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16

To explain why a negative sloping yield curve is bad, you have to start with a theory of the yield curve. The dominant theories for the term structure of interest rates are the rational expectations, liquidity preference, and market segmentation. (The first two theories are quite compatible with each other and have more standing so let's assume that view.) ...


15

Short Version : Two main uses I'm doing an arbitrage/statarb strategy (volatility for instance) which should not be dependant on the Delta (I'm an arbitragist). I HAVE to keep a product in my portfolio, but I don't want to be EXPOSED to it (I'm a market maker). Long Version : The goal of Dynamic Hedging is not down the line to earn risk free rate of ...


15

Big Picture Time-series variance is driven mostly by discount rates, whereas expected cash flows dominate the cross-sectional variance. These results are important because they highlight the value of focusing on both dimensions of stock prices and returns: time-series and cross-section. On the other hand, however, they also show that a single mechanism is ...


7

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


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 ...


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 ...


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

A discrete-time model only works in no-arbitrage land with discrete asset values. Furthermore, the number of allowable asset values per timestep is limited by the number of available securities. The tree is the classic example of this. Binomial trees "work", but if you make a one-step trinomial tree, you will find that you can no longer form a risk-free ...


6

I think there is an error implicit in your question. Dynamic delta hedging, even assuming the underlying process is a continuous martingale and trading entails zero transaction costs, only eliminates the directional risk. A number of residual risks remain, most notably volatility risk, embodied in both the gamma and vega. A dynamically hedged portfolio of ...


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, ...


5

You have to differentiate here between the risk-taking and the market-making side. As a risk-taker, like e.g. a hedge-fund, you are right, you could just buy the bond! But as a market-maker you sell these options but don't want to bear the risk, so you have to counterbalance it. You could of course counterbalance it with another option which would be the ...


5

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 ...


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

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

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


4

Theoretically, a rising yield curve is compensation for the additional duration risk. An inverted yield-curve is saying that the market thinks that: Next-year's figures for: growth plus inflation is less than Ten years' time's figures for: growth plus inflation Which means that expectations are either of a recession (some negative economic growth; and ...


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

Average net worth of people at bogleheads forum is very strong argument. Also, Dogs of the Dow is interesting approach for long term investing.


3

Alpha is easier to measure and easier to obtain in the cross-section than in the time-series. Low information coefficient combined with high breadth still make for a decent information ratio. The breadth of your strategies is always lower than you think. When markets collapse, correlation goes to one.


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 ...


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

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

Samuelson once quipped that the yield curve had successfully predicted 9 of the last 5 recessions. Explanations for why the yield curve inverts have been covered adequately above. But what does it mean for the economy? For the yield curve inversion to predict stock market performance enough to make an actual decision, the bond market would have to be more ...


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

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. ...


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

An inverted yield curve basically means that interest rates will be higher for the coming year than for the years following. That means that entities that need do borrow for short term purposes will do so at a greater cost that those borrowing for the long term. That is an unusual and "unnatural" relationship. All other things being equal, that will dampen ...


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