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14 votes
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 ...
Matthew Gunn's user avatar
  • 6,954
11 votes
Accepted

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 ...
demully's user avatar
  • 5,071
10 votes

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 $$\Delta \frac{S}{V} \lessgtr 1$$ ...
nbbo2's user avatar
  • 11.4k
10 votes
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-...
Pleb's user avatar
  • 4,286
9 votes
Accepted

Portfolio Risk Decomposition - different methodologies

Different portfolio risk decompositions answer different questions. Before discussing what method to use, first ask why you want a decomposition and what definition of risk are you using. Is the ...
Matthew Gunn's user avatar
  • 6,954
8 votes

non-subadditivity of VaR

Simple example where sub-additivity fails Let there be four possible outcomes $i=1,2,3,4$ that occur with equal probability $\frac{1}{4}$. Payoffs for $X$, $Y$, and $X + Y$ are given by: $$ X = \...
Matthew Gunn's user avatar
  • 6,954
8 votes

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 ...
Ilmari Karonen's user avatar
7 votes
Accepted

Mathematical Derivation of Residual Risk

Note that $\beta$ is the coefficient of the portfolio regressed on the benchmark. That is \begin{align*} r_P = \alpha+\beta r_B + \varepsilon, \end{align*} where $\varepsilon$ is the residual. The ...
Gordon's user avatar
  • 21.1k
7 votes
Accepted

EUR/CHF fx rate drop on the 15th of January 2015

What happened was totally unexpected end of peg against the euro @ 1.2CHF regime that Swiss central bank aborted. See some articles about it. As far as I know nobody in the markets knew, there was no ...
Jan Sila's user avatar
  • 732
7 votes
Accepted

Risk, required return and expected volatility - what is the relationship?

I think you may be interested in this QJE forthcoming article by Ian Martin. The key idea of the article (page 5) is that the expected return on the market can be decomposed as $E_t[R_{t+1}]-R_f = \...
fni's user avatar
  • 1,896
7 votes
Accepted

Which is riskier: a call option or the underlying?

As @ir7 did, I only briefly want to add to @noob2's spot-on answer. He's of course right and $\Lambda=\Delta\frac{S}{V}$ decides how risky the option is compared to the stock. Firstly, note that $\...
Kevin's user avatar
  • 16k
6 votes

Which risk-free interest rate to use in Black-Scholes equation

In theory, $r$ is a short-term safe interest rate, and it is constant through time though the theory does goes through with $\bar{r}$ (average $r$ from $t$ to $T$) in place or $r$. In practice, ...
vonjd's user avatar
  • 27.5k
6 votes
Accepted

non-subadditivity of VaR

VaR is not sub-additive in general. Relying on Mark Joshi comment, there are particular cases where it can be. Such cases occur for portfolios containing elliptically distributed risk factors. Of ...
JejeBelfort's user avatar
  • 1,219
6 votes

Which is riskier: a call option or the underlying?

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{...
ir7's user avatar
  • 5,043
6 votes
Accepted

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) $M$....
Kevin's user avatar
  • 16k
6 votes

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

A little bit of history. This goes back to the early days when the Black Scholes formula for options was proposed but was still new and somewhat mysterious. It was (and is) widely accepted in Finance ...
nbbo2's user avatar
  • 11.4k
5 votes

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).
Raskolnikov's user avatar
  • 1,527
5 votes

What are the some good measures of risk for options?

I don't have a reference for you but I have some experience. Risk management departments at hedge funds and banks would primarily look at the Var in order to capture the risk of an options portfolio. ...
dm63's user avatar
  • 17.2k
5 votes

Are smart beta and risk-parity the same?

This is a very good question. It can be argued that risk parity is one example of a smart beta strategy. Yet it is important to understand that both are coming from two different directions: risk ...
vonjd's user avatar
  • 27.5k
5 votes
Accepted

how can we know the residual return will be uncorrelated with the market return

Let us ignore the riskless rate for simplicity of the presentation. If you have (historical or simulated) return series $r_i$ for the portfolio and $r_i^M$ for the market, then the beta is the OLS ...
Richi Wa's user avatar
  • 13.7k
5 votes
Accepted

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 ...
Malick's user avatar
  • 2,582
5 votes
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, ...
vonjd's user avatar
  • 27.5k
5 votes
Accepted

What is an accepted method to calculate percent PnL from a short position?

A short position is a liability on your books, as the borrowed asset has to be returned to the owner. The return is then the percentage return of that liability. Assume that the shorted asset at ...
RRG's user avatar
  • 1,024
5 votes
Accepted

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 ...
RRL's user avatar
  • 3,680
5 votes
Accepted

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 ...
RobAbMo's user avatar
  • 131
5 votes
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 ...
Tim Wilding's user avatar
  • 1,406
5 votes
Accepted

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 ...
JoshK's user avatar
  • 2,613
5 votes

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...
Oscar's user avatar
  • 902
4 votes

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) , ...
RiskyScientist's user avatar
4 votes
Accepted

Could we have prevented the World Economic Crisis in 2008?

U.S. Government DID save American International Group (AIG) from bankruptcy, since it was considered too big to fail, actually: a lot of financial institutions were insured by AIG. This Investopedia ...
simmy's user avatar
  • 585

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