# Tag Info

Accepted

### cvxpy portfolio optimization with risk budgeting

The underlying problem: your ACTR constraints aren't convex The $i$th constraint on your risk contribution can be written: $$w_i \sum_j \sigma_{ij} w_j \leq c_i s$$ And this isn't a convex ...
• 7,004
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### Knightian uncertainty versus Black Swan event

I'm sure this falls short of proper philosophical precision, but here goes. Hark back to a slightly modified rehash of Donald Rumsfeld's infamous: Reports that say that something hasn't happened are ...
• 5,101

### Which is riskier: a call option or the underlying?

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 $$\Delta \frac{S}{V} \lessgtr 1$$ ...
• 11.6k
Accepted

### Realized Variance (realized volatility)

The TLDR; to your question: How can one use realized volatility as a volatility model to do out-of-sample prediction? You extend known models to incorporate additional information procured from high-...
• 4,726

### Conceptual problem with risk neutrality-What is a 'risk-neutral world', exactly?

I have masters degree in mathematics so the math isn't the problem; but, trying to get my head around financial math, I keep having problems with the concept of 'risk-neutrality'. I suspect you might ...

• 5,123
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### Risk-Neutrality: Discount factors of the $P$ world according to risk preferences?

You're right. Euler's equation states $$p_t=\mathbb E^\mathbb P_t[M_{t+1}X_{t+1}],$$ that is pricing under $\mathbb P$ requires you to know the stochastic discount factor (SDF, aka pricing kernel) $M$....
• 16.2k

### Lévy alpha-stable distribution and modelling of stock prices.

I asked this question 6 years ago, and in the meantime I came across this little volume: Lévy Processes in Finance: Pricing Financial Derivatives by Wim Schoutens (2003).
• 1,527
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### Overestimating or underestimating risk?

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 ...
• 2,582
Accepted

### Calculate risk measures (book recommendation)?

A good starting point is the following paper: Risk Measures in Quantitative Finance by Sovan Mitra (2009) From the abstract: "[...] Despite risk measurement’s central importance to risk management, ...
• 27.6k
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### Can portfolio Value-at-Risk be calculated analytically for multivariate t-distributed returns?

Let the $n-$dimensional vector of returns $\mathbf{r}$ have a multivariate t distribution with $\nu$ degrees of freedom. The marginal distribution of any component $r_i$ has a univariate t ...
• 3,700
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### Calculating beta to market

In a word, yes. That's a correct and valid view to take but, as you'll always find in finance, it really depends on context and the question that you're trying to answer. This is the case in markets ...
• 131
Accepted

### What is the industry standard way of calculating and annualizing performance metrics?

To give you an idea of industry standards for funds (although not hedge-fund specific), Morningstar and Trustnet both use monthly returns and annualize their data. See, for an example plucked at ...
• 1,416
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### What does 5 year OIS actually mean?

When people say OIS swap they mean an exchange of some sort of fixed cash flow and in return the receipt of daily OIS based on the "Fed Effective Rate" (FEDL01 Index on Bloomberg). The floating ...
• 2,653

### Why worry about fat tails, if you can use stoploss?

Because we are modelling the underlying price process, not the value process of your stop-loss portfolio...
• 902

### ES not elicitable

I think it was T. Gneiting in 2011 who first proved that ES is not elicitable (Making and Evaluating Point Forecasts, Journal of the American Statistical Association Volume 106, 2011 - Issue 494) , ...
Accepted

### IR Swaps - Curve sensitivity at maturity node

The value of a $T$ year payer swap on a coupon payment date at time $t$, or a new swap that is about to be traded today time $t$, is given by $$V(t) = (S(t,T)-C) \sum_{i=1}^N Z(t_i) \Delta_i$$ where ...
• 2,187

### IR Swaps - Curve sensitivity at maturity node

This is a common confusion, and it comes down to the difference between forward rates and swap rates. Swap rates are essentially the integral of forward rates (just like zero coupon rates). The ...
• 264

### Difference between risk and uncertainty

I am one of the people (a minority in Quant Finance) who think there is a difference between Risk and Knightian Uncertainty, and Alan Greenspan is another. Uncertainty explains what is meant by ...
• 9,402