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19 votes

Quantifying climate change risk

Here are some resources that I found useful when learning about this subject, in which I'm very interested. (Some may be more general ESG than just just climate.) Citigroup. Environmental and Social ...
Dimitri Vulis's user avatar
10 votes
Accepted

Intuitive explanation for expectiles

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 ...
Raskolnikov's user avatar
  • 1,527
10 votes
Accepted

Kelly criterion for normally distributed returns

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 ...
starovoitovs's user avatar
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
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
7 votes
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How to check if a portfolio has momentum bias

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: ...
Chris's user avatar
  • 1,643
7 votes
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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

What is the best alternative of Quantlib library

I did not tested it by now, but Google released a library similar to quantlib written in TensorFlow (tf-quant-finance). It may be worthwhile to test it (and to post here your views on it), because ...
lehalle's user avatar
  • 12.2k
6 votes
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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
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Construct a butterfly interest rate portfolio to eliminate PCA exposures

Let $S$ be your risk sarray, expressed in pv01, for each of your (implied) 10 instruments. You restrict the array to all zeroes except those corresponding to the 5Y, 7Y and 10Y risks, e.g. if 1Y:10Y ...
Attack68's user avatar
  • 10.5k
6 votes
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Variance attribution calculation from a covariance matrix

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 ...
nbbo2's user avatar
  • 11.4k
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
5 votes

How to construct a Risk-Parity portfolio?

Another approach to construct a risk parity portfolio would be to use the formulation proposed by Spinu [1]: $$\begin{array}{ll} \underset{\mathbf{w}}{\textsf{minimize}} & \frac{1}{2}\mathbf{w}^{T}...
Zé Vinícius's user avatar
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
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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
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Question on Rockafellar's Paper for optimisation of CVaR

On 1, I suspect that is a typo and that the second formula should sum to r. On 2, that is applying well-known techniques in how to handle piece-wise linear functions in an optimizer. For instance, ...
John's user avatar
  • 5,411
5 votes
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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 ...
RRL's user avatar
  • 3,680
5 votes
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Book recommendation

First, a word of caution One of the problem with mathematical finance, as well as the related field of financial economics is that there is more than enough to learn to fill your schedule several ...
Stéphane's user avatar
  • 2,476
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
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A comprehensive list of risk measures for different asset classes

VaR has the benefit that it is comparable across all asset classes, and can even be computed for multi-asset class portfolios. The downsides are that it either needs assumptions on the joint ...
Chris Taylor's user avatar
  • 5,931
4 votes
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What instruments help me receive a premium?

no, generally speaking only options has time premium. I strongly advise you to avoid mixing 2 positions (short 1 option, long another one) in your mind just because they are independent, so just ...
optionstrade.info's user avatar
4 votes
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Types of risk for stock investing

Just wanted to check that there is not any FX risk here, as the US investor has bought $ donimated stock, so it is irrelevant that Toyota is also traded in Japanese markets in Yen. An American ...
amdopt's user avatar
  • 4,348
4 votes

Hierarchical Risk Parity with allocation constraints?

EDITED You are right. We have to look town to the "leaves" in each iteration. I would do it the following way: If $L_i^{(j)}$ is the set of indices in the $j$ branch ($j \in \{1,2\}$), then we ...
vanguard2k's user avatar
  • 2,915
4 votes

Intuitive explanation for expectiles

That picture in the other answer is pretty slick (+1), so I will just add a note on why one can interpret the colors of those areas like that: Blue: Define $Y = (X-x)_+$. This is nonnegative r.v., ...
Taylor's user avatar
  • 544
4 votes
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Does longer time horizon necessarily imply reduced risk?

It depends upon how you define risk. Assume a constant, positive equity risk premium and an equity index following geometric Brownian motion (GBM): $$d \log S_t = \mu \, dt + \sigma \, dZ_t = (\hat{\...
RRL's user avatar
  • 3,680
4 votes
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Structured product sellers and div swaps

The paper is generally correct, but it is not a general statement, as in a general truth of options hedging in a theoretical context, rather a statement regarding how the structured derivs market is ...
Ivan's user avatar
  • 1,396
4 votes

Structured product sellers and div swaps

To add to the above on a more practical note: In general, SP desks make money on the individual product when the underlying declines. Dividends make the underlying decline, hence they are naturally ...
DMSTA's user avatar
  • 161
4 votes
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Semivariance calculation (downside deviation)

I am interested in Semivariance because I want to use it to compute the Sortino Ratio. I found an article on Sortino which answers to my question. Here is the link "Sortino ratio: A better measure of ...
Pithit's user avatar
  • 296

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