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 ...


9

A better, clearer, answer is to compute Lambda (leverage) of the option (link) and see if it is bigger or smaller than 1. Lambda is $\Delta \frac{S}{V}$ so we test $$\Delta \frac{S}{V} \lessgtr 1$$ which is what Joshi is saying in words: compare $\frac{1}{S}$ (delta to price for the stock, the delta of the stock is 1) to $\frac{\Delta}{V}$ (delta to price ...


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

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 ...


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

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

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

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 ...


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

The Strata project is the new pure Java market risk quant library from OpenGamma. For more information, see the documentation and GitHub. It is Apache v2 licensed. Strata takes the experience of the OG-Platform codebase referenced in the question and turns it into a library - no need for databases, servers or similar. Ease of use is a big focus and there ...


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 ...


6

No reply has been given so I wanted to at least give a visualisation of the expectiles. Suppose the curvy dashed line in my picture represents a cumulative distribution function of some random variable X. Then blue part corresponds exactly to $\mathbb{E}[(X-x)_+]$, while the orange surface corresponds to $\mathbb{E}[(X-x)_-]$. In the picture $x=1$. Now if ...


6

This problem can be expressed as the original Merton's portfolio problem. Consider wealth process defined by SDE $$ d X _ { t } = \frac { X _ { t } \alpha _ { t } } { S _ { t } } d S _ { t } + \frac { X _ { t } \left( 1 - \alpha _ { t } \right) } { S _ { t } ^ { 0 } } d S _ { t } ^ { 0 } $$ where $\alpha_t$ is proportion of the investment in the risky ...


6

It kind of depends what your objective is. First, momentum 'bias' isn't well-defined. Are you looking to eliminate momentum exposure for some reason? Momentum itself isn't even well-defined really: momentum over the trailing 1 year? Trailing 6m? Looking over 3-5y periods where mean-reversion is more at play? Generally, in the absence of a clearer ...


6

Suppose the covariance matrix is $V$ (which is n by n) and the weights are $w$ (of length n). Then the Portfolio Variance is $V_p = w^T V w$ and the Risk Contribution (in terms of variance) of asset $k$ is $RC_k=w_k \sum_j V[k,j]w_j$ in words this is "the weight of asset k times the inner product of the k-th row of $V$ and the weight vector". (Sometimes ...


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

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

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 ...


5

Autocorrelation of returns can be used as a proxy measure for liquidity of the asset. The degree of serial correlation in an asset’s returns can be viewed as a proxy for the magnitude of the frictions, and illiquidity is one of the most common forms of such frictions. A strongly liquid asset should reveal no serial autocorrelation. You can perhaps build ...


5

I would create categories, and work on risk parity among the categories. Otherwise, variance is not really a good measure of downside risk: Change your risk measure, use a rolling window historical VaR or Expected Shortfall at some horizon that matches your investment style. downside semi-variance could do the trick too if don't want to change your algo ...


5

On the N. N. Taleb's website, you can find all his papers collected in the bibliography he updates on his own site. Hope this will help.


5

Try to give David Spiegelhalter a read/listen to David Spiegelhalter's work and research. He is a statistician and a Professor of the Public Understanding of Risk at Cambridge England. Rather than new ways of calculating risk, he looks at ways of communicating risk to a general public that doesn't have any knowledge of stats. I Linked an interesting video-...


5

I cannot suggest some reference particularly, since the field is going to develop day by day, but, generally, you could take a look to: Engelmann, Bernd, and Robert Rauhmeier, eds. The Basel II risk parameters: estimation, validation, and stress testing. Springer Science & Business Media, 2006. Particularly, look at the chapter 4 and 5; the ...


5

Yes, it is correct. Underestimation: you under-estimate the risk, so you have more VaR violations than what your model predicts. Ex: With 100 observations, and a 99% VaR, you expect 1 violation but you observe 5 violations. Overestimation: you over-estimate the risk, i.e the risk is less important that you expect. You observe less VaR violations that you ...


5

Just a small addendum to @noob2's answer. The discrete shape of $\lambda$ is: $$\lambda \approx \frac{V_1 - V_0}{S_1 - S_0} \times \frac{S_0}{V_0} $$ which can be rewritten as $$ \lambda \approx \frac{\frac{V_1 - V_0}{V_0}}{\frac{S_1 - S_0}{S_0}} $$ which is as @noob2 said just the ratio of the relative returns for option and stock.


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