outflow, hence the PV is lower. I think the important is the word expected - you don't know what the actual cash flows going to be (at least not with 100% accuracy), ...


1

Economists generally think of three similar, but distinct, metrics of economic disparity: inequality of income, consumption and wealth. Income inequality is the most commonly cited measure, consumption inequality, though harder to measure, provides a better proxy of social welfare. Wealth is also an important metric since it can be inherited, unlike income. ...


1

Here's a try/start: Let $A,B$, and $C$ be three possible events, and let $U(event)$ be the utility derived from each event. For example, if event $A$ corresponds to the event of winning the lottery, then $U(A)$ will presumably be a very large value. By contrast, if event $C$ corresponds to the event of falling off a ladder and breaking an arm, $U(C)$ will ...


1

Sure, the variance of the total wealth can be expressed in terms of the variances and covariances of the prices of the assets. If $$ W = \sum_{i} \pi_i P_i $$ where $\pi_i$ is the total dollar amount invested in asset $i$ with price $P_i$. The variance of total wealth is then $$ Var(W) = \sum_i \pi_i Var(P_i) + \sum_i \sum_{j, j\neq i} \pi_i \pi_j Cov(P_i, ...


1

Checkout spectro.space - A CryptoCoin Analyzer with Spectrograms. I just launched it, and it's is a free web-based graphing tool that allows you to view over 2000 different cryptocurrencies, and a lot more coin-pairs. The semi-novel thing about spectro.space is the spectrogram graphs. I've been able to determine the onset of large price movements, both up ...


1

Something like a moving average smoother is akin to a low pass filter, the 'stochastics' of technical analysis crudely akin to a band pass filter. Going up the ladder of sophistication, you can see something like http://www.jstor.org/pss/3592665 or applications of wavelet decomposition. This paper from 1963 by GRANGER, CLIVE W. J., and MORGENSTERN, 0. ...


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