16

This is practically a textbook case begging for the Kelly criterion. In your specific example, the optimal trade size is $f^*A$, where $f^*$ maximizes the average rate of return $$\mathbb{E}[\log (X)]=0.5\log(1+0.3f)+0.5\log(1-0.23f).$$ Here $f$ is the fraction of the current capital to trade. A straightforward calculation yields that $$f^*=\frac{0.3-0.23}{...


15

Risk Parity is not about "having the same volatility", it is about having each asset contributing in the same way to the portfolio overall volatility. The volatility of the portfolio is defined as: $$\sigma(w)=\sqrt{w' \Sigma w}$$ The risk contribution of asset $i$ is computed as follows: $$\sigma_i(w)= w_i \times \partial_{w_i} \sigma(w)$$ You can then ...


14

Jennifer Bender of MSCI Barra has a paper from 2007 entitled: To Beta or Not to Beta: A Comparison of Historical Versus Fundamental Betas for Hedging Market Risk She deals specifically and exclusively with which method is superior for hedging long-only portfolios. Not surprisingly, she finds that Barra's approach is better. She tests long-only and long-...


11

I'm not sure about the "CAPM formula" that you are referring to. I assume you are referring to the estimated coefficient of a regression of a security on a market portfolio. That is to say \begin{equation} \beta_{security,market} = \frac{\sigma_{security,market}}{\sigma^2_{market}} \end{equation} The idiosyncratic risk is the portion of risk unexplained ...


9

I would use the identity and three step process that: $$\textrm{Total Variance} = \textrm{Systematic Variance} + \textrm{Unsystematic Variance}$$ You can calculate systematic variance via: $$\textrm{Systematic Risk} = \beta \cdot \sigma_\textrm{market} \Rightarrow \; \textrm{Systematic Variance} = (\textrm{Systematic Risk})^2$$ then you can rearrange ...


9

The risk-netural measure has a massively important property which is worth making very clear: The price of any trade is equal to the expectation of the trade’s winnings and losses under the risk-neutral measure. This property gives us a scheme for pricing derivatives: take a collection of prices of trades that exist in the market (eg swap rates, bond ...


9

Indeed, algorithmic trading is a very hidden subject. All I can help you with are some industry-specific terms which might speed up your search for relevant papers and information: Risk of ruin tables (Peak-to-valley) drawdown (maximum drawdown, duration of drawdown etc.) Number of consecutive losses Confidence intervals Empirical distributions (for risk ...


9

If you measure risk by the standard deviation of the portfolio return $$ \sigma = \sqrt{w^T \Sigma w}, $$ then it is usual to define risk contributions for each asset by $$ \sigma_i = w_i (\Sigma w)_i/\sigma, $$ then diversified could mean that these $\sigma_i$ are evenly spread over the assets in the portfolio. You find this approach and more in this paper ...


8

A market is said to be complete if any contingent claim can be replicated by an admissible (i.e. with value process bounded from below) self-financing (i.e. all gains and losses exactly offset each other) trading strategy, a so-called replicating strategy. This strategy being constructed from primary securities - the market prices of which are unique - it ...


7

What you refer to as the 99.5th percentile is known as the "Value-at-Risk." You are correct that you will need to make a distributional assumption, and there is a popular and well-researched approach to this problem, though I'm not certain it could be called "standard." I would recommend you use the "truncated Levy flight" distribution. James Xiong at ...


7

Step 1: Get your data from SQL into R -> http://www.r-bloggers.com/?s=SQL Step 2: Run your analysis/optimizations like -> http://www.r-bloggers.com/portfolio-optimization-in-r-part-1/ or http://blog.streeteye.com/blog/2012/01/portfolio-optimization-and-efficient-frontiers-in-r/ or via RMetrics: http://www.statistik.wiso.uni-erlangen.de/lehre/bachelor/...


7

if you take the variance of a single asset it scales as a quadratic, $$ var(\lambda X) = \lambda^2 var(X) $$ so it's not surprising that the general case gives a quadratic form.


6

There are all sorts of financial and non-financial risks. I define financial risk as all risks defined from events in the financial markets that affect all participants. Non-financial risks are all other forms of risk (including risks that a particular firm may face). Financial: Market value risk (interest rate risk, exchange prices, equity prices, ...


6

The Kelly criterion is a very popular bet-sizing method. Edward Thorp has written a great deal on this topic. You can try googling for more, or start with his review of the concept, or a recent paper, Medium Term Simulations of The Full Kelly and Fractional Kelly Investment Strategies. This is not specific to futures, but I'm not sure why you would need ...


6

Also, RiskMetrics' 'granular approach' may be of interest (I have no affiliation): See: I. Developing an Equity Factor Model for Risk II. The RiskMetrics 2006 Methodology, RM2006


6

The algorithm is certainly useful in that it is non-parametric, fast, and versatile. Meucci summarizes the advantages nicely: Unlike traditional copula techniques, CMA a) is not restricted to few parametric copulas such as elliptical or Archimedean; b) never requires the explicit computation of marginal cdf’s or quantile functions; c) does not ...


6

I am very happy with the following equivalent formulation for the risk budgeting problem (as presented in Bruder, Roncalli, 2012, Managing Risk Exposures using the Risk Budgeting Apporach): Let $b_i$, $\Sigma_{i=1}^n b_i =1$ be the risk budgets, $y_i$ the unscaled portfolio weights and $S$ the variance covariance matrix and $c$ arbitrary. $$ y^* = \text{...


6

I would entirely separate the investigation and analysis of volatility and correlation between two asset classes. Think of it this way: If volatility is extremely high then high fluctuation to both, the up and down side will contribute to the stability of high volatility. However, for correlations it makes a big difference whether the large move has been ...


6

I am a risk taker and I can say with confidence that you will never convince those individuals, you cited in your question, that they incur too much risk, because there will always be certain traders who prefer lottery tickets over longevity with the same firm (running high risk books unfortunately in the current environment runs equal to a free option; blow ...


5

Standard (read: regulators will accept it) could be a one day, 99% VaR calculated with two years of historical data. A minimum of one year of history is needed although this is not the norm. Typically the one-day VaR is transformed into a 10-day VaR by scaling the calculation by sqrt(10). However, the new market risk rule governs that one justify their ...


5

It is common. The smaller the tail area you are considering the harder it is to be right because the effect of the assumption on the distribution becomes more important. Think about it in the other direction: if your level is 50%, then pretty much any distributional assumption will do. The other issue is the length of the time horizon. As the horizon ...


5

Since both $ER$ and $S$ are gaussian random, why not just assume their dependence is captured by their covariance, and make your draws from the bivariate normal distribution? It is hard to construct any other way of making two marginal gaussians cointegrated. Even if the variables were not gaussian, you would probably find yourself relating them using a ...


5

OK, so you need to validate a one factor model with mean reversion, here are the questions I would ask myself For calibration Is the model capable of calibrating to both coterminals and caplets? If not how do I intend to calibrate it when pricing Callable Cap Floaters? Is the model capable of calibrating to skew? If not how do I intend to calibrate it ...


5

I am not sure why your question had so many upvotes because in currency markets anything else but triangular arbitrage does not exist. What is a quadrangular arb, I have never heard of it despite having traded fx among other asset classes for over ten years now. Think about it: Lets say you observe the price of EUR/USD. You can build triangular arbs by ...


5

While triangular arbitrages exists, they are a rare, short lived, and shallow. In several academic datasets they are very rarely seen, mainly for two reasons, market efficiency aside: (1) the time resolution of the data is not tick by tick but aggregated at some level (for example at 1 second intervals), (2) the dataset doesn't include all available quotes ...


5

Let's first restate the formula of the beta of a portfolio $P$ relative to a benchmark $B$: $$\beta_P=\frac{Cov(r_P,r_B)}{Var(r_B)} $$ As chrisaycock said in his comment, the key thing to understand is that the beta is a statistical measure computed relative to a benchmark. Hence, I believe that the real question you should be asking is: Which benchmark ...


5

There are a lot of code in Eric Zivots recent class in computational finance. http://spark-public.s3.amazonaws.com/compfinance/R%20code/portfolio.r http://spark-public.s3.amazonaws.com/compfinance/R%20code/testport.r http://spark-public.s3.amazonaws.com/compfinance/R%20code/rollingPortfolios.r Also, you can google some slides in his class where he ...


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